GMAT: Math 14

WEBVTT
Kind: captions
Language: en

00:00:02.020 --> 00:00:05.600
So we're at problem 76.

00:00:05.600 --> 00:00:08.119
Which of the following ratios
is most nearly equal to the

00:00:08.119 --> 00:00:13.920
ratio of 1 plus the square
root of 5 to 2.

00:00:13.920 --> 00:00:16.079
And then they give us a bunch of
integer choices, so this is

00:00:16.079 --> 00:00:19.290
really just a problem of
approximating what the square

00:00:19.290 --> 00:00:20.970
root of 5 is.

00:00:20.970 --> 00:00:23.370
So let's think about
this a little bit.

00:00:23.370 --> 00:00:29.100
So 2 is equal to the square
root of 4, or 2 squared is

00:00:29.100 --> 00:00:30.510
equal to 4.

00:00:30.510 --> 00:00:33.750
3 is equal to the square
root of 9.

00:00:33.750 --> 00:00:38.500
So the square root of 5 is going
to be a lot closer to 2.

00:00:38.500 --> 00:00:40.410
What's 2.1 squared?

00:00:40.410 --> 00:00:45.280
2.1 times 2.1 you get 21.

00:00:45.280 --> 00:00:48.570
0, 2 times 21 is 42.

00:00:48.570 --> 00:00:54.100
So then you get, 4.41
So 2.1 is equal to

00:00:54.100 --> 00:01:01.180
square root of 4.41.

00:01:01.180 --> 00:01:09.950
2.2 times 2.2, 2 is 44, 0, 44,
this gets pretty close to 5.

00:01:09.950 --> 00:01:11.550
8, 4.

00:01:11.550 --> 00:01:14.430
So 2.2 is I think about as close
as we're going to get.

00:01:17.780 --> 00:01:20.920
If we approximate the square
root of 5 is 2.2, and this is

00:01:20.920 --> 00:01:22.640
just an approximation, we just
have to figure out which

00:01:22.640 --> 00:01:30.990
choice is closest, 1 plus 2.2
over 2, that's equal to 3.2

00:01:30.990 --> 00:01:35.210
over 2, and that's not one of
the choices, because this

00:01:35.210 --> 00:01:37.200
really isn't an integer
choice.

00:01:37.200 --> 00:01:39.160
But let's see if I can
just express this,

00:01:39.160 --> 00:01:44.405
this is equal to 1.6.

00:01:44.405 --> 00:01:45.850
It'd give you 1.6:1.

00:01:45.850 --> 00:01:48.200
So we just have to find which
of the choices are roughly

00:01:48.200 --> 00:01:49.450
equal to 1.6:1.

00:01:51.190 --> 00:01:56.640
So choice A, 8:5.

00:01:59.260 --> 00:01:59.760
Well what is that?

00:01:59.760 --> 00:02:03.230
That's 1 and 3/5.

00:02:03.230 --> 00:02:05.920
Well that's exactly 1.6.

00:02:05.920 --> 00:02:07.630
So that's the choice I'm
going to go with.

00:02:07.630 --> 00:02:08.300
Let me look at the other ones.

00:02:08.300 --> 00:02:14.490
6:5 is going to be a lot closer
to 1, 6:5 is 1.2, 5:4

00:02:14.490 --> 00:02:16.900
is 1.25, 2:1 is 2.

00:02:16.900 --> 00:02:19.530
So choice A is the
best choice.

00:02:19.530 --> 00:02:21.990
Next question.

00:02:21.990 --> 00:02:25.340
Problem 77.

00:02:25.340 --> 00:02:28.900
Let me scroll down
a little bit.

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7 over 1/5 plus 5 over 1/7 is
equal to-- 7 divided by 1/5 is

00:02:39.470 --> 00:02:44.240
equal to 7 times 5, plus
5 divided by 1/7 is

00:02:44.240 --> 00:02:46.840
equal to 5 times 7.

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When you divide by a fraction,
it's the same thing as

00:02:48.950 --> 00:02:50.560
multiplying by its reciprocal.

00:02:50.560 --> 00:02:52.370
So 5 times 7.

00:02:52.370 --> 00:02:59.370
So this is equal to 35 plus 35,
which is equal to 70, and

00:02:59.370 --> 00:03:02.730
that's choice D.

