GMAT: Math 8

WEBVTT
Kind: captions
Language: en

00:00:00.820 --> 00:00:03.100
We're on problem 42.

00:00:03.100 --> 00:00:05.420
And they've drawn this little,
looks like a pie graph.

00:00:05.420 --> 00:00:07.380
And they say, in the circular
region with center o shown

00:00:07.380 --> 00:00:11.570
above, the two unshaded sections
constitute 3/7 and

00:00:11.570 --> 00:00:13.550
1/3 of the area of the
circular region.

00:00:13.550 --> 00:00:14.510
Fair enough.

00:00:14.510 --> 00:00:17.790
The shaded section constitutes
what fractional part of the

00:00:17.790 --> 00:00:19.650
area of the circular region?

00:00:19.650 --> 00:00:23.870
So the shaded section is just
the whole area minus these two

00:00:23.870 --> 00:00:25.350
fractions, right?

00:00:25.350 --> 00:00:30.370
So if you said what fraction of
the whole area is the whole

00:00:30.370 --> 00:00:31.690
area, you would say that's 1.

00:00:31.690 --> 00:00:33.460
And you would subtract out these
two areas to get the

00:00:33.460 --> 00:00:34.070
shaded area.

00:00:34.070 --> 00:00:41.570
So 1 minus 3/7 minus 1/3 is
equal to the fraction of the

00:00:41.570 --> 00:00:43.690
totally area that this
shaded area is.

00:00:43.690 --> 00:00:47.150
And let's just add or subtract
those fractions.

00:00:47.150 --> 00:00:49.980
The least common
multiple is 21.

00:00:49.980 --> 00:00:53.160
1 is the same thing as 21/21.

00:00:53.160 --> 00:00:55.120
Minus 3/7.

00:00:55.120 --> 00:00:57.180
Let's see, 7 goes
into 21 3 times.

00:00:57.180 --> 00:00:59.050
So 3 times 3 is 9.

00:00:59.050 --> 00:01:01.850
So this is the same thing
as minus 9 over 21.

00:01:01.850 --> 00:01:05.840
And minus 1/3 is the same thing
as minus 7 over 21.

00:01:05.840 --> 00:01:11.250
So this is equal to 21
minus 16 over 21.

00:01:11.250 --> 00:01:17.660
And that's 5/21, which
is choice D.

00:01:17.660 --> 00:01:18.910
Next question.

00:01:24.710 --> 00:01:25.920
0.3.

00:01:25.920 --> 00:01:26.900
[SNEEZES]

00:01:26.900 --> 00:01:28.560
Excuse me.

00:01:28.560 --> 00:01:30.150
My apologies.

00:01:30.150 --> 00:01:35.990
0.3 to the 5th over
0.3 to the 3rd.

00:01:35.990 --> 00:01:39.120
Well, anything to the 5th
divided by anything to the

00:01:39.120 --> 00:01:42.230
3rd, you could essentially say
divide the top and the bottom

00:01:42.230 --> 00:01:45.660
by 0.3 squared.

00:01:45.660 --> 00:01:47.050
Well, actually, you could divide
the top and the bottom

00:01:47.050 --> 00:01:48.630
by 0.3 cubed.

00:01:48.630 --> 00:01:53.280
You could say this is the same
thing as 0.3 to the 5th times

00:01:53.280 --> 00:01:55.240
0.3 to the minus third.

00:01:55.240 --> 00:01:56.950
That's just another
way of doing this.

00:01:56.950 --> 00:02:00.130
And so if you're dividing these
two numbers, you would

00:02:00.130 --> 00:02:01.050
subtract the exponents.

00:02:01.050 --> 00:02:01.920
But now we're multiplying.

00:02:01.920 --> 00:02:02.820
We're adding the exponents.

00:02:02.820 --> 00:02:05.666
But either way, it becomes
0.3 squared.

00:02:08.250 --> 00:02:11.190
And that is equal to 3
times 3, which is 9.

00:02:11.190 --> 00:02:13.430
And you're going to have two
numbers behind the decimal

00:02:13.430 --> 00:02:14.000
points, right?

00:02:14.000 --> 00:02:16.990
0.3 times 0.3.

00:02:16.990 --> 00:02:18.470
Two numbers behind the
decimal points.

00:02:18.470 --> 00:02:19.200
1, 2.

00:02:19.200 --> 00:02:21.110
So two numbers behind
the decimal point.

00:02:21.110 --> 00:02:22.626
So 0.09.

00:02:22.626 --> 00:02:27.780
Or another way of saying it
is 30% of 0.3 is 0.09.

00:02:27.780 --> 00:02:31.470
And that is choice C.

00:02:31.470 --> 00:02:36.510
44.

00:02:36.510 --> 00:02:40.680
In a horticultural experiment--
this is sounding

00:02:40.680 --> 00:02:47.050
interesting already-- 200 seeds
were planted in plot 1.

00:02:47.050 --> 00:02:51.440
So plot 1 got 200 seeds.

00:02:51.440 --> 00:02:56.550
And 300 were planted
in plot 2.

00:02:56.550 --> 00:03:01.140
So plot 2 got 300 seeds.

00:03:01.140 --> 00:03:12.760
If 57% of the seeds in plot 1
germinated, and 42% of the

00:03:12.760 --> 00:03:19.320
seeds in plot 2 germinated, what
percentage of the total

00:03:19.320 --> 00:03:23.810
number of planted seeds
germinated?

00:03:23.810 --> 00:03:26.620
So the total number of planted,
what percent?

00:03:26.620 --> 00:03:30.580
So how many total seeds
germinated is going to be 200

00:03:30.580 --> 00:03:33.020
times 0.57.

00:03:33.020 --> 00:03:35.090
That's how many in plot
1 germinated.

00:03:35.090 --> 00:03:40.350
Plus 300 times 42%, or 0.42.

00:03:40.350 --> 00:03:44.010
That's how many in plot
2 germinated.

00:03:44.010 --> 00:03:48.220
All of that divided by 500.

00:03:48.220 --> 00:03:48.510
Right?

00:03:48.510 --> 00:03:49.370
And how do I know 500?

00:03:49.370 --> 00:03:51.490
Because there were a
total of 500 seeds.

00:03:51.490 --> 00:03:56.550
So just to simplify the math,
we could just divide

00:03:56.550 --> 00:03:58.100
everything by 100, right
from the get go.

00:03:58.100 --> 00:04:00.720
So if you divide the bottom by
100 and the top by 100, you

00:04:00.720 --> 00:04:02.980
have to do both terms by 100.

00:04:02.980 --> 00:04:08.170
So you get 2 times 0.57 plus
3 times 0.42 divided by 5.

00:04:08.170 --> 00:04:10.360
2 times 0.57.

00:04:10.360 --> 00:04:11.610
That is what?

00:04:13.760 --> 00:04:22.190
Let's see, this is
1.14 plus 1.26.

00:04:22.190 --> 00:04:22.700
Is that right?

00:04:22.700 --> 00:04:25.020
3 times 4 is 12.

00:04:25.020 --> 00:04:26.780
3 times 2 is 6.

00:04:26.780 --> 00:04:27.080
Right?

00:04:27.080 --> 00:04:29.060
1.26.

00:04:29.060 --> 00:04:30.630
All of that over 5.

00:04:30.630 --> 00:04:32.100
This becomes what?

00:04:32.100 --> 00:04:40.390
This is equal to 2.4
divided by 5.

00:04:40.390 --> 00:04:44.360
And so 5 goes into 2.4.

00:04:44.360 --> 00:04:49.580
Let's see, goes into
4, 4 times 5 is 20.

00:04:49.580 --> 00:04:50.890
48.

00:04:50.890 --> 00:04:52.180
So 0.48.

00:04:52.180 --> 00:04:55.510
So the answer is 48%
or 100 times 0.48.

00:04:55.510 --> 00:04:59.020
And that's choice C.

00:04:59.020 --> 00:05:00.570
Question 45.

00:05:00.570 --> 00:05:02.170
Let's switch to a more
interesting color.

00:05:04.730 --> 00:05:10.150
3 and 8 are the lengths of two
sides of a triangular region.

00:05:10.150 --> 00:05:14.320
Which of the following can be
the length of the third side?

00:05:14.320 --> 00:05:15.580
OK.

00:05:15.580 --> 00:05:16.780
So let's think about
it a little bit.

00:05:16.780 --> 00:05:19.500
3 and 8 are the lengths of two
sides of a triangular region.

00:05:19.500 --> 00:05:20.600
Let me write their
choices down.

00:05:20.600 --> 00:05:22.210
Choice one is 5.

00:05:22.210 --> 00:05:24.270
I can easily imagine
a triangle that has

00:05:24.270 --> 00:05:29.520
sides 3, 8, and 5.

00:05:29.520 --> 00:05:31.152
That seems completely
reasonable.

00:05:31.152 --> 00:05:32.210
I'm just experimenting.

00:05:32.210 --> 00:05:33.890
I don't know where
this is going.

00:05:33.890 --> 00:05:34.590
8.

00:05:34.590 --> 00:05:36.100
Well, sure, that's just
an isosceles triangle.

00:05:36.100 --> 00:05:40.910
You can easily have a triangle
that has 8, 8, and 3.

00:05:40.910 --> 00:05:43.050
Choice three.

00:05:43.050 --> 00:05:45.200
11.

00:05:45.200 --> 00:05:46.440
Now, this is interesting.

00:05:46.440 --> 00:05:49.270
Let me ask you a question.

00:05:49.270 --> 00:05:50.710
Can I have a triangle that
looks like this?

00:05:50.710 --> 00:05:55.050
11 and then 3 and then 8.

00:05:55.050 --> 00:05:57.900
Is this possible?

00:05:57.900 --> 00:06:01.010
Well, no, because
3 plus 8 is 11.

00:06:01.010 --> 00:06:05.320
So the only way you're going to
get 11 is if you push this

00:06:05.320 --> 00:06:07.170
side all the way flat.

00:06:07.170 --> 00:06:08.600
That's the only way you're going
to get the length of

00:06:08.600 --> 00:06:10.340
this third side to be 11.

00:06:10.340 --> 00:06:12.450
In fact, 11 is the upper
bound on what this

00:06:12.450 --> 00:06:13.770
third side could be.

00:06:13.770 --> 00:06:14.960
Because imagine this.

00:06:14.960 --> 00:06:18.110
Imagine if I made the triangle
really flat, I made this angle

00:06:18.110 --> 00:06:21.080
right here really wide, as
close to 180 as I can.

00:06:21.080 --> 00:06:23.410
And I make it really flat.

00:06:23.410 --> 00:06:24.840
Right?

00:06:24.840 --> 00:06:28.710
If this length plus this length,
or this length plus

00:06:28.710 --> 00:06:32.170
this length is equal to 11,
this length is going to be

00:06:32.170 --> 00:06:34.040
shorter than it.

00:06:34.040 --> 00:06:37.000
This length right here has to
be shorter than this length

00:06:37.000 --> 00:06:38.400
plus this length, right?

00:06:38.400 --> 00:06:40.410
Because it's kind of a
straight-line distance between

00:06:40.410 --> 00:06:41.610
this point and this point.

00:06:41.610 --> 00:06:43.680
So 11 is the upper
bound, right?

00:06:43.680 --> 00:06:45.880
The only way to get 11 is if
you completely flatten out

00:06:45.880 --> 00:06:47.910
this triangle, at which point
that's not a triangle anymore.

00:06:47.910 --> 00:06:49.260
It'll be a line.

00:06:49.260 --> 00:06:50.960
So it can't be choice three.

00:06:50.960 --> 00:06:52.130
So the only possibility.

00:06:52.130 --> 00:06:53.910
They say, which of the following
can be the length of

00:06:53.910 --> 00:06:54.880
the third side?

00:06:54.880 --> 00:06:56.960
So it's only choices
one and two.

00:06:56.960 --> 00:07:01.030
And that is choice C.

00:07:01.030 --> 00:07:03.450
Next problem.

00:07:03.450 --> 00:07:06.880
46.

00:07:06.880 --> 00:07:15.650
How many integers n are there
such that 1 is less than 5n

00:07:15.650 --> 00:07:22.400
plus 5, which is less than 25?

00:07:22.400 --> 00:07:22.740
OK.

00:07:22.740 --> 00:07:28.610
So they say how many integers n
are there so that 5n plus 5.

00:07:28.610 --> 00:07:31.110
So they didn't say positive
integers, right?

00:07:31.110 --> 00:07:33.000
So that's an interesting
thing to keep in mind.

00:07:33.000 --> 00:07:35.040
So let's just try to simplify
this a little bit.

00:07:35.040 --> 00:07:39.330
Let's subtract 5 from all
sides of this double

00:07:39.330 --> 00:07:39.990
inequality.

00:07:39.990 --> 00:07:42.910
So if you subtract 5 from
everything you get minus 4 is

00:07:42.910 --> 00:07:50.410
less than 5n, which
is less than 20.

00:07:50.410 --> 00:07:51.640
Right?

00:07:51.640 --> 00:07:54.960
So another way you could say
it, is let's just divide

00:07:54.960 --> 00:07:56.770
everything by 5.

00:07:56.770 --> 00:07:58.890
So because 5 is positive you
don't have to change the

00:07:58.890 --> 00:07:59.470
inequalities.

00:07:59.470 --> 00:08:04.810
So you get minus 4/5 is less
than n, which is less than 20

00:08:04.810 --> 00:08:08.140
divided by 5, is 4.

00:08:08.140 --> 00:08:09.640
So now the question becomes
a lot simpler.

00:08:09.640 --> 00:08:12.940
How many integers n are
there such that this?

00:08:12.940 --> 00:08:16.200
How many integers are there
between minus 4/5 and 4?

00:08:16.200 --> 00:08:17.840
And it's not equal
to any of those.

00:08:17.840 --> 00:08:20.300
So 0 is an integer.

00:08:20.300 --> 00:08:22.770
1, 2, and 3.

00:08:22.770 --> 00:08:25.510
So there are 4 integers.

00:08:25.510 --> 00:08:27.080
So that is B.

00:08:31.760 --> 00:08:33.190
OK, next problem.

00:08:33.190 --> 00:08:42.370
47.

00:08:42.370 --> 00:08:49.710
A car dealer sold x used cars
and y new cars during May.

00:08:49.710 --> 00:08:56.410
So number used is equal to x.

00:08:56.410 --> 00:09:00.650
Number new is equal to y.

00:09:00.650 --> 00:09:01.750
During May.

00:09:01.750 --> 00:09:05.910
If the number of used cars sold
was 10 greater than the

00:09:05.910 --> 00:09:09.320
number new cars, which of the
following expresses this

00:09:09.320 --> 00:09:10.070
relationship?

00:09:10.070 --> 00:09:15.140
So the number of used cars, x,
was 10 greater than the number

00:09:15.140 --> 00:09:16.850
of new cars.

00:09:16.850 --> 00:09:21.480
So it's 10 greater than y, so
it equals y plus 10, right?

00:09:21.480 --> 00:09:24.740
This says that the number of
used cars is 10 more than the

00:09:24.740 --> 00:09:27.330
number of new cars.

00:09:27.330 --> 00:09:29.460
So we just have to look for
that. x is equal to y plus 10.

00:09:29.460 --> 00:09:31.260
That's choice D.

00:09:33.770 --> 00:09:35.810
I think we have time
for one more.

00:09:35.810 --> 00:09:41.110
48.

00:09:41.110 --> 00:09:44.820
If a 10% deposit that has been
paid toward the purchase of a

00:09:44.820 --> 00:09:48.890
certain product is $110,
how much more

00:09:48.890 --> 00:09:51.060
remains on the product?

00:09:51.060 --> 00:09:56.150
So essentially they're saying,
110 is 10% of what number?

00:09:56.150 --> 00:09:57.200
That's the first thing
you have to say.

00:09:57.200 --> 00:10:04.780
So 110 is equal to 0.1
times what number?

00:10:04.780 --> 00:10:08.050
So that's the price.

00:10:08.050 --> 00:10:10.280
Let's call that the original
price of the product.

00:10:10.280 --> 00:10:12.550
So the original price of the
product is going to be what?

00:10:12.550 --> 00:10:16.430
It's going to be 110 divided
by 0.1, which is

00:10:16.430 --> 00:10:18.570
just this times 10.

00:10:18.570 --> 00:10:23.390
Which is 1,100, right?

00:10:23.390 --> 00:10:24.850
Just add a 0.

00:10:24.850 --> 00:10:26.455
So that's original purchase
price of the product.

00:10:29.180 --> 00:10:30.990
The deposit is $110 and
they want to know

00:10:30.990 --> 00:10:32.100
what do you have left.

00:10:32.100 --> 00:10:35.310
So you're going to put
$110 deposit on it.

00:10:35.310 --> 00:10:37.340
This was the original
purchase price.

00:10:37.340 --> 00:10:41.935
You put $110 deposit.

00:10:41.935 --> 00:10:45.590
Let's see, 1,100 minus 100 would
be 1,000, but then we

00:10:45.590 --> 00:10:46.210
have another 10.

00:10:46.210 --> 00:10:48.540
So it would be 990.

00:10:48.540 --> 00:10:51.340
So that is choice B.

00:10:51.340 --> 00:10:52.300
And you could do it
the other way.

00:10:52.300 --> 00:10:55.880
You could just do a little
bit of borrowing.

00:10:55.880 --> 00:10:57.500
Anyway, you get the idea.

00:10:57.500 --> 00:11:00.970
And you would get choice
B, which is 990.

00:11:00.970 --> 00:11:01.810
And I'm out of time.

00:11:01.810 --> 00:11:03.450
See you in the next video.


GMAT: Math 6

WEBVTT
Kind: captions
Language: en

00:00:00.850 --> 00:00:03.580
We're on problem 30.

00:00:03.580 --> 00:00:04.890
Let's see, they've drawn
a circle there.

00:00:04.890 --> 00:00:06.850
If o is the center of the circle
above, what fraction of

00:00:06.850 --> 00:00:08.360
the circle is shaded?

00:00:08.360 --> 00:00:10.270
Let me draw that.

00:00:10.270 --> 00:00:12.200
They draw a circle.

00:00:12.200 --> 00:00:14.930
And then they have two lines
that go through the center,

00:00:14.930 --> 00:00:16.815
essentially.

00:00:16.815 --> 00:00:20.310
And one line looks like that.

00:00:20.310 --> 00:00:25.155
Another line looks something
like that.

00:00:28.820 --> 00:00:32.040
So they tell us that this
is the center, o.

00:00:32.040 --> 00:00:35.980
They tell us this
is 150 degrees.

00:00:35.980 --> 00:00:37.950
So the question is, what
fraction of the circular

00:00:37.950 --> 00:00:39.000
region is shaded?

00:00:39.000 --> 00:00:41.760
And the shaded region is this.

00:00:41.760 --> 00:00:44.840
This is the shaded region.

00:00:44.840 --> 00:00:47.570
So we just have to figure out
what percentage of the total

00:00:47.570 --> 00:00:49.780
degrees of the circle
are shaded.

00:00:49.780 --> 00:00:51.030
So let's think about
it this way.

00:00:51.030 --> 00:00:55.570
If this is 150 degrees, what
is this angle right here?

00:00:55.570 --> 00:00:58.980
Well, this angle and
150 degrees are

00:00:58.980 --> 00:01:01.270
supplementary, right?

00:01:01.270 --> 00:01:03.780
So this angle plus this angle
is going to be equal to 180.

00:01:03.780 --> 00:01:06.720
So 30 plus 150 is
equal to 180.

00:01:06.720 --> 00:01:08.550
And then you could either say,
oh, these are opposite angles,

00:01:08.550 --> 00:01:09.160
so they're equal.

00:01:09.160 --> 00:01:11.260
Or you can make the same
argument here, that 150 plus

00:01:11.260 --> 00:01:13.890
this angle has to be equal to
180, so this angle is also

00:01:13.890 --> 00:01:15.360
equal to 30.

00:01:15.360 --> 00:01:18.570
So what is the total angle
measure of the shaded region?

00:01:18.570 --> 00:01:19.680
You have 30 degrees here.

00:01:19.680 --> 00:01:20.750
And you have 30 degrees here.

00:01:20.750 --> 00:01:23.030
So a total of 60 degrees.

00:01:23.030 --> 00:01:24.720
And the whole circle is
how many degrees?

00:01:24.720 --> 00:01:26.450
If you run it all the way around
the circle, how many

00:01:26.450 --> 00:01:27.670
degrees is that?

00:01:27.670 --> 00:01:30.220
Well, that's 360 degrees.

00:01:30.220 --> 00:01:32.920
So 60/360.

00:01:32.920 --> 00:01:35.600
That's 1/6 of the circle
is shaded.

00:01:35.600 --> 00:01:39.120
And that is choice C.

00:01:39.120 --> 00:01:41.190
Question 31.

00:01:41.190 --> 00:01:43.430
This was question 30.

00:01:43.430 --> 00:01:44.830
Question 31.

00:01:44.830 --> 00:01:58.400
If Juan takes 11 seconds to run
y yards-- so y yards for

00:01:58.400 --> 00:02:02.020
every 11 seconds.

00:02:02.020 --> 00:02:04.560
Well, another way you could
think about it is, y/11 yards

00:02:04.560 --> 00:02:05.600
per second.

00:02:05.600 --> 00:02:06.330
Fair enough.

00:02:06.330 --> 00:02:09.190
How many seconds will
it take him to run x

00:02:09.190 --> 00:02:11.193
yards at the same rate?

00:02:14.180 --> 00:02:18.740
So he is going at y
yards per second.

00:02:18.740 --> 00:02:21.690
So how long will it take
him to go x yards?

00:02:21.690 --> 00:02:25.350
Well, if I said that I'm going
at 5 miles per hour, how long

00:02:25.350 --> 00:02:27.510
will it take me to
go 10 miles?

00:02:27.510 --> 00:02:30.390
Let's say I go 5
miles per hour.

00:02:30.390 --> 00:02:32.030
Or let's say 5 meters
per hour.

00:02:32.030 --> 00:02:35.020
How long will take me
to go 10 meters?

00:02:35.020 --> 00:02:38.600
You would say 10 divided
by 5 is equal to 2.

00:02:38.600 --> 00:02:39.960
2 hours.

00:02:39.960 --> 00:02:43.710
So likewise, we have
his speed.

00:02:43.710 --> 00:02:45.930
That's his speed we're talking
about, how fast he runs.

00:02:45.930 --> 00:02:53.720
His speed is y/11 yards
per second.

00:02:53.720 --> 00:02:55.580
And we want to know how
long will it take

00:02:55.580 --> 00:02:57.600
him to run x yards.

00:02:57.600 --> 00:03:01.990
So we could just take x divided
by the speed, divided

00:03:01.990 --> 00:03:06.762
by y/11, and we'll get the
answer in seconds.

00:03:06.762 --> 00:03:09.770
And you could work out the
units, but x divided by y/11,

00:03:09.770 --> 00:03:15.700
that's the same thing as x
times 11/y, equals 11x/y.

00:03:15.700 --> 00:03:20.030
Another way to view it is this
is equal to the rate.

00:03:20.030 --> 00:03:23.120
And we know, from probably the
first day in physics, that

00:03:23.120 --> 00:03:25.220
distance is equal to
rate times time.

00:03:25.220 --> 00:03:27.840
This might be an easier way
for you to think about it.

00:03:27.840 --> 00:03:30.480
However it best forms
connections in your brain.

00:03:30.480 --> 00:03:32.060
Distance is equal to
rate times time.

00:03:32.060 --> 00:03:35.680
They tell us that the distance
is x, and that the rate is

00:03:35.680 --> 00:03:41.750
y/11 yards per second.

00:03:41.750 --> 00:03:43.970
So y/11 times t is equal to x.

00:03:43.970 --> 00:03:47.870
So if you want to find t, you
do x divided by y/11.

00:03:47.870 --> 00:03:53.130
Anyway, and you get 11x/y,
which is choice A.

00:03:53.130 --> 00:03:59.960
Question 32.

00:03:59.960 --> 00:04:02.375
John has 10 pairs of
matched socks.

00:04:05.760 --> 00:04:10.060
If he loses 7 individual socks,
what is the greatest

00:04:10.060 --> 00:04:14.140
number of pairs of matched
socks he can have left?

00:04:14.140 --> 00:04:16.500
So he loses 7.

00:04:16.500 --> 00:04:19.649
He loses 7 socks.

00:04:19.649 --> 00:04:20.519
So think about it.

00:04:20.519 --> 00:04:23.590
If you wanted to optimize the
number of matched pairs,

00:04:23.590 --> 00:04:25.280
what's the worst
case scenario?

00:04:25.280 --> 00:04:30.510
The worst case scenario is if
every one of these socks came

00:04:30.510 --> 00:04:32.360
out of a different pair.

00:04:32.360 --> 00:04:36.660
Because then he'd be left with 7
socks that had their brother

00:04:36.660 --> 00:04:37.990
socks, or whatever you want
to call it, their

00:04:37.990 --> 00:04:39.510
twin socks are gone.

00:04:39.510 --> 00:04:40.620
So that's the worst case.

00:04:40.620 --> 00:04:42.420
But we want to think of what
the best case-- what's the

00:04:42.420 --> 00:04:44.480
best case if you want to
preserve the number of pairs

00:04:44.480 --> 00:04:45.680
you have left?

00:04:45.680 --> 00:04:47.580
If you want to preserve the
number of pairs you have left,

00:04:47.580 --> 00:04:53.590
the 7 should have as many
pairs as possible in it.

00:04:53.590 --> 00:05:01.160
So if 7 could be made of 3
pairs and 1 lone socks.

00:05:01.160 --> 00:05:03.970
This is kind of the best case
scenario if he wants to have

00:05:03.970 --> 00:05:06.890
the greatest number of
matched socks left.

00:05:06.890 --> 00:05:11.020
So 7 could be 3 pairs and 1 lone
socks, in which case he'd

00:05:11.020 --> 00:05:13.440
be left with what?

00:05:13.440 --> 00:05:15.000
So these 3 pairs
would be gone.

00:05:15.000 --> 00:05:17.340
Remember, he has 10 pairs.

00:05:17.340 --> 00:05:19.330
Let's keep in mind, those
aren't 10 socks.

00:05:19.330 --> 00:05:21.910
He has 10 pairs.

00:05:21.910 --> 00:05:23.660
Let's say that he just
loses 3 pairs.

00:05:23.660 --> 00:05:27.030
Then he'll just have 7
pairs left, right?

00:05:27.030 --> 00:05:30.410
But then if he loses 1 more
sock, then he's only going to

00:05:30.410 --> 00:05:31.400
have 6 pairs left.

00:05:31.400 --> 00:05:33.530
He's going to have 6
pairs and one sock.

00:05:33.530 --> 00:05:36.080
So he's going to have 6 matched
pairs left, and

00:05:36.080 --> 00:05:39.400
that's choice B.

00:05:39.400 --> 00:05:43.330
Question 33.

00:05:43.330 --> 00:05:45.560
The worst case, if the question
was the other way--

00:05:45.560 --> 00:05:47.040
maybe I'm just overly
fascinated with this

00:05:47.040 --> 00:05:49.170
question-- but if the question
was the other way, what's the

00:05:49.170 --> 00:05:53.660
worst case if-- what's the
minimum number of pairs that

00:05:53.660 --> 00:05:54.630
he has left?

00:05:54.630 --> 00:05:58.340
You could say, well, each of
these socks exactly destroy 1

00:05:58.340 --> 00:06:01.850
pair, so losing 7 socks
destroys 7 pairs.

00:06:01.850 --> 00:06:05.090
So at the worst case, if each of
these were a different sock

00:06:05.090 --> 00:06:07.640
from a different pair, he
would have 3 pairs left.

00:06:07.640 --> 00:06:09.350
But anyway, that's not
what they ask, so I

00:06:09.350 --> 00:06:11.090
shouldn't focus on it.

00:06:11.090 --> 00:06:13.990
23.

00:06:13.990 --> 00:06:17.300
What is the lowest positive
integer that is divisible by

00:06:17.300 --> 00:06:21.280
each of the numbers 1 through
7, inclusive.

00:06:21.280 --> 00:06:24.620
1 through 7, including
1 and 7.

00:06:24.620 --> 00:06:26.580
So let's think of
a number that's

00:06:26.580 --> 00:06:27.690
divisible by all of these.

00:06:27.690 --> 00:06:29.890
So it has to be divisible
by 7, right?

00:06:29.890 --> 00:06:34.770
7's a prime number, so it has
to be divisible by 7.

00:06:34.770 --> 00:06:37.010
It has to be divisible by 6.

00:06:37.010 --> 00:06:39.910
And 7 and 6 share no common
factor, so the number is going

00:06:39.910 --> 00:06:42.220
to be at least 7 times 6.

00:06:42.220 --> 00:06:48.600
It has to be divisible by 5,
because 5 is a prime number,

00:06:48.600 --> 00:06:50.230
and because that doesn't
share any factor with

00:06:50.230 --> 00:06:51.300
any of these numbers.

00:06:51.300 --> 00:06:56.300
It has to be divisible
by 4, right?

00:06:56.300 --> 00:06:56.760
Think about it.

00:06:56.760 --> 00:07:00.360
6 is 2 times 3.

00:07:00.360 --> 00:07:03.890
So to make it divisible by 4,
you only have to multiply it

00:07:03.890 --> 00:07:05.000
by another 2.

00:07:05.000 --> 00:07:07.630
So it has 2 times 2 in its
prime factorization.

00:07:07.630 --> 00:07:09.420
Maybe that's how I should
be writing it.

00:07:09.420 --> 00:07:10.585
It has to be divisible by 7.

00:07:10.585 --> 00:07:12.870
It has to be divisible by 6,
which is the same way as

00:07:12.870 --> 00:07:15.450
saying it has to be divisible
by 2 times 3.

00:07:15.450 --> 00:07:17.930
It has to be divisible by 5.

00:07:17.930 --> 00:07:19.906
It has to be divisible by 4.

00:07:19.906 --> 00:07:23.610
But we already have one
of 4's factors here?