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78.

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From January 1, 1991, to January
1, 1993, the number of

00:03:10.930 --> 00:03:14.030
people enrolled in health
maintenance organizations

00:03:14.030 --> 00:03:21.220
increased by 15%.

00:03:21.220 --> 00:03:27.980
The enrollment on January
1, 1993 was 45 million.

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How many million people, to
the nearest million, were

00:03:30.070 --> 00:03:32.310
rolled in health maintenance
organizations

00:03:32.310 --> 00:03:34.630
on January 1, 1991?

00:03:34.630 --> 00:03:36.730
OK, so let's just call this x.

00:03:36.730 --> 00:03:38.140
That's what they want to know,
they want to know how many

00:03:38.140 --> 00:03:40.680
million people were
enrolled in 1991.

00:03:40.680 --> 00:03:46.070
So when x increased by 15%,
you got to 45 million.

00:03:46.070 --> 00:03:49.410
So remember, not 15% of
x is 45 million, x

00:03:49.410 --> 00:03:51.380
increases by 15%.

00:03:51.380 --> 00:03:54.630
So let me write an extra step
that I normally don't do.

00:03:54.630 --> 00:04:00.080
So you could view it as
x plus 15% x, right?

00:04:00.080 --> 00:04:03.520
This is x, and then you're
increasing it by 15% of x, is

00:04:03.520 --> 00:04:06.300
going to be equal
to 45 million.

00:04:06.300 --> 00:04:12.490
And then this is 1x plus 0.15x,
so that's 1.15x is

00:04:12.490 --> 00:04:14.240
equal to 45 million.

00:04:14.240 --> 00:04:15.970
And you could also just go
straight to this step.

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In fact, you usually can once
you get used to it.

00:04:17.480 --> 00:04:20.130
You can say, 15% increase,
that's the same thing as

00:04:20.130 --> 00:04:22.770
multiplying by 1.15.

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So x is equal to 45 divided by
1.15, and we're going to have

00:04:31.820 --> 00:04:35.230
to do a little bit of division
to figure this out.

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115 divided by 45, add a couple
of 0's So it's 1.15

00:04:44.510 --> 00:04:49.270
divide by 45, so that's the same
thing as 115, take the

00:04:49.270 --> 00:04:54.220
decimal place, go 2 to the
right, going to 4,500.

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115 goes into 450
how many times?

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Does it go into it 4 times?

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No, that'd be 460, so it
goes into it 3 times.

00:05:03.250 --> 00:05:09.820
3 times 115 is 345.

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This difference is 105,
bring down a 0.

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115 goes into 1,050
how many times?

00:05:21.440 --> 00:05:30.060
If I did 8, 800, I think it's 8
times, because 9 would be--

00:05:30.060 --> 00:05:35.040
actually 900 plus 90 plus 45,
actually it would be 9 times.

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9 times 5 is 45.

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9 times 1 is 9 plus 4 is 13.

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9 times 9 is 1-- I'm sorry,
is 9, plus 1 is 10.

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You have a remainder 15, bring
down the 0, that goes 1 time.

00:05:55.600 --> 00:05:57.610
So we already have the
decimal point.

00:05:57.610 --> 00:05:59.710
And all their choices
are in integers.

00:05:59.710 --> 00:06:04.310
So this is closest to B, 39.

00:06:04.310 --> 00:06:06.630
And I wanted to get that last
decimal point, because maybe

00:06:06.630 --> 00:06:08.850
that was 39.9, in which
case 40 would

00:06:08.850 --> 00:06:10.770
be the closest choice.

00:06:10.770 --> 00:06:13.480
Sometimes they get
tricky like that.

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Next question.

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79.

00:06:18.700 --> 00:06:35.120
R is the set of positive odd
integers less than 50.

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And S is equal to squares
of R, squares of the

00:06:43.730 --> 00:06:45.210
numbers in that set.

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How many elements does the

00:06:46.430 --> 00:06:51.190
intersection of R and S contain?

00:06:51.190 --> 00:06:54.930
OK, so we have to say,
positive odd

00:06:54.930 --> 00:06:56.160
editors less than 50.

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So we have to think, how many
positive odd integers less

00:06:59.480 --> 00:07:03.540
than 50 are squares of
other positive odd

00:07:03.540 --> 00:07:06.750
integers less than 50.

00:07:06.750 --> 00:07:09.330
It doesn't take a long time to
figure out all of the squares

00:07:09.330 --> 00:07:10.870
between 1 and 50.

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It's 1, 2, 4, 9, 16, 25,
they start increasing

00:07:19.950 --> 00:07:26.320
pretty fast, 36, 49.

00:07:26.320 --> 00:07:29.650
Now we know that they
have to be positive,

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these are all positive.

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We know they have to be odd,
because we're looking for

00:07:33.830 --> 00:07:37.690
things that are both squares
and they're in set R.

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They're squares, and they're
squares of other

00:07:39.380 --> 00:07:40.680
things in set R.

00:07:40.680 --> 00:07:42.620
So let's take out all
the even numbers.

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Can't be 36, can't be 2, can't
be 4, can't be 16.

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1 is 1 squared.

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So 1 is in set R, it's a
positive odd integer less than

00:08:00.160 --> 00:08:03.810
50, and it is a square of
another positive odd integer

00:08:03.810 --> 00:08:06.570
less than 50, a square
of itself.

00:08:06.570 --> 00:08:08.090
So 1 counts.

00:08:08.090 --> 00:08:10.460
9 is 3 squared.

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9 itself is a positive odd
integer less than 50, and it's

00:08:15.600 --> 00:08:19.350
also the square of 3, which is
another positive odd integer

00:08:19.350 --> 00:08:19.940
less than 50.

00:08:19.940 --> 00:08:21.900
So 9 counts.

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25, same logic.

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It's a positive odd integer less
than 50, it's the square

00:08:25.380 --> 00:08:27.360
of 5, which is the same.

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And 49, same thing.

00:08:28.850 --> 00:08:32.090
Square of 7, both 49 and
7 are positive odd

00:08:32.090 --> 00:08:33.610
integers less than 50.

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So I found four.

00:08:35.360 --> 00:08:36.610
So that's C.

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Question 80.

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A retail appliance store priced
a video recorder at 20%

00:08:50.640 --> 00:08:55.260
above the wholesale
cost of $200.

00:08:55.260 --> 00:08:58.090
We could just go, 20% above
200, that's going to

00:08:58.090 --> 00:09:01.520
be 1.2 times 200.

00:09:01.520 --> 00:09:04.820
If a store employee applied the
10% employee discount to

00:09:04.820 --> 00:09:07.500
the retail price to buy the
recorder, how much did the

00:09:07.500 --> 00:09:08.980
employee pay for the recorder?

00:09:08.980 --> 00:09:11.020
So this is the retail price.

00:09:11.020 --> 00:09:12.890
This was the wholesale price,
that's what the store bought

00:09:12.890 --> 00:09:16.010
it for, this is what a
non-employee would have to

00:09:16.010 --> 00:09:17.600
pay, 1.2 times 200.

00:09:17.600 --> 00:09:20.610
And then the employee
got a 10% discount.

00:09:20.610 --> 00:09:23.450
So essentially the
employee paid the

00:09:23.450 --> 00:09:25.330
retail price times 0.9.

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So what's 1.2 times 200?

00:09:32.290 --> 00:09:39.320
200 times 1.2.

00:09:39.320 --> 00:09:40.140
Let's just do it out.

00:09:40.140 --> 00:09:44.060
2 times 200 is 400.

00:09:44.060 --> 00:09:44.760
Add a zero.

00:09:44.760 --> 00:09:48.440
1 times 200 is 200.

00:09:48.440 --> 00:09:50.640
And we have one point behind the
decimal-- well let's add

00:09:50.640 --> 00:09:52.560
them up, you get 2400.

00:09:52.560 --> 00:09:56.720
We have one digit behind the
decimal, so it's 240.

00:09:56.720 --> 00:09:59.730
So the retail price is 240, and
we have to multiply that

00:09:59.730 --> 00:10:01.750
times 0.9 to figure out what
the employee paid.

00:10:01.750 --> 00:10:04.240
They got a 10% discount, which
is another way of saying they

00:10:04.240 --> 00:10:07.100
played 90% of the
retail price.