00:07:23.610 --> 00:07:26.640
It's 2, so we just have to
multiply it by another 2.

00:07:26.640 --> 00:07:28.586
So this is to say it's
divisible by 4.

00:07:28.586 --> 00:07:30.440
It has to be divisible by 3.

00:07:30.440 --> 00:07:32.660
Well, it's already
divisible by 3.

00:07:32.660 --> 00:07:34.810
It has to be divisible by 2.

00:07:34.810 --> 00:07:36.470
It's already divisible by
2, actually, twice.

00:07:36.470 --> 00:07:39.100
It has to be divisible by 1, and
that's already the case.

00:07:39.100 --> 00:07:40.950
So this is the number.

00:07:40.950 --> 00:07:42.710
And notice, I was very
careful not to

00:07:42.710 --> 00:07:44.070
have extra prime factors.

00:07:44.070 --> 00:07:47.290
If I just did 7 times 6, times
5, times 4, times 3, times 2,

00:07:47.290 --> 00:07:50.100
times 1, I would have gotten a
number that is divisible by

00:07:50.100 --> 00:07:52.700
all of them, but it wouldn't
have been the smallest one.

00:07:52.700 --> 00:07:54.130
So anyway, what is
this number?

00:07:54.130 --> 00:07:56.750
Let's do the small numbers
first. Well, I'll do the big

00:07:56.750 --> 00:07:59.510
number first. 7 times 5 is 35.

00:07:59.510 --> 00:08:03.600
2 times 3 is 6, times 2 is 12.

00:08:03.600 --> 00:08:08.540
So 35 times 12.

00:08:08.540 --> 00:08:13.580
35 times 2 is 70-- 0,
1 times 35-- is 350.

00:08:13.580 --> 00:08:16.360
And then I have 0.

00:08:16.360 --> 00:08:18.460
7 plus 5 is 12.

00:08:18.460 --> 00:08:19.900
420.

00:08:19.900 --> 00:08:22.010
That is choice A.

00:08:22.010 --> 00:08:23.580
And you can feel good about
it, because it's also the

00:08:23.580 --> 00:08:26.350
lowest number on their list.

00:08:26.350 --> 00:08:29.140
Next question.

00:08:29.140 --> 00:08:33.809
34.

00:08:33.809 --> 00:08:38.710
What percentage of 30 is 12?

00:08:38.710 --> 00:08:43.750
So 12 is equal to some
decimal times 30.

00:08:43.750 --> 00:08:45.420
And we could convert
that decimal,

00:08:45.420 --> 00:08:46.940
eventually, to a percent.

00:08:46.940 --> 00:08:48.490
We just multiply it by 100.

00:08:48.490 --> 00:08:55.680
So x is equal to 30-- sorry,
is equal to 12/30, which is

00:08:55.680 --> 00:09:04.970
the same thing as 4/10,
which equals 0.4.

00:09:04.970 --> 00:09:06.990
And if you wanted to write a
decimal as a percent, you just

00:09:06.990 --> 00:09:07.930
multiply it by 100.

00:09:07.930 --> 00:09:11.040
That is equal to 40%.

00:09:11.040 --> 00:09:14.280
And that is choice D.

00:09:14.280 --> 00:09:16.500
And these can be confusing, so
it's very important to write

00:09:16.500 --> 00:09:17.160
it that way.

00:09:17.160 --> 00:09:19.910
What percentage of 30 is 12?

00:09:19.910 --> 00:09:22.380
So 12 is what percentage
of 30?

00:09:22.380 --> 00:09:23.720
It's going to be a
smaller number.

00:09:23.720 --> 00:09:26.660
You can kind of think, 12
is what fraction of 30?

00:09:26.660 --> 00:09:29.390
Or you could say 12/30 equals
what as a percentage?

00:09:29.390 --> 00:09:30.870
It equals x percent.

00:09:30.870 --> 00:09:31.950
You could think of
it that way, too.

00:09:31.950 --> 00:09:32.860
It's all the same thing.

00:09:32.860 --> 00:09:35.440
The important thing is
to be able to parse

00:09:35.440 --> 00:09:36.630
the language correctly.

00:09:36.630 --> 00:09:38.050
Anyway.

00:09:38.050 --> 00:09:42.720
35.

00:09:42.720 --> 00:09:53.430
If 1.5 over 0.2 plus x is equal
to 5, then x is equal

00:09:53.430 --> 00:09:54.690
to-- let's just solve it.

00:09:54.690 --> 00:09:58.520
Multiply both sides of this
equation by 0.2 plus x.

00:10:02.630 --> 00:10:03.920
On the left-hand side,
it cancels out.

00:10:03.920 --> 00:10:05.230
We just have 1.5.

00:10:05.230 --> 00:10:08.950
On the right-hand side,
what's 5 times 0.2?

00:10:08.950 --> 00:10:09.780
It's 1, right?

00:10:09.780 --> 00:10:11.620
0.2 is the same thing
as 20% or 1/5.

00:10:11.620 --> 00:10:13.080
So it's 5 times 1/5.

00:10:13.080 --> 00:10:17.010
That's 1-- you can think of it
a bunch of ways-- plus 5x.

00:10:17.010 --> 00:10:18.490
Subtract 1 from both sides.

00:10:18.490 --> 00:10:24.810
You have 0.5-- 1.5 minus 1
is 0.5-- is equal to 5x.

00:10:24.810 --> 00:10:28.660
So x is equal to 0.5
divided by 5.

00:10:28.660 --> 00:10:31.170
Well, that's just
equal to 0.1.

00:10:31.170 --> 00:10:33.720
The answer is B.

00:10:33.720 --> 00:10:35.620
See you in the next video.


GMAT: Math 7

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:02.940
We're on problem 36.

00:00:02.940 --> 00:00:04.450
They've drawn a little
graph here.

00:00:04.450 --> 00:00:07.170
So let's draw it up
for ourselves.

00:00:07.170 --> 00:00:09.560
So that's the y-axis.

00:00:09.560 --> 00:00:12.720
That is the x-axis.

00:00:12.720 --> 00:00:14.070
And then they have this point.

00:00:14.070 --> 00:00:17.090
Let's see, minus 1.

00:00:17.090 --> 00:00:23.160
They say, 1, 2, 3.

00:00:23.160 --> 00:00:23.910
Let's see.

00:00:23.910 --> 00:00:26.000
1, 2.

00:00:26.000 --> 00:00:28.360
And then they have this line
segment PQ that goes

00:00:28.360 --> 00:00:30.330
from 0, minus 1.

00:00:30.330 --> 00:00:32.290
Let me draw that in
a different color.

00:00:32.290 --> 00:00:34.270
It goes from 0, minus
1 to 3 comma 2.

00:00:34.270 --> 00:00:43.380
So it goes from there, so
3, so roughly there.

00:00:43.380 --> 00:00:46.030
I think that's about as
good as I can do.

00:00:49.530 --> 00:00:51.780
And the way they drew it,
it intersects 1 here.

00:00:51.780 --> 00:00:53.530
And so this would be 3.

00:00:53.530 --> 00:00:56.890
This is the point 3 comma 2.

00:00:56.890 --> 00:00:59.410
And they say in the figure
above, the point on segment

00:00:59.410 --> 00:01:03.290
PQ, so they say this is point
P, this is point Q.

00:01:03.290 --> 00:01:08.390
The point on PQ that is twice
as far from P as from Q.

00:01:08.390 --> 00:01:12.500
So the point is on this segment,
so this point is

00:01:12.500 --> 00:01:13.420
someplace around here.

00:01:13.420 --> 00:01:15.550
We could find points that are
away from the segment that are

00:01:15.550 --> 00:01:17.160
twice as far from P as
from Q, but they say

00:01:17.160 --> 00:01:19.170
it's on this segment.

00:01:19.170 --> 00:01:22.190
So let's think about
it a little bit.

00:01:22.190 --> 00:01:26.380
If we just look at how do we
get from P to Q, we go 3 to

00:01:26.380 --> 00:01:30.280
the right, right? x increases
by 3 and y

00:01:30.280 --> 00:01:33.210
increases by 3, right?

00:01:33.210 --> 00:01:37.240
So if we wanted to go 2/3 along
the way, what if we just

00:01:37.240 --> 00:01:44.520
increased x by 2 to get to x is
equal to 2 and increased y

00:01:44.520 --> 00:01:46.310
by 2, right?

00:01:46.310 --> 00:01:49.650
So the x's and y's only
increase by 2/3

00:01:49.650 --> 00:01:51.240
of the way to Q.

00:01:51.240 --> 00:01:52.490
So then that would
be the point.

00:01:55.240 --> 00:01:58.230
x is 2 and then y is 1.

00:01:58.230 --> 00:02:04.000
That would be the point
2 comma 1, which is B.

00:02:04.000 --> 00:02:06.590
Next question.

00:02:06.590 --> 00:02:12.200
37.

00:02:12.200 --> 00:02:18.560
If a positive integer n is
divisible by both 5 and 7,

00:02:18.560 --> 00:02:22.050
than n must be divisible by
which of the following?

00:02:22.050 --> 00:02:23.270
Let's see, they give
us a couple of

00:02:23.270 --> 00:02:24.595
choices: I, II and III.

00:02:27.140 --> 00:02:29.800
So they say it has to
be divisible by 12.

00:02:29.800 --> 00:02:32.370
No, that's not the case.

00:02:32.370 --> 00:02:34.350
35 is divisible by 5 and 7.

00:02:34.350 --> 00:02:36.960
It's not divisible by 12.

00:02:36.960 --> 00:02:38.290
35.

00:02:38.290 --> 00:02:40.090
Well, sure.

00:02:40.090 --> 00:02:45.460
If you're divisible by 5 and
7, that means it's equal to

00:02:45.460 --> 00:02:49.290
some constant times
5 times 7, right?

00:02:49.290 --> 00:02:52.110
And this could be a bunch of
numbers multiplied together.

00:02:52.110 --> 00:02:56.780
But that means it's equal to 35
times some other integer,

00:02:56.780 --> 00:03:00.010
and that integer could have
a bunch of other factors.

00:03:00.010 --> 00:03:00.510
So, right.

00:03:00.510 --> 00:03:03.700
It has to be divisible by 35.

00:03:03.700 --> 00:03:06.110
And statement III is 70.

00:03:06.110 --> 00:03:09.220
Well, no, 35 is divisible
by 5 and 7, but it's not

00:03:09.220 --> 00:03:10.680
divisible by 70.

00:03:10.680 --> 00:03:12.920
So statement III is not right.

00:03:12.920 --> 00:03:14.360
So it's II only.

00:03:14.360 --> 00:03:16.430
So that's C.

00:03:16.430 --> 00:03:20.780
Question 38.

00:03:20.780 --> 00:03:28.340
If 4 is one solution to the
equation x squared plus 3x

00:03:28.340 --> 00:03:32.575
plus k is equal to 10,
so 4 is one solution.

00:03:32.575 --> 00:03:38.980
So that means if I were to
factor this, it'll be x minus

00:03:38.980 --> 00:03:43.530
4 times x plus or minus
something else, because we

00:03:43.530 --> 00:03:48.060
know that x minus 4 equals 0,
which tells us that x is equal

00:03:48.060 --> 00:03:50.080
to 4 is one of the solutions.

00:03:50.080 --> 00:03:51.800
So what are they going
to ask us?

00:03:51.800 --> 00:03:54.830
They're going to say, where k
is a constant, what is the

00:03:54.830 --> 00:03:56.080
other solution?

00:03:58.830 --> 00:04:02.070
So let's think about
it a little bit.

00:04:02.070 --> 00:04:05.650
Well, actually, let me rewrite
it a little different.

00:04:05.650 --> 00:04:07.840
I didn't realize that they
said this is equal to 10.

00:04:07.840 --> 00:04:09.740
So let's subtract 10
from both sides.

00:04:09.740 --> 00:04:13.600
We get x squared plus 3x-- you
essentially want to find the

00:04:13.600 --> 00:04:21.829
roots of this quadratic-- plus
k minus 10 is equal to 0.

00:04:21.829 --> 00:04:23.280
And you want to factor
it, right?

00:04:23.280 --> 00:04:24.450
You could factor
any quadratic.

00:04:24.450 --> 00:04:30.180
It's going to be x plus
a times x plus b.

00:04:30.180 --> 00:04:31.760
And they're telling us
that 4 is one of

00:04:31.760 --> 00:04:33.170
the solutions, right?

00:04:33.170 --> 00:04:37.210
4 is one of the solutions,
so minus 4 could be a.

00:04:37.210 --> 00:04:41.620
So this would be x minus 4 times
some other number, x

00:04:41.620 --> 00:04:44.200
plus b, is equal to 0.

00:04:44.200 --> 00:04:46.590
And I said positive
4 in the solution.

00:04:46.590 --> 00:04:48.360
Why did I put a minus 4 here?

00:04:48.360 --> 00:04:50.740
Because think about it.

00:04:50.740 --> 00:04:53.270
If we factor this quadratic and
we get this, that's tells

00:04:53.270 --> 00:04:56.540
us either x minus 4 is
0 or x plus b is 0.

00:04:56.540 --> 00:05:03.390
If x minus 4 is 0, then the
solution is x is equal to 4,

00:05:03.390 --> 00:05:05.770
so that's why I wrote
x minus 4 there.

00:05:05.770 --> 00:05:10.440
But anyway, let's figure
out what b could be.

00:05:10.440 --> 00:05:13.780
So if we multiply this out to
try to pattern match it with

00:05:13.780 --> 00:05:22.540
this, we get x times x is x
squared minus 4x plus b times

00:05:22.540 --> 00:05:29.310
x, and then you have minus
4 times b, so minus 4b.

00:05:29.310 --> 00:05:34.840
So then this is equal to x
squared, and then we could

00:05:34.840 --> 00:05:40.620
write it plus b minus
4 times x.

00:05:40.620 --> 00:05:43.760
I just factored an x out of
these two terms, right?

00:05:43.760 --> 00:05:49.500
And so you get b minus 4
minus 4b is equal to 0.

00:05:49.500 --> 00:05:50.730
So now you just pattern
match it.

00:05:50.730 --> 00:05:55.190
You say b minus 4-- x squared
equals x squared.

00:05:55.190 --> 00:05:57.890
b minus 4x has to be
equal to 3x, right?

00:05:57.890 --> 00:05:58.830
We're just pattern matching.

00:05:58.830 --> 00:06:01.200
That's the only first-degree
x term there.

00:06:01.200 --> 00:06:04.750
So b minus 4 has to be equal--
x has to be equal to 3x.

00:06:04.750 --> 00:06:06.700
We don't even care about k.

00:06:06.700 --> 00:06:13.490
So b minus 4 has to be equal
to 3, or b is equal to 7.

00:06:17.590 --> 00:06:18.560
Oh, right, right.

00:06:18.560 --> 00:06:19.870
So they want to know what
the other solution is.

00:06:19.870 --> 00:06:20.770
They don't want to
know what b is.

00:06:20.770 --> 00:06:21.650
And I was looking and
was like, oh, wow,

00:06:21.650 --> 00:06:22.810
there isn't a 7 there.

00:06:22.810 --> 00:06:23.960
There's a negative 7.

00:06:23.960 --> 00:06:26.130
So that tells us that the
factorization of this

00:06:26.130 --> 00:06:28.490
problem-- I would have gotten
that wrong if they put a 7

00:06:28.490 --> 00:06:32.240
there, because I wasn't
careful-- is x minus 4 times x

00:06:32.240 --> 00:06:35.800
plus 7 is equal to 0, right?

00:06:35.800 --> 00:06:38.770
So we already said we could say
x minus 4 is equal to 0.

00:06:38.770 --> 00:06:40.150
And that's where we get
the 4 solution.

00:06:40.150 --> 00:06:43.180
Or we could say x plus
7 is equal to 0.

00:06:43.180 --> 00:06:44.590
Subtract 7 from both sides.

00:06:44.590 --> 00:06:47.280
The other solution is x
is equal to minus 7.

00:06:47.280 --> 00:06:49.920
That was a careless mistake I
almost made, but I got saved

00:06:49.920 --> 00:06:50.942
by the choices.

00:06:50.942 --> 00:06:53.950
So that's choice A.

00:06:53.950 --> 00:06:55.890
Next problem.

00:06:55.890 --> 00:07:01.370
39.

00:07:01.370 --> 00:07:05.720
If x is equal to negative
3, what is the

00:07:05.720 --> 00:07:11.020
value of minus 3x squared?

00:07:11.020 --> 00:07:14.120
So I don't know, maybe they're
trying to test your ability to

00:07:14.120 --> 00:07:18.280
do order of operations
or something.

00:07:18.280 --> 00:07:21.920
So this is equal to minus 3
times minus three squared,

00:07:21.920 --> 00:07:23.810
right? x squared.

00:07:23.810 --> 00:07:27.260
So this is equal to minus
3 times positive 9.

00:07:27.260 --> 00:07:31.240
Minus 3 squared is positive 9,
which equals minus 27, which

00:07:31.240 --> 00:07:32.490
is choice A.

00:07:35.790 --> 00:07:37.040
Next question.

00:07:40.260 --> 00:07:44.920
40.

00:07:44.920 --> 00:07:51.560
29 squared plus 29, over
29 is equal to?

00:07:51.560 --> 00:07:53.180
Well, let's just divide
the numerator and the

00:07:53.180 --> 00:07:54.160
denominator by 29.

00:07:54.160 --> 00:07:57.160
What's 29 squared?

00:07:57.160 --> 00:08:01.790
This is the same thing as 29
squared over 29 plus-- I'm

00:08:01.790 --> 00:08:06.130
just going to separate these
two terms out-- plus 29/29.

00:08:06.130 --> 00:08:08.530
29 squared divided by 29.

00:08:08.530 --> 00:08:10.360
x squared divided by x is x.

00:08:10.360 --> 00:08:12.490
29 squared divided
by 29 is 29.

00:08:12.490 --> 00:08:16.640
29 divided by 29 is 1,
so it equals 30.

00:08:16.640 --> 00:08:19.300
So that is choice E.

00:08:19.300 --> 00:08:25.210
Problem 41.

00:08:25.210 --> 00:08:36.030
If x is equal to 1 minus 3t and
y is equal to 2t minus 1.

00:08:36.030 --> 00:08:38.980
So I'm going to write
it like this.

00:08:38.980 --> 00:08:41.490
minus 1 plus 2t.

00:08:41.490 --> 00:08:44.610
I just want to put the t's
under each other, right?

00:08:44.610 --> 00:08:45.860
2t minus 1.

00:08:48.840 --> 00:08:52.940
For what value of t
does x equal y?

00:08:52.940 --> 00:08:56.340
OK, so let's just set x equal
y and solve for t.

00:08:56.340 --> 00:09:00.950
So we could just say if x is
equal to y, we get 1 minus 3t

00:09:00.950 --> 00:09:03.250
has to equal this, which
is 2t minus 1.

00:09:05.770 --> 00:09:07.790
Let's add 3t to both sides.

00:09:07.790 --> 00:09:11.110
So you get 1-- 3t goes
away from there--

00:09:11.110 --> 00:09:13.550
equals 5t, minus 1.

00:09:13.550 --> 00:09:14.680
Add 1 to both sides.

00:09:14.680 --> 00:09:17.130
You get 2 is equal to 5t.

00:09:17.130 --> 00:09:19.220
Divide both sides by 5.

00:09:19.220 --> 00:09:24.570
You get t is equal to 5/2,
which is choice A.

00:09:27.550 --> 00:09:29.100
And I'm almost out of time.

00:09:29.100 --> 00:09:30.900
The next one has a diagram,
which always takes me some

00:09:30.900 --> 00:09:33.850
time to draw, so I'll see
you in the next video.


GMAT: Math 2

WEBVTT
Kind: captions
Language: en

00:00:00.490 --> 00:00:01.840
We're on problem 7.

00:00:01.840 --> 00:00:05.100
And they drew this graph, so I
guess I'll draw it as well.

00:00:05.100 --> 00:00:07.920
That's the x-axis.

00:00:07.920 --> 00:00:09.170
That's the y-axis.

00:00:11.690 --> 00:00:20.010
Let's see, they draw 1, 2,
and they draw 1, 2, 3.

00:00:20.010 --> 00:00:24.640
And then the graph goes through
here and then curves

00:00:24.640 --> 00:00:26.530
up like that and actually
goes through

00:00:26.530 --> 00:00:28.060
this point right there.

00:00:28.060 --> 00:00:30.320
It goes through y is equal
to 3, at least the

00:00:30.320 --> 00:00:31.340
way they drew it.

00:00:31.340 --> 00:00:37.630
On the graph before, when x
equals 1/2, y is equal to 2.

00:00:37.630 --> 00:00:40.380
So they're saying that
this point right here

00:00:40.380 --> 00:00:43.510
is 1/2 comma 2.

00:00:43.510 --> 00:00:45.760
Fair enough.

00:00:45.760 --> 00:00:48.260
And when x is equal to
1, y is equal to 1.

00:00:48.260 --> 00:00:50.480
So they're saying that this
point right here-- I'll do it

00:00:50.480 --> 00:00:52.560
in a different color, just to
not make it too confusing--

00:00:52.560 --> 00:00:56.830
that point right there is
the point 1 comma 1.

00:00:56.830 --> 00:01:00.180
The graph is symmetrical with
respect to the vertical line

00:01:00.180 --> 00:01:01.270
at x equals 2.

00:01:01.270 --> 00:01:03.410
So that means that it's a
mirror image around that

00:01:03.410 --> 00:01:05.340
vertical line.

00:01:05.340 --> 00:01:08.910
According to the graph when
x is equal to 3, y

00:01:08.910 --> 00:01:10.480
should be equal to?

00:01:10.480 --> 00:01:16.850
So when x is equal to 3, we are
1 away from the line x is

00:01:16.850 --> 00:01:20.010
equal to 2, or what the line is
a mirror image of, right?

00:01:20.010 --> 00:01:23.750
So when we were 1 to the
left of it, that's when

00:01:23.750 --> 00:01:25.360
x is equal to 1.

00:01:25.360 --> 00:01:27.400
And we learned y
is equal to 1.

00:01:27.400 --> 00:01:31.160
So for 1 to the right-- and this
is symmetric around this

00:01:31.160 --> 00:01:35.430
line-- then we're going to have
the same height, right?

00:01:35.430 --> 00:01:38.100
So when we were 1 to the
left, the height was 1.

00:01:38.100 --> 00:01:40.350
When we're 1 to the right, the
height should also be 1.

00:01:40.350 --> 00:01:42.710
So this should be the
point 3 comma 1.

00:01:42.710 --> 00:01:46.350
So the choice is E.

00:01:46.350 --> 00:01:49.010
All that other information was
kind of a waste of time.

00:01:49.010 --> 00:01:51.470
Next problem.

00:01:51.470 --> 00:01:55.250
Problem 8.

00:01:55.250 --> 00:02:02.880
When 1/10% of 5,000--
I always like to

00:02:02.880 --> 00:02:03.820
get these into decimals.

00:02:03.820 --> 00:02:08.710
1/10% that equals this divided
by 100, so it's 1/1,000.

00:02:08.710 --> 00:02:11.420
So it's 0.001.

00:02:11.420 --> 00:02:19.840
So 0.001 times 5,000 is
subtracted from 1/10 of 5,000.

00:02:19.840 --> 00:02:21.310
The difference is-- OK.

00:02:21.310 --> 00:02:30.820
So they're saying 1/10 of 5,000
minus 1/1,000 of 5,000.

00:02:30.820 --> 00:02:31.020
Right?

00:02:31.020 --> 00:02:33.570
That's 1/10 of a percent
is 1,000.

00:02:33.570 --> 00:02:39.430
So you get 500 minus 5, right?

00:02:39.430 --> 00:02:45.400
That's 495, which is choice D.

00:02:45.400 --> 00:02:48.080
Problem 9.

00:02:48.080 --> 00:02:54.520
Which of the following is the
value of the square root of

00:02:54.520 --> 00:02:55.990
the cube root.

00:03:00.270 --> 00:03:02.200
So let's see.

00:03:02.200 --> 00:03:03.420
How many 0's do they have?

00:03:03.420 --> 00:03:06.250
1, 2, 3, 4.

00:03:06.250 --> 00:03:12.340
1, 2, 3, 4, 6, 4.

00:03:12.340 --> 00:03:12.710
OK.

00:03:12.710 --> 00:03:13.870
So there's-- how many
total numbers are

00:03:13.870 --> 00:03:14.480
behind the decimal point?

00:03:14.480 --> 00:03:17.630
1, 2, 3, 4, 5, 6.

00:03:17.630 --> 00:03:18.320
So it's a cube root.

00:03:18.320 --> 00:03:22.550
So some number times itself 3
times is equal to 0.0064.

00:03:22.550 --> 00:03:25.590
And you know whenever you
multiply decimals, you add up

00:03:25.590 --> 00:03:27.280
the number of spots behind
the decimal point.

00:03:27.280 --> 00:03:30.170
If I have two numbers that have
two numbers to the right

00:03:30.170 --> 00:03:31.495
of the decimal point and
I multiply them,

00:03:31.495 --> 00:03:32.950
I end up with 4.

00:03:32.950 --> 00:03:35.150
So if you just wanted to eyeball
this, you'd say, well,

00:03:35.150 --> 00:03:36.520
first of all, what number
to the third

00:03:36.520 --> 00:03:38.320
power is equal to 64?

00:03:38.320 --> 00:03:41.000
Well 4 to the third power
is equal to 64, right?

00:03:41.000 --> 00:03:45.640
It's equal to 16 times 4,
which is equal to 64.

00:03:45.640 --> 00:03:47.900
So this should have a
4 some place in it.

00:03:47.900 --> 00:03:48.890
It should look like a 4.

00:03:48.890 --> 00:03:50.570
It's going to be a decimal
number because obviously the

00:03:50.570 --> 00:03:53.270
number has gotten smaller
when I took the

00:03:53.270 --> 00:03:54.650
exponent of this number.

00:03:54.650 --> 00:03:59.050
And the clue is how
many places are

00:03:59.050 --> 00:03:59.980
there behind the decimal?

00:03:59.980 --> 00:04:03.610
1, 2, 3, 4, 5, 6.

00:04:03.610 --> 00:04:05.430
And I'm multiplying whatever
this number is

00:04:05.430 --> 00:04:07.330
times itself 3 times.

00:04:07.330 --> 00:04:11.210
So in order to get 6 digits
behind the decimal point, that

00:04:11.210 --> 00:04:13.440
original number probably
has two digits

00:04:13.440 --> 00:04:14.760
behind the decimal point.

00:04:14.760 --> 00:04:18.495
So my initial kind of
estimation is going

00:04:18.495 --> 00:04:19.470
to have a 4 in it.

00:04:19.470 --> 00:04:21.800
And it's going to be 0.04.

00:04:21.800 --> 00:04:23.770
And I'm pretty sure
I'm right here.

00:04:23.770 --> 00:04:28.040
Well, you could try it out for
yourself, but 0.04 times 0.04.

00:04:28.040 --> 00:04:30.100
You say, oh, 4 times 4 is 16.

00:04:30.100 --> 00:04:35.220
But I'm going to have now 1,
2, 3, 4 spaces behind the

00:04:35.220 --> 00:04:37.020
decimal point.

00:04:37.020 --> 00:04:43.960
And then if you multiply that
times 0.04, 4 times 16 is 64.

00:04:43.960 --> 00:04:48.150
And now I'm going to have 1,
2, 3, 4, 5, 6 spaces behind

00:04:48.150 --> 00:04:50.850
the decimal point.

00:04:50.850 --> 00:04:53.930
And I get 0.000064, which
is exactly there.

00:04:53.930 --> 00:04:59.400
So the problem now boils down
to square root of 0.04.

00:04:59.400 --> 00:05:01.030
And you use the exact
same logic.

00:05:01.030 --> 00:05:02.820
That is equal to 0.2.

00:05:02.820 --> 00:05:06.120
And try to square 0.2, you'll
get 0.04 right?

00:05:06.120 --> 00:05:07.770
0.2 times 0.2.

00:05:07.770 --> 00:05:09.510
You say 2 times 2 is 4.

00:05:09.510 --> 00:05:11.930
And I have 1, 2 spaces behind
the decimal point.

00:05:14.820 --> 00:05:18.690
0.04, and that's D.

00:05:18.690 --> 00:05:23.350
Problem 10.

00:05:23.350 --> 00:05:27.920
Raffle tickets numbered
consecutively from 101 through

00:05:27.920 --> 00:05:34.480
350 are placed in a box.

00:05:34.480 --> 00:05:37.800
What is the probability that a
ticket selected at random will

00:05:37.800 --> 00:05:42.020
have a number with a hundreds
digit of 2?

00:05:42.020 --> 00:05:45.290
So we're essentially saying,
out of this collection how

00:05:45.290 --> 00:05:48.140
many of them have a hundreds
digit of 2.

00:05:48.140 --> 00:05:55.940
So essentially it's going to be
anything from 200 to 299.

00:05:55.940 --> 00:05:59.040
Well that's essentially
100 digits, right?

00:05:59.040 --> 00:06:00.850
Those are 100 numbers
that have a

00:06:00.850 --> 00:06:03.460
hundreds digit of 2, right?

00:06:03.460 --> 00:06:04.800
Think about it.

00:06:04.800 --> 00:06:06.020
200 by itself would be 1.

00:06:06.020 --> 00:06:08.770
From 200 to 1 would be 2.

00:06:08.770 --> 00:06:12.000
So 200 to anything would be
that anything plus 1.

00:06:12.000 --> 00:06:16.550
So there's 100 numbers
that satisfy it.

00:06:19.090 --> 00:06:22.000
And then how many numbers
are we picking from?

00:06:22.000 --> 00:06:26.000
Well, if it was from 100 to
350 it be 250 numbers.

00:06:26.000 --> 00:06:29.570
But since it's from 101 to 350,
we're picking from a pool

00:06:29.570 --> 00:06:37.750
of 249 numbers.

00:06:37.750 --> 00:06:40.120
Right?

00:06:40.120 --> 00:06:44.200
Although let me think
about that.