00:10:07.100 --> 00:10:11.320
So 240 times 0.9.

00:10:11.320 --> 00:10:15.750
9 times 0 is zero, 9 times
4 is 36, 9 times 2

00:10:15.750 --> 00:10:18.020
is 18 plus 3, 21.

00:10:18.020 --> 00:10:20.860
We have one number behind the
decimal point, so the employee

00:10:20.860 --> 00:10:25.090
paid $216, which is choice B.

00:10:25.090 --> 00:10:26.890
Now I'm out of time,
I'll continue

00:10:26.890 --> 00:10:28.690
this in the next video.


GMAT: Math 15

WEBVTT
Kind: captions
Language: en

00:00:01.170 --> 00:00:05.830
We're on problem 81.

00:00:05.830 --> 00:00:13.810
They give us this equation, y
is equal to 248 minus 398x.

00:00:13.810 --> 00:00:17.340
Which of the following values of
x gives the greatest value

00:00:17.340 --> 00:00:18.990
of y in the equation above?

00:00:22.590 --> 00:00:31.440
To get as large a possible y,
y is 248 minus this thing.

00:00:31.440 --> 00:00:33.860
So what we want to do is, since
we're subtracting this

00:00:33.860 --> 00:00:36.300
from 248, we want to
minimize this.

00:00:36.300 --> 00:00:37.890
As small as this can be.

00:00:37.890 --> 00:00:41.010
And even if we can make what
we're subtracting negative,

00:00:41.010 --> 00:00:43.450
that'd be awesome, because when
you subtract a negative,

00:00:43.450 --> 00:00:45.590
then that'll get us above 248.

00:00:45.590 --> 00:00:47.510
And actually, if we look at all
of the choices, they have

00:00:47.510 --> 00:00:49.670
one negative number there.

00:00:49.670 --> 00:00:52.350
You might say if we put
a 0 here, then y

00:00:52.350 --> 00:00:53.220
is going to be 248.

00:00:53.220 --> 00:00:57.270
But what if we put a negative
number in for x, they have as

00:00:57.270 --> 00:00:58.350
choice E, negative 1.

00:00:58.350 --> 00:01:00.060
What happens when we put
negative 1 there?

00:01:00.060 --> 00:01:05.900
Then y is equal to 248 minus
negative 1 times 398, so it's

00:01:05.900 --> 00:01:09.715
minus minus negative 398,
which is the same

00:01:09.715 --> 00:01:10.980
thing as plus 398.

00:01:10.980 --> 00:01:12.510
So that's actually the maximum
point, because we're

00:01:12.510 --> 00:01:14.180
subtracting a negative.

00:01:14.180 --> 00:01:16.830
That's even better than
subtracting 0, and it's way

00:01:16.830 --> 00:01:18.610
better than subtracting a
positive, if we're trying to

00:01:18.610 --> 00:01:19.930
maximize y.

00:01:19.930 --> 00:01:21.180
So the choice is E.

00:01:23.810 --> 00:01:26.140
82.

00:01:26.140 --> 00:01:32.630
Machine A produces bolts at a
uniform rate of 120 bolts

00:01:32.630 --> 00:01:37.130
every 40 seconds.

00:01:37.130 --> 00:01:40.230
So that's the same as-- 120
bolts every 40 seconds is the

00:01:40.230 --> 00:01:43.205
same thing as 3 bolts
per second.

00:01:46.270 --> 00:01:47.630
OK, that's A.

00:01:47.630 --> 00:01:49.820
Let me write that
down, that's A.

00:01:49.820 --> 00:01:53.680
Machine B produces bolts at a
uniform rate of, so this is B,

00:01:53.680 --> 00:01:59.020
of 120 bolts every 20 seconds.

00:01:59.020 --> 00:02:03.290
Well that's equal to
5 bolts per second.

00:02:03.290 --> 00:02:06.410
If the two machines run
simultaneously, how many

00:02:06.410 --> 00:02:08.330
seconds will it take for
them to produce a

00:02:08.330 --> 00:02:09.940
total of 200 bolts?

00:02:09.940 --> 00:02:11.450
So if you're running
simultaneously, what's your

00:02:11.450 --> 00:02:12.290
speed per second?

00:02:12.290 --> 00:02:14.350
This one's going to do 3 per
second, this one's going to do

00:02:14.350 --> 00:02:15.830
5 per second.

00:02:15.830 --> 00:02:19.030
So if they run simultaneously,
you're going to be producing 8

00:02:19.030 --> 00:02:20.390
per second, 3 plus 5.

00:02:20.390 --> 00:02:23.570
So 8 bolts per second is
their combined rate.

00:02:23.570 --> 00:02:26.180
And we want to know how
many seconds will it

00:02:26.180 --> 00:02:28.100
take to do 200 bolts.

00:02:28.100 --> 00:02:33.990
So we just take 200 bolts
divided by 8 seconds.

00:02:33.990 --> 00:02:37.370
Another way with distance,
distance is equal to rate

00:02:37.370 --> 00:02:41.110
times time, I guess you could
view this as production is

00:02:41.110 --> 00:02:43.700
equal to rate times time.

00:02:43.700 --> 00:02:46.610
Normally rate is how fast you're
moving per second, now

00:02:46.610 --> 00:02:48.860
it's how much you're producing
per second, so your total

00:02:48.860 --> 00:02:52.440
production is going to be your
rate times time, and then your

00:02:52.440 --> 00:02:53.790
time is going to be
the production

00:02:53.790 --> 00:02:54.780
divided by the rate.

00:02:54.780 --> 00:02:58.090
But sometimes when you think too
much in terms of formulas,

00:02:58.090 --> 00:02:58.970
you lose the intuition.

00:02:58.970 --> 00:03:02.720
But I just wanted to show you
that there is a formula for

00:03:02.720 --> 00:03:04.000
it, if you need one.

00:03:04.000 --> 00:03:06.440
But the easiest way to think
it, I have to produce 200

00:03:06.440 --> 00:03:10.320
bolts, if I said I produce
100 every second,

00:03:10.320 --> 00:03:11.610
it'll take me 2 seconds.

00:03:11.610 --> 00:03:14.030
So if I have to produce 8
every second, I take 200

00:03:14.030 --> 00:03:15.280
divided by 8.

00:03:17.500 --> 00:03:20.890
And I can even do the units, 200
bolts divided by 8 bolts

00:03:20.890 --> 00:03:22.530
per second.

00:03:22.530 --> 00:03:29.640
That's equal to 200 over 8 times
bolts times-- if this

00:03:29.640 --> 00:03:31.790
isn't the denominator, you just
inverse it when you go

00:03:31.790 --> 00:03:34.100
out-- seconds per bolt, the
bolts can't [UNINTELLIGIBLE].

00:03:34.100 --> 00:03:36.470
So you know you got the units
right, so to some degree that

00:03:36.470 --> 00:03:37.560
should give you conviction
that you

00:03:37.560 --> 00:03:38.730
got the formula right.

00:03:38.730 --> 00:03:41.310
And 200 divided by 8 is 25.

00:03:41.310 --> 00:03:43.440
So it's 25 seconds.

00:03:43.440 --> 00:03:46.070
It's choice B.

00:03:46.070 --> 00:03:52.310
Problem 83.

00:03:52.310 --> 00:04:00.285
What is the decimal equivalent
of 1/5 to the fifth power?

00:04:03.725 --> 00:04:04.770
So let's think about this.

00:04:04.770 --> 00:04:07.710
Let's write 1/5 as a decimal,
that's 0.2.

00:04:07.710 --> 00:04:12.110
So it's 0.2 to the 5th power.

00:04:12.110 --> 00:04:13.980
Let's just multiply it out.

00:04:13.980 --> 00:04:17.940
0.2 times 0.2 is
equal to what?

00:04:17.940 --> 00:04:20.200
2 times 2, and we have
two digits behind the

00:04:20.200 --> 00:04:23.000
decimal, so it's 0.04.

00:04:23.000 --> 00:04:24.870
And you multiply
that times 0.2.

00:04:28.950 --> 00:04:31.460
2 times 4 is 8, and now we have
three numbers behind the

00:04:31.460 --> 00:04:33.660
decimal point, that's
going to be equal to

00:04:33.660 --> 00:04:40.450
0.008 One, two, three.

00:04:40.450 --> 00:04:42.180
Three numbers behind
the decimal.