00:06:44.200 --> 00:06:45.450
Let me think about that.

00:06:47.960 --> 00:06:52.170
Right, we're picking from
a pool of-- I just

00:06:52.170 --> 00:06:52.540
want to make sure.

00:06:52.540 --> 00:07:01.370
If it was 101 to 102, we would
be picking from a pool of--

00:07:01.370 --> 00:07:04.570
Right, we're picking from a pool
of 249 numbers, so the

00:07:04.570 --> 00:07:09.510
odds of having a number with a
2 in the hundreds digit will

00:07:09.510 --> 00:07:16.220
be 100/249.

00:07:16.220 --> 00:07:20.210
So that is choice E.

00:07:20.210 --> 00:07:26.530
I'm just making sure that I
haven't made a-- Actually no,

00:07:26.530 --> 00:07:28.690
I'm going to take that back.

00:07:28.690 --> 00:07:32.420
If I said from 300 to 350,
that's 51 digits.

00:07:32.420 --> 00:07:36.625
If I say 101 to 350, that's
not 249 digits.

00:07:36.625 --> 00:07:38.770
I made a mistake.

00:07:38.770 --> 00:07:41.040
Because we're including
101, right?

00:07:41.040 --> 00:07:45.600
So it would actually
be 250 digits.

00:07:45.600 --> 00:07:47.020
Sorry, it's 250 numbers.

00:07:47.020 --> 00:07:49.360
We're picking from a
bag of 250 numbers.

00:07:49.360 --> 00:07:50.140
Think about it.

00:07:50.140 --> 00:07:53.230
If it was from 101-- you have
to make sure you get your

00:07:53.230 --> 00:07:56.730
boundaries right on these-- if
we said from 101 to 105, how

00:07:56.730 --> 00:07:57.340
many are this?

00:07:57.340 --> 00:08:03.490
This would be 101, 102,
103, 104, and 105.

00:08:03.490 --> 00:08:05.260
That's 1, 2, 3, 4, 5.

00:08:05.260 --> 00:08:05.950
It's 5 digits.

00:08:05.950 --> 00:08:10.960
So it's 105 minus 101 plus 1.

00:08:10.960 --> 00:08:14.040
So similarly, the bag, the
number of digits we can pick

00:08:14.040 --> 00:08:18.400
from, is going to be 350
minus 101 plus 1,

00:08:18.400 --> 00:08:20.430
which is equal to 250.

00:08:20.430 --> 00:08:25.840
So anyway, out of the bag of
250, 100 numbers satisfy it.

00:08:25.840 --> 00:08:28.820
So we're going to have 100 in
250 chance of picking the

00:08:28.820 --> 00:08:29.840
right number.

00:08:29.840 --> 00:08:33.240
And if we divide the top and the
bottom by 50-- that's the

00:08:33.240 --> 00:08:36.789
greatest common divisor--
we get 2/5.

00:08:36.789 --> 00:08:40.200
And that is choice A.

00:08:40.200 --> 00:08:42.909
And I got a little cautious
because I saw that they had

00:08:42.909 --> 00:08:44.860
all these choices that were
really close to each other.

00:08:44.860 --> 00:08:47.720
And they all seemed to test,
like choices D and E, they all

00:08:47.720 --> 00:08:49.970
seemed to test whether you got
the boundaries right, whether

00:08:49.970 --> 00:08:52.180
you really counted the
pool correctly.

00:08:52.180 --> 00:08:53.700
And whether you really
counted the

00:08:53.700 --> 00:08:54.750
number of digits correctly.

00:08:54.750 --> 00:08:57.810
And I always have to go through
the exercise of let me

00:08:57.810 --> 00:09:00.430
make sure whether or not I need
to count 101, whether I

00:09:00.430 --> 00:09:01.810
can just subtract them,
or whether it's the

00:09:01.810 --> 00:09:02.890
fractions plus 1.

00:09:02.890 --> 00:09:04.450
I always have to clarify
that in my own brain.

00:09:04.450 --> 00:09:06.490
Maybe that was easier for you.

00:09:06.490 --> 00:09:10.710
Question 11.

00:09:10.710 --> 00:09:15.990
On Monday, a person mailed 8
packages weighing an average

00:09:15.990 --> 00:09:21.560
of 12 and 3/8 pounds.

00:09:21.560 --> 00:09:23.420
And on Tuesday, 4 packages.

00:09:23.420 --> 00:09:25.100
So this is 8.

00:09:25.100 --> 00:09:26.830
Weighed that much.

00:09:26.830 --> 00:09:32.200
And on Tuesday, 4 packages
weighing an average of 15 and

00:09:32.200 --> 00:09:34.160
1/4 pounds.

00:09:34.160 --> 00:09:37.380
What was the average weight in
pounds of all packages the

00:09:37.380 --> 00:09:39.400
person mailed on both days?

00:09:39.400 --> 00:09:41.420
So essentially you have to take
the sum of the weights of

00:09:41.420 --> 00:09:43.220
all of them and divide
by the total, right?

00:09:43.220 --> 00:09:45.260
So what's the sum of the
weights of all of them?

00:09:45.260 --> 00:09:47.490
So the sum of the weights of
these 8 packages-- we know

00:09:47.490 --> 00:09:49.000
their average.

00:09:49.000 --> 00:09:52.590
So the sum of the weights is
going to be 8 times 12 and

00:09:52.590 --> 00:10:01.100
3/8-- that's the sum of all of
these-- plus 4 times the

00:10:01.100 --> 00:10:01.810
weight of these.

00:10:01.810 --> 00:10:06.060
Plus 4 times 15 and 1/4.

00:10:06.060 --> 00:10:07.350
And we're going to divide
that by the

00:10:07.350 --> 00:10:08.490
total number of packages.

00:10:08.490 --> 00:10:11.330
Divided by 12.

00:10:11.330 --> 00:10:13.370
So this is equal
to, let's see.

00:10:13.370 --> 00:10:15.110
What's 8 times 12?

00:10:15.110 --> 00:10:19.230
8 times 12 is 96.

00:10:19.230 --> 00:10:22.040
And what's 8 times 3/8?

00:10:22.040 --> 00:10:23.980
So it's 96 plus 3.

00:10:23.980 --> 00:10:26.170
You could view 12 and
3/8 as 12 plus 3/8.

00:10:26.170 --> 00:10:29.170
So I kind of just did a
distributive property there.

00:10:29.170 --> 00:10:30.330
You could turn this
into an improper

00:10:30.330 --> 00:10:33.150
fraction, if that's easier.

00:10:33.150 --> 00:10:35.730
And then plus-- what's
4 times 15?

00:10:35.730 --> 00:10:37.410
It's 60, right?

00:10:37.410 --> 00:10:40.100
And then 4 times 1/4 is 1.

00:10:40.100 --> 00:10:41.830
All of that over 12.

00:10:41.830 --> 00:10:47.420
And so we have 99 plus 61.

00:10:47.420 --> 00:10:49.770
All of that over 12.

00:10:49.770 --> 00:10:54.760
Which is equal to 160/12.

00:10:54.760 --> 00:10:55.150
Let's see.

00:10:55.150 --> 00:10:56.650
Does 12 go into 160?

00:10:56.650 --> 00:11:00.210
12 times 12 is 144.

00:11:00.210 --> 00:11:01.150
Let me think about this.

00:11:01.150 --> 00:11:04.030
So let me just divide
top and bottom by 4.

00:11:04.030 --> 00:11:11.020
So you get 40/3.

00:11:11.020 --> 00:11:11.330
And let's see.

00:11:11.330 --> 00:11:13.650
All of the answers they have
it in terms of fractions.

00:11:13.650 --> 00:11:16.150
So 3 goes into 40
how many times?

00:11:16.150 --> 00:11:17.760
It goes into 13, right?

00:11:17.760 --> 00:11:18.950
13 times 3 is 39.

00:11:18.950 --> 00:11:20.580
So it's 13 with remainder 1.

00:11:20.580 --> 00:11:25.420
So 13 and 1/3 times,
so A is the answer.

00:11:25.420 --> 00:11:28.860
So the average of all of the
packages on both days are 13

00:11:28.860 --> 00:11:30.310
and 1/3 pounds.

00:11:30.310 --> 00:11:32.130
See you in the next video.


GMAT: Math 3

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:03.310
We're on problem 12.

00:00:03.310 --> 00:00:10.140
0.1 plus 0.1 squared plus
0.1 to the third.

00:00:12.850 --> 00:00:14.340
So that's the same
thing as 0.1.

00:00:14.340 --> 00:00:16.129
What's 0.1 squared?

00:00:16.129 --> 00:00:19.070
It's 1 times 1 with 2 numbers
to the right of the decimal,

00:00:19.070 --> 00:00:20.440
so it's 0.01.

00:00:20.440 --> 00:00:21.920
And then to the third power.

00:00:21.920 --> 00:00:26.000
You're just going to end
up 1/10 of that, right?

00:00:26.000 --> 00:00:27.790
0.01 times 0.1.

00:00:27.790 --> 00:00:29.510
Well that's 1 with 3 numbers
to the right

00:00:29.510 --> 00:00:30.270
of the decimal point.

00:00:30.270 --> 00:00:33.580
If I'm going to add them
all up, I get 1, 1, 1.

00:00:33.580 --> 00:00:36.380
And that is answer B.

00:00:36.380 --> 00:00:39.380
They're making sure you can
multiply your decimals.

00:00:39.380 --> 00:00:40.980
Problem 13.

00:00:40.980 --> 00:00:42.380
If you have trouble with
decimals, you might want to

00:00:42.380 --> 00:00:44.540
get on the Kahn Academy-- the
actual application, it's

00:00:44.540 --> 00:00:47.890
free-- and just work through the
basic arithmetic, because

00:00:47.890 --> 00:00:49.400
we have actually a bunch of
things on multiplying

00:00:49.400 --> 00:00:49.930
decimals and stuff.

00:00:49.930 --> 00:00:51.620
You have to start at 1 plus 1,
but it makes sure you don't

00:00:51.620 --> 00:00:52.890
have any holes in
your knowledge.

00:00:52.890 --> 00:00:55.160
It eventually gets to algebra
and trigonometry and calculus.

00:00:55.160 --> 00:00:56.470
You might find that useful.

00:00:56.470 --> 00:00:58.220
Anyway, question 13.

00:00:58.220 --> 00:01:01.020
A carpenter constructed a
rectangular sandbox with a

00:01:01.020 --> 00:01:05.790
capacity of 10 cubic feet.

00:01:05.790 --> 00:01:10.590
If the carpenter were to make a
similar box twice as long--

00:01:10.590 --> 00:01:18.090
2 times length-- twice as wide--
2 times width-- and

00:01:18.090 --> 00:01:21.290
twice as high as the first
sandbox, what would be the

00:01:21.290 --> 00:01:26.320
capacity in cubic feet of
the second sandbox?

00:01:26.320 --> 00:01:30.080
So you might want to visualize
it, right?

00:01:30.080 --> 00:01:32.990
The best way to visualize it
is probably how many of the

00:01:32.990 --> 00:01:33.940
old ones could fit?

00:01:33.940 --> 00:01:36.830
So if this was one of the old
ones, and now I'm going to

00:01:36.830 --> 00:01:40.300
make a new one that's
2 times the size in

00:01:40.300 --> 00:01:41.610
every dimension, right?

00:01:41.610 --> 00:01:43.600
That's 2 times the height.

00:01:43.600 --> 00:01:51.410
So essentially, I could increase
the width by 2.

00:01:51.410 --> 00:01:55.580
Increase the depth by 2, or
whatever you want to call it.

00:01:55.580 --> 00:01:56.830
Right?

00:01:56.830 --> 00:02:00.330
And then I'm going to increase
the height by 2.

00:02:00.330 --> 00:02:03.680
And I'm going to have
trouble drawing.

00:02:03.680 --> 00:02:06.990
So how many of the original
sandboxes-- that's what they

00:02:06.990 --> 00:02:09.900
want to know-- how many of the
original sandboxes essentially

00:02:09.900 --> 00:02:11.390
could fit into the new one?

00:02:11.390 --> 00:02:14.490
Well, 2 in 1 direction
times 2 times 2.

00:02:14.490 --> 00:02:18.160
So 2 times 2 times
2 is equal to 8.

00:02:18.160 --> 00:02:20.650
So another way to think of it,
you could view the old sandbox

00:02:20.650 --> 00:02:24.030
as almost a unit, like one
cubic unit sandbox.

00:02:24.030 --> 00:02:26.500
And now we're going to go
2 in every direction.

00:02:26.500 --> 00:02:31.330
So we could fit 8 of the old
sandboxes into the new one.

00:02:31.330 --> 00:02:34.030
And the old one had
a capacity of 10.

00:02:34.030 --> 00:02:40.120
So 8 times that is equal to 80
cubic feet, which is choice D.

00:02:40.120 --> 00:02:44.010
Question 14.

00:02:44.010 --> 00:02:45.530
And these, at least so far,
I think these are

00:02:45.530 --> 00:02:46.500
on the easier end.

00:02:46.500 --> 00:02:47.980
They'll probably get harder,
but so far they're a lot

00:02:47.980 --> 00:02:50.040
faster than the data
sufficiency ones.

00:02:50.040 --> 00:02:53.610
Which of the following cannot
be a value of 1

00:02:53.610 --> 00:02:56.570
over x minus 1?

00:02:56.570 --> 00:02:58.730
And I think this is one of the
ones where we have to look at

00:02:58.730 --> 00:03:00.700
the choices.

00:03:00.700 --> 00:03:01.910
1.

00:03:01.910 --> 00:03:02.630
Negative 1.

00:03:02.630 --> 00:03:05.060
So can we pick x so this
is negative 1?

00:03:05.060 --> 00:03:07.570
Well sure, if x is equal to 0,
1 divided by negative 1 is

00:03:07.570 --> 00:03:08.220
negative 1.

00:03:08.220 --> 00:03:12.830
So it's not negative 1 because
that can be a value for that.

00:03:12.830 --> 00:03:14.170
0.

00:03:14.170 --> 00:03:15.390
Well, this is interesting.

00:03:15.390 --> 00:03:18.510
How can we ever make
this equal to 0?

00:03:18.510 --> 00:03:22.010
The only way we can get this
close to 0 is if the

00:03:22.010 --> 00:03:26.700
denominator becomes a really
huge number, right?

00:03:26.700 --> 00:03:28.290
But it'll never be equal to 0.

00:03:28.290 --> 00:03:30.000
It'll just be a really, really,
really small fraction.

00:03:30.000 --> 00:03:31.800
This approaches 0 as x
approaches infinity.

00:03:31.800 --> 00:03:34.440
But this will never equal 0.

00:03:34.440 --> 00:03:37.335
So the answer is B.

00:03:41.890 --> 00:03:43.650
All of the other things are
completely possible.

00:03:43.650 --> 00:03:47.706
You just have to realize, you
should just see choice B, and

00:03:47.706 --> 00:03:49.770
is like, how could this
ever equal 0?

00:03:49.770 --> 00:03:52.170
Because the numerator
is never equaling 0.