00:04:42.180 --> 00:04:43.820
So this is 2 to the third.

00:04:43.820 --> 00:04:47.650
And then 0.008 times 0.2,
let me write this is

00:04:47.650 --> 00:04:50.180
to the third power.

00:04:50.180 --> 00:04:53.340
That's equal to 2 times 8 is 16,
and then how many numbers

00:04:53.340 --> 00:04:55.090
do we have behind the
decimal point?

00:04:55.090 --> 00:04:57.390
One, two, three, four.

00:04:57.390 --> 00:05:02.110
So we're going to have point
one, two, three, four.

00:05:02.110 --> 00:05:03.840
So that's to the 4th power.

00:05:03.840 --> 00:05:10.460
We have one left, so 0.0016
times 0.2 is equal to,

00:05:10.460 --> 00:05:12.400
2 times 16 is 32.

00:05:12.400 --> 00:05:15.700
And now we have one, two, three,
four, five numbers

00:05:15.700 --> 00:05:16.660
behind the decimal point.

00:05:16.660 --> 00:05:21.930
So one, two, three,
four, five.

00:05:21.930 --> 00:05:25.375
That's the answer, and
that is choice A.

00:05:29.850 --> 00:05:31.970
Actually the easiest way to
think about it is, without

00:05:31.970 --> 00:05:34.280
even having to do this, you
could've said, what's 2 to the

00:05:34.280 --> 00:05:35.630
fifth power?

00:05:35.630 --> 00:05:38.740
2 to the fifth power is 32.

00:05:38.740 --> 00:05:40.360
And actually that alone, because
there's only one

00:05:40.360 --> 00:05:42.650
choice that even has a 32 behind
the decimal point.

00:05:42.650 --> 00:05:45.470
And you can say, every time I
take to a power, I'm adding

00:05:45.470 --> 00:05:48.100
one digit behind the decimal
point, so it's going to be 32,

00:05:48.100 --> 00:05:49.630
but it's going to have five
numbers behind the decimal

00:05:49.630 --> 00:05:53.870
point, so point one, two,
three, four, five.

00:05:53.870 --> 00:05:56.420
I did it the slow way.

00:05:56.420 --> 00:06:01.390
Next question, 84.

00:06:01.390 --> 00:06:08.240
90 minus 8 times 20-- I'll write
it the way they did-- 20

00:06:08.240 --> 00:06:12.265
divided by 4, all of
that over 1/2.

00:06:12.265 --> 00:06:14.420
This is just a fast
simplification problem.

00:06:14.420 --> 00:06:17.720
That becomes 90 minus-- what's
20 divided by 4?

00:06:17.720 --> 00:06:18.900
20 by 4 is 5.

00:06:18.900 --> 00:06:23.160
5 times 8 is 40, all
that over 1/2.

00:06:23.160 --> 00:06:29.030
That becomes 50 over 1/2, which
is the same thing as 50

00:06:29.030 --> 00:06:32.190
times 2 over 1, which
is equal to 100.

00:06:32.190 --> 00:06:33.470
That's choice C.

00:06:33.470 --> 00:06:36.090
That's just one you just have
to do quickly and not make a

00:06:36.090 --> 00:06:37.340
careless mistake.

00:06:40.410 --> 00:06:42.210
I did it quickly, I don't know
if I did a careless mistake.

00:06:42.210 --> 00:06:43.580
Let's see, 85.

00:06:43.580 --> 00:06:47.690
A dealer originally bought 100
identical batteries at a total

00:06:47.690 --> 00:06:49.460
cost of q dollars.

00:06:49.460 --> 00:06:53.750
So q is equal to
100 batteries.

00:06:53.750 --> 00:07:00.620
If each battery was sold at 50%
above the original cost,

00:07:00.620 --> 00:07:05.050
so b is the cost each battery
was sold at, so b is going to

00:07:05.050 --> 00:07:09.060
be 50% above the original cost.
So it's going to be 1.5

00:07:09.060 --> 00:07:12.610
times the original cost. This is
50% above the original cost

00:07:12.610 --> 00:07:13.570
per battery.

00:07:13.570 --> 00:07:18.600
Then in terms of q, for
how many dollars was

00:07:18.600 --> 00:07:21.090
each battery sold?

00:07:30.630 --> 00:07:33.600
A dealer originally bought 100
identical batteries at a total

00:07:33.600 --> 00:07:35.730
cost of q dollars.

00:07:35.730 --> 00:07:40.330
If each battery was sold--
oh I'm sorry.

00:07:40.330 --> 00:07:48.310
So this is the cost. So q is
equal to 100 times what the

00:07:48.310 --> 00:07:50.100
dealer paid for it.

00:07:50.100 --> 00:07:52.510
A dealer originally bought 100
identical batteries at the

00:07:52.510 --> 00:07:55.480
total cost of q dollars.

00:07:55.480 --> 00:07:59.750
If each battery was sold at 50%
above the original cost

00:07:59.750 --> 00:08:05.900
per battery, this is the
original cost, is equal to 1.5

00:08:05.900 --> 00:08:12.170
times the cost. In terms of q,
for how many dollars was each

00:08:12.170 --> 00:08:13.440
battery sold?

00:08:13.440 --> 00:08:16.740
So let's write q in terms of the
cost. So cost is equal to

00:08:16.740 --> 00:08:17.785
q divided by 100.

00:08:17.785 --> 00:08:20.380
Just divided both sides of
that equation by 100.

00:08:20.380 --> 00:08:23.600
And then we could just
substitute c, or the cost

00:08:23.600 --> 00:08:26.960
here, the selling price
is 150% of this.

00:08:26.960 --> 00:08:31.000
So selling price is equal
to 1.5 times c,

00:08:31.000 --> 00:08:35.600
which is q over a 100.

00:08:35.600 --> 00:08:37.640
And let's see how they did it.

00:08:37.640 --> 00:08:41.780
So selling price is equal
to 1.5q over 100.

00:08:41.780 --> 00:08:44.080
I don't expect to see
that as a choice.

00:08:44.080 --> 00:08:50.250
But if we multiply the top and
the bottom by 2, that equals

00:08:50.250 --> 00:08:55.960
3q over 200.

00:08:55.960 --> 00:08:58.220
That's choice A.

00:08:58.220 --> 00:08:59.690
Just need to make sure you
get your variables

00:08:59.690 --> 00:09:02.260
right on that one.

00:09:02.260 --> 00:09:08.350
Problem 86.

00:09:08.350 --> 00:09:11.620
In an increasing sequence of ten
consecutive integers, the

00:09:11.620 --> 00:09:14.160
sum of the first five
integers is 560.

00:09:14.160 --> 00:09:18.840
What is the sum of the last five
integers in the sequence?

00:09:18.840 --> 00:09:21.070
OK, ten consecutive integers.

00:09:21.070 --> 00:09:26.220
So x plus 1 plus x plus-- let me
write it this way-- x plus

00:09:26.220 --> 00:09:29.490
1 plus x plus 2, well actually
the first one, let's call it

00:09:29.490 --> 00:09:36.470
x, x plus 3, x plus 4.

00:09:36.470 --> 00:09:38.890
This right here is going to be
the first five consecutive

00:09:38.890 --> 00:09:41.560
integers if we start at x.

00:09:41.560 --> 00:09:45.180
When you take the sum of those--
well the sum of those

00:09:45.180 --> 00:09:49.270
is 1, 2, 3, 4, 5x.

00:09:49.270 --> 00:09:54.060
Let's see, 1 plus 2 is 3, 3 plus
3 is 6, 6 plus 4 is 10.

00:09:54.060 --> 00:10:01.970
5x plus 10 is going to
be equal to 560.

00:10:01.970 --> 00:10:02.470
Fair enough.

00:10:02.470 --> 00:10:05.390
Or we could say 5x
is equal to 550.

00:10:05.390 --> 00:10:08.010
I think we can use
that information.

00:10:08.010 --> 00:10:10.540
Now what is the next five
integers going to be?

00:10:10.540 --> 00:10:18.420
It's going to be x plus 5, x
plus 6, x plus 7, x plus 8,

00:10:18.420 --> 00:10:19.830
and x plus 9.

00:10:19.830 --> 00:10:21.960
These are five, and what
do those add up to be.

00:10:21.960 --> 00:10:29.520
That's 5x plus-- 5 plus 6
is 11 plus 7 is 18 plus

00:10:29.520 --> 00:10:33.120
8 is 26 plus 9.