00:03:52.170 --> 00:03:54.530
This can only approach 0 if the
denominator gets really,

00:03:54.530 --> 00:03:55.260
really, really big.

00:03:55.260 --> 00:03:56.590
It will just become a really
small fraction.

00:03:56.590 --> 00:03:59.160
But it'll never, ever equal 0.

00:03:59.160 --> 00:04:00.970
And you could even try.

00:04:00.970 --> 00:04:06.490
1 over x minus 1
is equal to 0.

00:04:06.490 --> 00:04:07.470
You can try to solve it.

00:04:07.470 --> 00:04:09.450
If you multiply both sides
by x minus 1, you get

00:04:09.450 --> 00:04:10.390
1 is equal to 0.

00:04:10.390 --> 00:04:12.130
It's impossible.

00:04:12.130 --> 00:04:13.920
Undefined.

00:04:13.920 --> 00:04:17.529
15.

00:04:17.529 --> 00:04:19.660
A bakery opened yesterday
with a daily

00:04:19.660 --> 00:04:25.820
supply of 40 dozen rolls.

00:04:25.820 --> 00:04:29.040
Half of the rolls were
sold by noon.

00:04:29.040 --> 00:04:33.020
1/2 by noon.

00:04:33.020 --> 00:04:36.630
And 80% of the remaining rolls
were sold between noon and

00:04:36.630 --> 00:04:37.880
closing time.

00:04:37.880 --> 00:04:45.370
80% remaining, noon
and closing.

00:04:45.370 --> 00:04:47.840
How many dozen rolls had not
been sold when the bakery

00:04:47.840 --> 00:04:49.050
closed yesterday?

00:04:49.050 --> 00:04:51.090
OK, half sold by noon.

00:04:51.090 --> 00:04:55.420
So 20 sold by noon.

00:04:55.420 --> 00:04:58.370
And 20 left.

00:04:58.370 --> 00:04:58.960
Right?

00:04:58.960 --> 00:05:03.470
And they said 80% of the
remaining rolls were sold

00:05:03.470 --> 00:05:06.070
between noon and closing time.

00:05:06.070 --> 00:05:07.690
So we could view it two ways.

00:05:07.690 --> 00:05:10.320
If you wanted to do it really
fast, you're like, OK, 20% of

00:05:10.320 --> 00:05:12.860
the remaining rolls
will not be sold.

00:05:12.860 --> 00:05:13.470
Right?

00:05:13.470 --> 00:05:18.340
So you could say 20% of the
remaining rolls-- so times

00:05:18.340 --> 00:05:20.500
20-- don't get sold, right?

00:05:20.500 --> 00:05:23.770
If 80% get sold, 20%
don't get sold.

00:05:23.770 --> 00:05:26.010
And that equals what?

00:05:26.010 --> 00:05:29.360
We could say 20 times
20 is 400.

00:05:29.360 --> 00:05:31.150
Two spaces behind the
decimal point.

00:05:31.150 --> 00:05:32.580
And that makes sense.

00:05:32.580 --> 00:05:33.585
20% is 1/5.

00:05:33.585 --> 00:05:36.140
So 1/5 of 20 is 4.

00:05:36.140 --> 00:05:39.670
So 4 rolls don't get sold
when it closed.

00:05:39.670 --> 00:05:40.770
You could do it the
other way around.

00:05:40.770 --> 00:05:43.360
You could say, OK, how many sold
between, at this time,

00:05:43.360 --> 00:05:46.290
80% of 20 is 16 more sell.

00:05:46.290 --> 00:05:47.970
16 sell.

00:05:47.970 --> 00:05:50.900
And then you can say, OK, how
many total were sold?

00:05:50.900 --> 00:05:53.830
Well, 20 plus 16, 36.

00:05:53.830 --> 00:05:55.910
And then 40 minus
36 is also 4.

00:05:55.910 --> 00:05:57.240
It takes a little bit more
time, but it gets

00:05:57.240 --> 00:06:00.080
you the same answer.

00:06:00.080 --> 00:06:02.490
Eventually time is what you'll
have to focus on.

00:06:02.490 --> 00:06:03.740
Once you are confident
that you can get

00:06:03.740 --> 00:06:05.240
every problem right.

00:06:05.240 --> 00:06:08.710
What is the combined area in
square inches of the front and

00:06:08.710 --> 00:06:16.330
back of a rectangular sheet of
paper measuring 8.5 by 11?

00:06:16.330 --> 00:06:21.910
So it's essentially going to
be 2 times 8.5 times 11.

00:06:21.910 --> 00:06:24.440
If you just multiplied 8.5 times
11, that would give you

00:06:24.440 --> 00:06:25.720
the area of one side.

00:06:25.720 --> 00:06:26.880
So we want the area
of both sides.

00:06:26.880 --> 00:06:28.390
It's going to be 2 times that.

00:06:28.390 --> 00:06:30.680
And I want to do this first,
just so I can get rid of this

00:06:30.680 --> 00:06:31.400
mixed number.

00:06:31.400 --> 00:06:33.180
So 8.5 times 2.

00:06:33.180 --> 00:06:38.180
That's 17, times 11, which
is going to be what?

00:06:38.180 --> 00:06:40.550
17 times 11 is 170.

00:06:40.550 --> 00:06:44.080
Because that's 17 times
10, plus 17.

00:06:44.080 --> 00:06:46.850
So that's 187.

00:06:46.850 --> 00:06:48.100
That's choice E.

00:06:50.840 --> 00:06:53.520
Let's do problem 17.

00:06:53.520 --> 00:06:57.280
150 is what percent of 30?

00:06:57.280 --> 00:07:05.860
So 150 is equal to x percent
of 30 times 30.

00:07:05.860 --> 00:07:08.360
Or another way we could write
that is-- well, let me just

00:07:08.360 --> 00:07:09.330
write it as a variable.

00:07:09.330 --> 00:07:10.700
Let's figure it out
as a decimal.

00:07:10.700 --> 00:07:12.450
And then once you know
a decmial, it's

00:07:12.450 --> 00:07:13.630
easy to convert that.

00:07:13.630 --> 00:07:20.150
So 150 is equal to
x of 36 or 36x.

00:07:20.150 --> 00:07:22.490
This is some number times 36.

00:07:22.490 --> 00:07:23.820
Divide both sides by 36.

00:07:23.820 --> 00:07:29.200
You get x is equal to 150/36.

00:07:29.200 --> 00:07:32.390
Let's see, I think we can divide
the top and the bottom.

00:07:32.390 --> 00:07:34.830
Definitely we can divide
them by 6.

00:07:34.830 --> 00:07:38.640
6 goes into 150 25 times.

00:07:38.640 --> 00:07:45.810
And it goes into 36 6 times.

00:07:45.810 --> 00:07:48.170
Right?

00:07:48.170 --> 00:07:49.490
Oh wait, what am I doing?

00:07:49.490 --> 00:07:50.900
It's 30.

00:07:50.900 --> 00:07:52.390
My own handwriting
got me caught up.

00:07:52.390 --> 00:07:54.540
This is a much easier problem
than what I was doing.

00:07:54.540 --> 00:07:59.080
They're saying 150 is what
percent of 30, right?

00:07:59.080 --> 00:08:00.910
So it's x times 30.

00:08:00.910 --> 00:08:01.510
This is easy.

00:08:01.510 --> 00:08:02.940
You divide both sides by 30.

00:08:02.940 --> 00:08:04.750
I mistakenly wrote 36 there.

00:08:04.750 --> 00:08:08.540
Divide both sides by 30, you
get 5 is equal to x, right?

00:08:08.540 --> 00:08:11.440
If you wanted to write 5 as a
percentage, you just multiply

00:08:11.440 --> 00:08:12.810
both sides by 100.

00:08:12.810 --> 00:08:17.440
So you could say x
is equal to 500%.

00:08:17.440 --> 00:08:18.520
And that makes sense.

00:08:18.520 --> 00:08:20.990
150 is 5 times 30.

00:08:20.990 --> 00:08:22.450
100% of 30 is 30.

00:08:22.450 --> 00:08:24.370
200% of 30 is 60.

00:08:24.370 --> 00:08:24.960
And so forth.

00:08:24.960 --> 00:08:27.390
So 500% of 30 is 150.

00:08:27.390 --> 00:08:29.280
That took me too long I think.

00:08:29.280 --> 00:08:31.640
E.

00:08:31.640 --> 00:08:33.730
Got to make sure your
handwriting is good.

00:08:33.730 --> 00:08:35.490
Next question.

00:08:35.490 --> 00:08:37.570
18.

00:08:37.570 --> 00:08:45.890
The ratio 2:1/3 is equal to--
Well, 2 divided by 1/3 is

00:08:45.890 --> 00:08:51.570
equal to 2 times 3/1, which
is equal to 6/1.

00:08:51.570 --> 00:08:55.700
So 2:1/3 is the same thing
as the ratio of 6:1,

00:08:55.700 --> 00:08:59.490
which is choice A.

00:08:59.490 --> 00:08:59.840
Right?

00:08:59.840 --> 00:09:02.880
2:1/3 is equal to 6:1.

00:09:02.880 --> 00:09:05.750
Another way to think about
it is 2 is 6 times 1/3.

00:09:05.750 --> 00:09:07.760
And 6 is 6 times 1.

00:09:07.760 --> 00:09:08.380
Same thing.

00:09:08.380 --> 00:09:11.000
So 18 is A.

00:09:11.000 --> 00:09:12.620
Next question.

00:09:12.620 --> 00:09:14.990
19.

00:09:14.990 --> 00:09:21.830
Running at the same constant
rate, 6 identical machines can

00:09:21.830 --> 00:09:25.173
produce a total of 270
bottles per minute.

00:09:30.220 --> 00:09:34.400
At this rate, how many bottles
could 10 such machines produce

00:09:34.400 --> 00:09:37.230
in 4 minutes?

00:09:37.230 --> 00:09:41.500
OK, so how much does each
produce per minute?

00:09:41.500 --> 00:09:49.200
So 1 machine will produce
270 divided by

00:09:49.200 --> 00:09:52.330
6 bottles per minute.

00:09:52.330 --> 00:09:53.310
Right?

00:09:53.310 --> 00:09:54.500
That's one machine.

00:09:54.500 --> 00:09:56.070
I just divided both
sides by 6.

00:09:56.070 --> 00:09:57.800
6 machines produce that.

00:09:57.800 --> 00:10:03.060
So 10 machines would produce 10
times as many per minute.

00:10:03.060 --> 00:10:07.990
So 10 times this is
2,700 divided by

00:10:07.990 --> 00:10:10.360
6 bottles per minute.

00:10:10.360 --> 00:10:12.180
And if they want to know how
much 10 machines are going to

00:10:12.180 --> 00:10:14.420
produce in 4 minutes, you just
multiply this times 4.

00:10:17.720 --> 00:10:19.800
So this is how much they produce
in 1 minute, so the

00:10:19.800 --> 00:10:27.870
answer's going to be 2,700
times 4 divided by 6.

00:10:27.870 --> 00:10:30.240
So let me see if I can do
this math fast. So 6 is

00:10:30.240 --> 00:10:33.130
equal to 2 times 3.

00:10:33.130 --> 00:10:40.610
If you divide 2,700
by 3, that's 900.

00:10:40.610 --> 00:10:41.990
And 3 divided by 3 is 1.

00:10:41.990 --> 00:10:44.450
And then 4 divided by 2 is 2.

00:10:44.450 --> 00:10:48.360
So 900 times 2 is
equal to 1,800.

00:10:48.360 --> 00:10:50.730
And that is choice B.

00:10:50.730 --> 00:10:51.820
And I'm all out of time.

00:10:51.820 --> 00:10:53.580
See you in the next video.


GMAT: Math 1

WEBVTT
Kind: captions
Language: en

00:00:01.730 --> 00:00:02.980
We're on problem 1.

00:00:06.440 --> 00:00:09.060
A project scheduled to be
carried out over a single

00:00:09.060 --> 00:00:14.070
fiscal year has a budget
of $12,600.

00:00:14.070 --> 00:00:17.820
Divide it into 12 equal
monthly allocations.

00:00:17.820 --> 00:00:19.440
So if we divide it by 12
how much are we going

00:00:19.440 --> 00:00:21.180
to spend per month?

00:00:21.180 --> 00:00:24.620
So that's $1,050 per month.

00:00:24.620 --> 00:00:24.950
Right?

00:00:24.950 --> 00:00:27.040
12,000 divided by 12 is 1,000.

00:00:27.040 --> 00:00:29.550
600 divided by 12 is 50.

00:00:29.550 --> 00:00:33.440
So they're going to spend
$1,050 per month.

00:00:33.440 --> 00:00:36.340
At the end of the fourth month
of that fiscal year, the total

00:00:36.340 --> 00:00:40.800
amount actually spent on
the project was 4,580.

00:00:40.800 --> 00:00:48.680
So 4,580 after four months.

00:00:48.680 --> 00:00:51.920
By how much was the project
over its budget?

00:00:51.920 --> 00:00:53.120
Well, let's see how much
they should have

00:00:53.120 --> 00:00:55.470
spent after four months.

00:00:55.470 --> 00:00:56.670
So after four months
they should have

00:00:56.670 --> 00:00:59.380
spent 1,050 times 4.

00:00:59.380 --> 00:01:00.040
That's what?

00:01:00.040 --> 00:01:02.340
That's 4,000.

00:01:02.340 --> 00:01:03.390
4 times 50.

00:01:03.390 --> 00:01:04.890
200.

00:01:04.890 --> 00:01:07.240
That's how much they should have
spent after four months

00:01:07.240 --> 00:01:08.100
if they were on budget.

00:01:08.100 --> 00:01:10.330
They ended up spending 4,580.

00:01:10.330 --> 00:01:13.430
So let's see how much
they spent too much.

00:01:13.430 --> 00:01:17.040
They spent $380 too much.

00:01:17.040 --> 00:01:19.770
And that is choice A.

00:01:19.770 --> 00:01:22.160
Next question.

00:01:22.160 --> 00:01:24.150
Question 2.

00:01:24.150 --> 00:01:30.950
For which of the following
values of n is 100 plus n over

00:01:30.950 --> 00:01:34.390
n not an integer?

00:01:34.390 --> 00:01:36.500
We could simplify this.

00:01:36.500 --> 00:01:41.730
This is the same thing as 100
over n plus n over n, which is

00:01:41.730 --> 00:01:45.150
equal to 100 over n plus 1.

00:01:45.150 --> 00:01:47.760
So in order for this not
to be an integer--

00:01:47.760 --> 00:01:49.000
this is the same thing.

00:01:49.000 --> 00:01:51.190
1 is clearly an integer,
so this can't

00:01:51.190 --> 00:01:52.370
be an integer, right?

00:01:52.370 --> 00:01:54.850
So we have to pick an n that
is essentially not

00:01:54.850 --> 00:01:56.160
divisible into 100.

00:01:56.160 --> 00:01:58.510
So what are their choices?

00:01:58.510 --> 00:01:59.590
So they say 1.

00:01:59.590 --> 00:02:01.880
Well 100 is clearly
divisible by 1.

00:02:01.880 --> 00:02:03.030
You'll get an integer there.

00:02:03.030 --> 00:02:04.380
So it's not 1.

00:02:04.380 --> 00:02:04.740
2.

00:02:04.740 --> 00:02:07.250
100 is clearly divisible by 2.

00:02:07.250 --> 00:02:08.710
100 divided by 2 is 50.

00:02:08.710 --> 00:02:09.930
That's not it.

00:02:09.930 --> 00:02:11.180
3.

00:02:11.180 --> 00:02:12.380
100 divided by 3.

00:02:12.380 --> 00:02:13.900
That's 33.333.

00:02:13.900 --> 00:02:14.840
That's not an integer.

00:02:14.840 --> 00:02:19.940
So choice 3 will not produce
an integer if it's selected

00:02:19.940 --> 00:02:21.635
for n, so we're at C.

00:02:21.635 --> 00:02:23.640
The answer is C.

00:02:23.640 --> 00:02:25.290
Next question.

00:02:25.290 --> 00:02:26.960
3.

00:02:26.960 --> 00:02:30.580
Rectangular floors x and
y have equal area.

00:02:30.580 --> 00:02:34.520
If floor x is 12 by 18--
let me draw that.

00:02:34.520 --> 00:02:36.630
This is floor x.

00:02:36.630 --> 00:02:41.840
They say it's 12 by 18.

00:02:41.840 --> 00:02:46.360
And floor y is 9 feet wide.

00:02:46.360 --> 00:02:48.560
What is the length of
floor y in feet?

00:02:48.560 --> 00:02:50.330
OK, I didn't have to
draw this, I think.

00:02:54.600 --> 00:02:57.810
So floor y is 9 feet wide.

00:03:01.130 --> 00:03:03.250
So they're saying it has the
same area, so essentially

00:03:03.250 --> 00:03:05.660
they're saying that
9 times-- and they

00:03:05.660 --> 00:03:07.105
want to know its length.

00:03:07.105 --> 00:03:08.730
So let's call that l.

00:03:08.730 --> 00:03:14.890
So the area of floor y, which is
9l, is equal to the area of

00:03:14.890 --> 00:03:19.825
floor x, which is equal
to 18 soon. times 12.

00:03:19.825 --> 00:03:22.450
And I even multiply this out,
because I don't know off the

00:03:22.450 --> 00:03:24.960
top of my head what 18 times 12
is, but we can just divide

00:03:24.960 --> 00:03:28.090
both sides by 9, and we get l is
equal to-- let's divide the

00:03:28.090 --> 00:03:28.960
18 by the 9.

00:03:28.960 --> 00:03:32.045
2 times 12, which
is equal to 24.

00:03:32.045 --> 00:03:35.460
And that's choice E.

00:03:35.460 --> 00:03:36.710
Next problem.

00:03:39.200 --> 00:03:41.360
Problem 4.

00:03:41.360 --> 00:03:44.390
A case contains c cartons.

00:03:44.390 --> 00:03:52.410
Each carton contains b boxes and
each box contains c-- OK,

00:03:52.410 --> 00:03:53.970
so c cartons.

00:03:53.970 --> 00:03:57.715
OK, case is equal
to c cartons.

00:04:01.710 --> 00:04:06.845
Carton is equal to b boxes.

00:04:10.930 --> 00:04:22.210
And then they say a box is
equal to 100 paper clips.

00:04:22.210 --> 00:04:25.350
How many paper clips are
contained in 2 cases?

00:04:25.350 --> 00:04:32.620
So we could say 2 cases is equal
to 2c cartons, right?

00:04:38.540 --> 00:04:41.640
So each carton has
how many boxes?

00:04:41.640 --> 00:04:43.830
Has b boxes, right?

00:04:43.830 --> 00:04:49.480
So this is going to be
equal to 2 times c.

00:04:49.480 --> 00:04:49.700
Right?

00:04:49.700 --> 00:04:52.150
That's how many cartons, and
each carton has b boxes.

00:04:52.150 --> 00:04:55.260
So it's going to be equal
to 2cb boxes.

00:04:55.260 --> 00:04:58.450
And then each of these boxes
is going to have 100 paper

00:04:58.450 --> 00:05:00.650
clips, so times 100.

00:05:00.650 --> 00:05:08.450
So that is equal to
200cb paper clips.

00:05:08.450 --> 00:05:09.630
And that is choice C.

00:05:09.630 --> 00:05:12.770
They wrote bc instead of cb,
but that's the same thing.

00:05:12.770 --> 00:05:16.500
So that is choice C.

00:05:16.500 --> 00:05:18.460
Next question.

00:05:18.460 --> 00:05:21.590
Question 5.

00:05:21.590 --> 00:05:25.790
The sum of prime numbers that
are greater than 60, but less

00:05:25.790 --> 00:05:27.640
than 70 is?

00:05:27.640 --> 00:05:28.510
So let's just think of them.

00:05:28.510 --> 00:05:30.590
60 is not prime so that
doesn't work.

00:05:30.590 --> 00:05:34.290
61 as far as I can
tell is prime.

00:05:34.290 --> 00:05:34.740
Right?

00:05:34.740 --> 00:05:36.460
I can't think of any numbers
that go into it, although

00:05:36.460 --> 00:05:37.840
maybe I'm missing a few.

00:05:37.840 --> 00:05:38.900
62 isn't prime.

00:05:38.900 --> 00:05:39.700
That's even.

00:05:39.700 --> 00:05:43.930
63 is 9 times 7.

00:05:43.930 --> 00:05:44.660
That's not prime.

00:05:44.660 --> 00:05:46.040
64 is 8 times 8.

00:05:46.040 --> 00:05:47.050
65.

00:05:47.050 --> 00:05:48.280
That's not prime,
divisible by 5.

00:05:48.280 --> 00:05:48.910
66?

00:05:48.910 --> 00:05:49.810
Nope.

00:05:49.810 --> 00:05:50.860
67.

00:05:50.860 --> 00:05:56.650
Is 67 prime?

00:05:56.650 --> 00:05:57.810
Let's see, 67.

00:05:57.810 --> 00:05:59.440
I think it is.

00:05:59.440 --> 00:06:01.490
I can't think of any numbers
that go into it.

00:06:01.490 --> 00:06:02.560
68 is not prime.

00:06:02.560 --> 00:06:03.090
It's even.

00:06:03.090 --> 00:06:05.540
69 is divisible by 3.

00:06:05.540 --> 00:06:07.170
And 70 is clearly not prime.

00:06:07.170 --> 00:06:10.020
So if I'm right, these are
the two prime numbers.

00:06:10.020 --> 00:06:12.030
Let me make sure 61
is not divisible.

00:06:12.030 --> 00:06:14.430
It's not divisible by 3.

00:06:14.430 --> 00:06:15.890
It's not divisible by 7.

00:06:15.890 --> 00:06:18.400
Yes, 61.

00:06:18.400 --> 00:06:22.950
17 times 3 is 51.

00:06:22.950 --> 00:06:23.780
Yes.

00:06:23.780 --> 00:06:25.620
I can't think of anything.

00:06:25.620 --> 00:06:28.340
So if we add these two numbers
up, I get 128.

00:06:28.340 --> 00:06:29.250
So choice B.

00:06:29.250 --> 00:06:31.300
I hope that's right.

00:06:31.300 --> 00:06:33.970
Next question.

00:06:33.970 --> 00:06:35.900
Question 6. you

00:06:35.900 --> 00:06:39.310
A rainstorm increased the amount
of water stored in

00:06:39.310 --> 00:06:44.840
state J reservoirs from
124 billion gallons

00:06:44.840 --> 00:06:48.500
to 138 billion gallons.

00:06:48.500 --> 00:06:51.480
If the storm increased the
amount of water in the

00:06:51.480 --> 00:07:02.980
reservoirs to 82% of total
capacity, approximately how

00:07:02.980 --> 00:07:07.160
many billion gallons of water
were the reservoirs short of

00:07:07.160 --> 00:07:11.090
total capacity prior
to the storm?

00:07:11.090 --> 00:07:13.490
So, let's see.

00:07:13.490 --> 00:07:16.610
How many billions prior
to the storm.

00:07:16.610 --> 00:07:18.940
So this is 82% of
total capacity.

00:07:22.060 --> 00:07:25.820
So capacity is going
to be equal to 138

00:07:25.820 --> 00:07:29.160
divided by 0.82, right?

00:07:29.160 --> 00:07:30.510
Well, maybe I skipped a step.

00:07:30.510 --> 00:07:31.390
Let me write that.

00:07:31.390 --> 00:07:35.810
82% of total capacity
is equal to 138.

00:07:35.810 --> 00:07:38.970
So you divide both sides by
82%, or 0.82, and you get

00:07:38.970 --> 00:07:46.292
capacity is equal to
138/0.82, right?

00:07:46.292 --> 00:07:50.770
And then they want to know how
many billions of gallons of

00:07:50.770 --> 00:07:53.420
water were the reservoirs short
of total capacity prior

00:07:53.420 --> 00:07:54.090
to the storm.

00:07:54.090 --> 00:07:55.650
So it's going to be this
number-- this is total

00:07:55.650 --> 00:08:01.620
capacity-- minus what they were
prior to the storm, 124.

00:08:01.620 --> 00:08:04.200
So we just have to do a little
bit of mathematics.

00:08:04.200 --> 00:08:06.120
I don't know if they allow you
to use a calculator, but I

00:08:06.120 --> 00:08:07.690
think we can do this
on our own.

00:08:07.690 --> 00:08:12.550
0.82 goes into 138.

00:08:12.550 --> 00:08:18.410
And we could take this decimal
point two over, so we can move

00:08:18.410 --> 00:08:21.340
this decimal point
two to the right.

00:08:21.340 --> 00:08:22.410
So we get that there.

00:08:22.410 --> 00:08:26.330
So it becomes 82 goes into
13,800 how many times.

00:08:26.330 --> 00:08:29.930
So 82 goes into 138 1 time.

00:08:29.930 --> 00:08:31.080
We get 6.

00:08:31.080 --> 00:08:33.230
13 minus 8 is 56.

00:08:33.230 --> 00:08:35.429
560.

00:08:35.429 --> 00:08:38.490
82 goes into 560--
Well, let's see.

00:08:38.490 --> 00:08:45.610
80 goes into 56 6 times.

00:08:45.610 --> 00:08:49.780
6 times 82 is 12, plus 1.

00:08:49.780 --> 00:08:51.100
6 times 8 is 48.

00:08:51.100 --> 00:08:53.560
49.

00:08:53.560 --> 00:08:55.890
And then we're left
with, let's see.

00:08:55.890 --> 00:08:57.751
What is that?

00:08:57.751 --> 00:09:00.040
This becomes a 5.

00:09:00.040 --> 00:09:02.230
This becomes 15.

00:09:02.230 --> 00:09:06.720
So we're left with 68.

00:09:06.720 --> 00:09:08.100
680.

00:09:08.100 --> 00:09:15.980
82 goes into 680 8 times.

00:09:15.980 --> 00:09:18.480
8 times 2 is 16.

00:09:18.480 --> 00:09:20.110
8 times 8 is 64.

00:09:20.110 --> 00:09:21.940
65.

00:09:21.940 --> 00:09:24.720
And you're left with, I don't
know, what is this?

00:09:24.720 --> 00:09:25.880
24.

00:09:25.880 --> 00:09:26.810
240.

00:09:26.810 --> 00:09:28.720
So after the decimal it keeps
going, but the total capacity

00:09:28.720 --> 00:09:30.390
is about 168.

00:09:30.390 --> 00:09:31.580
So how short were they?

00:09:31.580 --> 00:09:34.830
168 minus 124.

00:09:34.830 --> 00:09:39.040
So 68 minus 24 is 44 gallons.

00:09:39.040 --> 00:09:42.030
And that's choice E.

00:09:42.030 --> 00:09:43.765
They give you a little bit of
hairy decimal problems. I

00:09:43.765 --> 00:09:45.970
don't know if calculators
are allowed, but we

00:09:45.970 --> 00:09:47.280
did it without one.

00:09:47.280 --> 00:09:48.730
Problem 7.

00:09:48.730 --> 00:09:49.960
Actually, I'm almost of time.

00:09:49.960 --> 00:09:51.320
I'll continue this in
the next video.

00:09:51.320 --> 00:09:52.570
See


GMAT: Math 5

WEBVTT
Kind: captions
Language: en

00:00:00.940 --> 00:00:02.300
We're on problem 24.

00:00:02.300 --> 00:00:05.180
A rope 40 feet long is
cut into two pieces.

00:00:05.180 --> 00:00:06.430
Let's draw that.

00:00:10.050 --> 00:00:11.520
Let's say that's where
I cut them.

00:00:11.520 --> 00:00:15.100
If one piece is 18 feet longer
than the other, what is the

00:00:15.100 --> 00:00:16.790
length in feet of the
shorter piece?

00:00:16.790 --> 00:00:18.630
So let's say this is
the shorter piece.

00:00:18.630 --> 00:00:20.283
This is the longer piece.

00:00:20.283 --> 00:00:25.220
x plus 18.

00:00:25.220 --> 00:00:27.030
And they also tell us that both
pieces combined-- it's a

00:00:27.030 --> 00:00:29.490
40-foot long rope, so if I add
these together it should be

00:00:29.490 --> 00:00:30.620
equal to 40.

00:00:30.620 --> 00:00:35.256
So x plus x, plus 18
is equal to 40.

00:00:35.256 --> 00:00:41.150
x plus x is equal to 2x,
plus 18 is equal to 40.

00:00:41.150 --> 00:00:44.320
And then I get 2x is equal to--
subtract 18 from both

00:00:44.320 --> 00:00:45.240
sides, that's what?

00:00:45.240 --> 00:00:46.480
22.

00:00:46.480 --> 00:00:49.680
x is equal to 11.

00:00:49.680 --> 00:00:50.350
Next problem.

00:00:50.350 --> 00:00:51.940
Let me switch colors.

00:00:51.940 --> 00:00:56.620
25.

00:00:56.620 --> 00:00:58.570
The Earth travels around
the sun at a speed of

00:00:58.570 --> 00:01:05.676
approximately 18.5
miles per second.

00:01:10.530 --> 00:01:13.470
This approximate speed is
how many miles per hour?

00:01:13.470 --> 00:01:15.470
So how many seconds are
there in a mile?

00:01:15.470 --> 00:01:20.150
So you have 60 seconds
per minute.

00:01:20.150 --> 00:01:25.240
And then you have times
60 minutes per hour.

00:01:25.240 --> 00:01:28.040
So you get 60 times
60 is 3,600.

00:01:28.040 --> 00:01:29.220
And the units work out, too.

00:01:29.220 --> 00:01:30.640
Minutes in the denominator.

00:01:30.640 --> 00:01:32.140
Minutes in the numerator.

00:01:32.140 --> 00:01:36.120
So you get 3,600 seconds
per hour.

00:01:36.120 --> 00:01:40.050
So 18.5 miles per second, you're
going to go 3,600 times

00:01:40.050 --> 00:01:40.960
as far in an hour.

00:01:40.960 --> 00:01:48.030
So let's multiply that times
3,600 seconds per hour.

00:01:48.030 --> 00:01:50.090
And you'll get whatever
this number is.

00:01:50.090 --> 00:01:51.050
So let's multiply it out.

00:01:51.050 --> 00:01:53.130
18.5.

00:01:53.130 --> 00:01:57.170
I'm going to multiply it times
36 and then add two 0's later.

00:01:57.170 --> 00:02:00.020
6 times 5 is 30.

00:02:00.020 --> 00:02:04.700
6 times 8 is 48, plus 3 is 51.

00:02:04.700 --> 00:02:08.580
6 times 1 is 6, plus 5 is 11.

00:02:08.580 --> 00:02:12.400
3 times 5 is 15.

00:02:12.400 --> 00:02:17.060
3 times 8 is 24, plus 1 is 25.

00:02:17.060 --> 00:02:20.660
3 times 1 is 3, plus 2 is 5.

00:02:20.660 --> 00:02:25.120
And so you get a 0,
a 6, a 6, and a 6.

00:02:25.120 --> 00:02:27.530
And then I have one number
behind the decimal point.

00:02:27.530 --> 00:02:32.580
So 18.5 times 36 is 666.

00:02:32.580 --> 00:02:34.990
But I'm multiplying it not
by 36 but by 3,600.

00:02:34.990 --> 00:02:39.840
So 18.5 times 3,600 is going to
be equal to this times 100.

00:02:39.840 --> 00:02:43.500
So 66,600.

00:02:43.500 --> 00:02:44.520
And the units work out.

00:02:44.520 --> 00:02:45.640
Second in the denominator.

00:02:45.640 --> 00:02:46.820
Second in the numerator.

00:02:46.820 --> 00:02:50.060
Miles per hour.

00:02:50.060 --> 00:02:50.990
And that's choice D.

00:02:50.990 --> 00:02:52.915
And they didn't even let you
approximate it, because choice

00:02:52.915 --> 00:02:53.880
C is really close.

00:02:53.880 --> 00:02:55.960
You really have to, as far as
I can tell, go through the

00:02:55.960 --> 00:02:57.840
multiplication.

00:02:57.840 --> 00:02:59.190
Next problem.

00:02:59.190 --> 00:03:02.780
26.

00:03:02.780 --> 00:03:08.060
If the quotient a/b is
positive-- that's what they're

00:03:08.060 --> 00:03:11.490
telling us-- which of the
following must be true?

00:03:11.490 --> 00:03:15.140
So if a/b is positive, that
essentially tells us that a

00:03:15.140 --> 00:03:17.290
and b have to have the
same sign, right?

00:03:17.290 --> 00:03:18.970
The only way you can get a
positive number when you

00:03:18.970 --> 00:03:23.740
divide two numbers is if they're
both positive, or

00:03:23.740 --> 00:03:26.040
they're both negative.

00:03:26.040 --> 00:03:28.420
If they were different signs--
if one was positive and one

00:03:28.420 --> 00:03:29.810
was negative, or one was
negative and one was

00:03:29.810 --> 00:03:31.820
positive-- then this would
be a negative number.

00:03:31.820 --> 00:03:34.810
So this tells us that they're
the same sign.

00:03:34.810 --> 00:03:41.700
So statement A, choice A, tells
us a is greater than 0.

00:03:41.700 --> 00:03:43.190
No, this doesn't have
to be true.

00:03:43.190 --> 00:03:45.970
They both could be
less than 0.

00:03:45.970 --> 00:03:47.700
B tells us that b is
greater than 0.

00:03:47.700 --> 00:03:49.030
Once again, this isn't
necessarily true.

00:03:49.030 --> 00:03:52.340
They both could be less than 0
and this would still be true.

00:03:52.340 --> 00:03:54.380
Choice C.

00:03:54.380 --> 00:03:56.930
ab is greater than 0.

00:03:56.930 --> 00:03:58.200
Well, think about it.

00:03:58.200 --> 00:04:02.200
This implies that both a and b
have to have the same sign.

00:04:02.200 --> 00:04:05.140
If a and b have the same sign
when I multiply them, I'm

00:04:05.140 --> 00:04:07.770
still going to get a number
bigger than 0, right?

00:04:07.770 --> 00:04:09.950
A positive times a positive
is a positive.

00:04:09.950 --> 00:04:11.680
A negative times a negative
is a positive.

00:04:11.680 --> 00:04:15.100
So it's choice C.

00:04:15.100 --> 00:04:16.630
Problem 27.

00:04:16.630 --> 00:04:21.459
And I saw this coming, so I
drew this ahead of time.

00:04:21.459 --> 00:04:22.730
Actually, no I didn't.

00:04:22.730 --> 00:04:26.680
Well, I thought I had drawn
it ahead of time.

00:04:26.680 --> 00:04:29.370
Let me actually open it up.

00:04:29.370 --> 00:04:33.010
I thought I had drawn it.

00:04:33.010 --> 00:04:34.240
Oh, well, it must have
gotten erased.

00:04:34.240 --> 00:04:37.270
Well, let's just do it
in real time, then.

00:04:37.270 --> 00:04:39.830
So it says, the dots on the
graph above indicate the

00:04:39.830 --> 00:04:42.560
weights and fuel efficiency
ratings for 20 cars.

00:04:42.560 --> 00:04:49.250
How many of the cars weigh more
than 2,500 pounds-- so

00:04:49.250 --> 00:04:57.510
weight is more than 2,500--
and also get more than 25

00:04:57.510 --> 00:04:58.470
miles per gallon?

00:04:58.470 --> 00:05:04.510
So fuel efficiency is more
than 22 miles per gallon.

00:05:04.510 --> 00:05:08.120
And notice, they said more than
22, not 22 miles or more.

00:05:08.120 --> 00:05:13.270
And they said more than 2,500,
not 2,500 pounds or more.

00:05:13.270 --> 00:05:17.840
Let me just draw the part of the
graph that seems relevant.

00:05:17.840 --> 00:05:25.160
So if that's the weight axis--
so they have a couple at 25,

00:05:25.160 --> 00:05:29.980
26, 27, 28, 29, 30.

00:05:29.980 --> 00:05:35.500
And then, we want to
know above 22.

00:05:35.500 --> 00:05:38.270
So let me actually
draw all of it.

00:05:38.270 --> 00:05:40.360
So that's 25.

00:05:40.360 --> 00:05:42.050
I'm only drawing part of the
graph because I don't want to

00:05:42.050 --> 00:05:42.900
go through the exercise.

00:05:42.900 --> 00:05:44.530
Because I actually already
did it and I can't find

00:05:44.530 --> 00:05:45.640
it, all of a sudden.

00:05:45.640 --> 00:05:48.550
But I don't want to stop
recording this video.

00:05:48.550 --> 00:05:50.050
So 20.

00:05:50.050 --> 00:05:52.040
This is 22.

00:05:52.040 --> 00:05:52.990
This is 24.

00:05:52.990 --> 00:05:58.250
They don't label the 22
on their drawing.

00:05:58.250 --> 00:06:03.290
This is 26.

00:06:03.290 --> 00:06:06.480
This is 28.

00:06:06.480 --> 00:06:08.920
And so they want to know
everything that weighs more

00:06:08.920 --> 00:06:10.200
than 2,500 pounds.

00:06:10.200 --> 00:06:13.680
So everything to the
right of that.

00:06:13.680 --> 00:06:18.240
Because all of these tend to
be on integer numbers.

00:06:18.240 --> 00:06:19.620
None of them are in between.

00:06:19.620 --> 00:06:24.540
And they say, and get more
than 22 miles per gallon.

00:06:24.540 --> 00:06:27.350
So let me draw all of the
ones that apply there.

00:06:27.350 --> 00:06:33.060
So let's see, at 2,600 pounds,
there's two, at 24 and 26

00:06:33.060 --> 00:06:34.310
miles per gallon.

00:06:38.430 --> 00:06:41.735
At 2,600 there's two
points right there.

00:06:41.735 --> 00:06:46.190
At 2,700 there are
three points.

00:06:46.190 --> 00:06:54.920
1, 2, but the other one falls
on the 22 miles per gallon,

00:06:54.920 --> 00:06:57.080
but we're talking about
greater than that.

00:06:57.080 --> 00:07:01.573
And then-- let's see, that's 26,
27-- 28 has one down here

00:07:01.573 --> 00:07:03.040
and one up here.

00:07:03.040 --> 00:07:05.610
When I say 28, I mean
2,800 pounds.

00:07:05.610 --> 00:07:07.470
I'm just trying to
draw it for you.

00:07:07.470 --> 00:07:08.690
And then the rest of them.

00:07:08.690 --> 00:07:10.940
There's two here and
there's one here.

00:07:10.940 --> 00:07:12.570
But all we care about
is the ones in this.

00:07:12.570 --> 00:07:13.700
There's a bunch more
over here.

00:07:13.700 --> 00:07:16.580
I could draw them real fast, if
you want me to, just so you

00:07:16.580 --> 00:07:19.046
can visualize the graph.

00:07:19.046 --> 00:07:21.140
So it looks something
like that.

00:07:21.140 --> 00:07:25.590
And then there's
one more here.

00:07:25.590 --> 00:07:27.033
But all we care about
is this range, and

00:07:27.033 --> 00:07:28.480
there's 1, 2, 3, 4, 5.

00:07:28.480 --> 00:07:29.565
Five of those.

00:07:29.565 --> 00:07:31.190
So the answer is B.

00:07:31.190 --> 00:07:35.190
A lot of work for a fairly
straightforward problem.

00:07:35.190 --> 00:07:37.430
Let me get some clean space.

00:07:37.430 --> 00:07:41.230
Problem 28.

00:07:41.230 --> 00:07:47.150
How many minutes does it take
John to type y words if he

00:07:47.150 --> 00:07:52.960
types at a rate of x
words per minute?

00:07:52.960 --> 00:07:54.850
Now, this is a fairly
straightforward thing, but it

00:07:54.850 --> 00:07:55.450
can get confusing.

00:07:55.450 --> 00:07:56.690
Do I divide x by y?

00:07:56.690 --> 00:07:57.480
Y by x?

00:07:57.480 --> 00:08:00.170
I think a lot of times this
becomes a lot simpler if you

00:08:00.170 --> 00:08:01.640
just pick numbers.

00:08:01.640 --> 00:08:05.640
So if we just phrased it, how
long does it take him to type

00:08:05.640 --> 00:08:11.360
100 words if he can type,
I don't know,

00:08:11.360 --> 00:08:14.870
50 words per minute?

00:08:14.870 --> 00:08:16.820
Now your brain would say, oh,
if I can do 50 words per

00:08:16.820 --> 00:08:19.280
minute, it's going to take me
2 minutes to do 100 words.

00:08:19.280 --> 00:08:20.680
And how did you get 2 minutes?

00:08:20.680 --> 00:08:24.290
You said 100 divided by 50.

00:08:24.290 --> 00:08:28.510
So if you need to type y words
and you can type at x words

00:08:28.510 --> 00:08:32.370
per minute, the answer
is y divided by x.

00:08:34.895 --> 00:08:38.350
Let's see, that's not
one of the choices.

00:08:38.350 --> 00:08:40.590
But I think they've made a
mistake, because this is a

00:08:40.590 --> 00:08:43.179
simple enough problem that
I have conviction.

00:08:43.179 --> 00:08:45.330
And if you look at the choices,
choice A and choice

00:08:45.330 --> 00:08:47.820
B, at least in the book I have,
they wrote x/y, so I

00:08:47.820 --> 00:08:50.740
think that's a typo.

00:08:50.740 --> 00:08:53.590
One of those probably should
have read y/x.

00:08:53.590 --> 00:08:54.720
So I'm going to stick
by my answer.

00:08:54.720 --> 00:08:56.800
I think this was another
mistake in the book.

00:08:56.800 --> 00:08:57.900
y/x.

00:08:57.900 --> 00:08:59.740
You might want to check the
answer key, just to make sure,

00:08:59.740 --> 00:09:06.270
but I have no doubt in my
conviction on this one.

00:09:06.270 --> 00:09:08.520
Let me see, do I have time
for the next one?

00:09:08.520 --> 00:09:09.760
Well, sure.

00:09:09.760 --> 00:09:10.990
Problem 29.

00:09:10.990 --> 00:09:12.240
I'm running out of space.

00:09:14.560 --> 00:09:17.610
The square root-- this is just
to make sure you know how to

00:09:17.610 --> 00:09:21.990
do square roots-- of 16 times
20, in order of operations,

00:09:21.990 --> 00:09:26.290
plus 8 times 32.

00:09:26.290 --> 00:09:30.060
So there's a bunch of ways we
could think about this, but

00:09:30.060 --> 00:09:31.760
the easiest way, instead
of doing all of the

00:09:31.760 --> 00:09:34.440
multiplication, let's see if we
can factor 16 out of both

00:09:34.440 --> 00:09:36.830
of these numbers.

00:09:36.830 --> 00:09:38.230
You could multiple them out
and try to figure out the

00:09:38.230 --> 00:09:40.360
square root, but it'll
take you a long time.

00:09:40.360 --> 00:09:46.360
So if we rewrite this as
16 times 20 plus, what?

00:09:46.360 --> 00:09:51.950
This could also be written
if we took-- 32

00:09:51.950 --> 00:09:56.780
is 16 times 2, right?

00:09:56.780 --> 00:10:01.980
So 8 times 32 is the same thing
as 8 times 16 times 2,

00:10:01.980 --> 00:10:05.720
which is the same thing
as 16 times 16.

00:10:05.720 --> 00:10:07.140
So we could have rewritten
this as 8 times 32

00:10:07.140 --> 00:10:09.110
is 16, times 16.

00:10:09.110 --> 00:10:11.580
So if we're factoring
a 16 out, that's 16

00:10:11.580 --> 00:10:14.550
times 20, plus 16.

00:10:14.550 --> 00:10:17.380
If you were to just multiply
this out it would be 16 times

00:10:17.380 --> 00:10:21.000
20, plus 16 times 16, which is
the same thing as 8 times 32.

00:10:21.000 --> 00:10:22.060
And I'm doing all of this.

00:10:22.060 --> 00:10:24.830
You could just do the math
yourself, but it takes a lot

00:10:24.830 --> 00:10:26.470
of time if you don't
have a calculator.

00:10:26.470 --> 00:10:28.390
Well now, you can say, well,
this is the same thing as the

00:10:28.390 --> 00:10:35.490
square root of 16 times the
square root of 20 plus 16.

00:10:35.490 --> 00:10:38.480
Well, this is plus or minus 4,
although I don't think they're

00:10:38.480 --> 00:10:41.120
going to make us worry about
the negative square root.

00:10:41.120 --> 00:10:42.290
So let's just say it's 4.

00:10:42.290 --> 00:10:44.410
Looking at the choices--yeah,
everything 's positive.

00:10:44.410 --> 00:10:46.180
So it's 4 times.

00:10:46.180 --> 00:10:46.880
And then, what's this?

00:10:46.880 --> 00:10:49.190
The square root of 36.

00:10:49.190 --> 00:10:54.860
So that equals 4 times 6,
which is equal to 24.

00:10:54.860 --> 00:10:56.880
And that's choice B.

00:10:56.880 --> 00:10:58.740
Se you in the next video.