00:10:33.120 --> 00:10:34.440
26 plus 9 is 35.

00:10:34.440 --> 00:10:37.200
So that's 5x plus 35.

00:10:37.200 --> 00:10:40.710
And they want to know what
this is equal to.

00:10:40.710 --> 00:10:42.130
That's the next five.

00:10:42.130 --> 00:10:44.930
Well we know what 5x
is, it's equal 550.

00:10:44.930 --> 00:10:50.200
From this set up, so it's going
to be equal to 550 plus

00:10:50.200 --> 00:10:58.990
35, which is equal to 35
plus 550, which is 585.

00:10:58.990 --> 00:11:00.070
That's choice A.

00:11:00.070 --> 00:11:02.260
And the trick here to being able
to do it fast is just to

00:11:02.260 --> 00:11:04.910
recognize that you didn't have
to solve all the way for x.

00:11:04.910 --> 00:11:07.150
That you could reuse this
5x when you took the

00:11:07.150 --> 00:11:08.820
sum of the next five.

00:11:08.820 --> 00:11:11.730
And I'm all out of time, see
you in the next video.


GMAT: Math 13

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:05.660
We're on problem 70.

00:00:05.660 --> 00:00:17.530
If x plus 5 is greater than 2,
and x minus 3 is less than 7,

00:00:17.530 --> 00:00:20.055
the value of x must be between
which of the following pairs

00:00:20.055 --> 00:00:21.300
of numbers?

00:00:21.300 --> 00:00:23.630
Well for this top one, let's
just subtract 5 from both

00:00:23.630 --> 00:00:24.495
sides of this equation.

00:00:24.495 --> 00:00:28.710
If you subtract 5 from both
sides, you get x is greater

00:00:28.710 --> 00:00:33.390
than, what's 2 minus 5, x
is greater than minus 3.

00:00:33.390 --> 00:00:34.970
For this bottom one, let's
add four to both

00:00:34.970 --> 00:00:36.720
sides of the equation.

00:00:36.720 --> 00:00:39.150
So x minus 3-- sorry,
lets add 3 to both

00:00:39.150 --> 00:00:40.045
sides of this equation.

00:00:40.045 --> 00:00:45.430
So x minus 3 plus 3, that's x,
is less than, what's 7 plus 3?

00:00:45.430 --> 00:00:46.410
10.

00:00:46.410 --> 00:00:50.460
So x is greater than minus 3--
I just wrote this the other

00:00:50.460 --> 00:00:57.610
way around-- and it's
less than 10.

00:00:57.610 --> 00:01:00.890
So that's A.

00:01:00.890 --> 00:01:07.000
Problem 71, a gym class can be
divided into 8 teams with an

00:01:07.000 --> 00:01:11.480
equal number of players on each
team-- 8, that means you

00:01:11.480 --> 00:01:16.130
get an equal number-- or into 12
teams with an equal number

00:01:16.130 --> 00:01:17.380
on each team.

00:01:20.060 --> 00:01:21.000
Fair enough.

00:01:21.000 --> 00:01:23.330
What is the lowest possible
number of

00:01:23.330 --> 00:01:25.040
students in the class?

00:01:25.040 --> 00:01:26.640
So essentially it's saying, that
the number of students in

00:01:26.640 --> 00:01:29.600
the classes is divisible
by both 8 and 12.

00:01:29.600 --> 00:01:31.580
So what they want to know is,
what's the smallest number

00:01:31.580 --> 00:01:34.390
that's divisible by
both 8 and 12.

00:01:34.390 --> 00:01:36.330
That's the least common
multiple of 8 and 12.

00:01:36.330 --> 00:01:38.600
That might ring a bell
from middle school.

00:01:38.600 --> 00:01:41.490
So what's the smallest number
that's divisible by 8 and 12?

00:01:41.490 --> 00:01:42.980
So let's think about
8's multiples.

00:01:42.980 --> 00:01:44.510
8 is indivisible by 12.

00:01:44.510 --> 00:01:46.740
16 is indivisible by 12.

00:01:46.740 --> 00:01:47.950
What about 24?

00:01:47.950 --> 00:01:50.390
Well yeah, sure, 24 is
divisible by 12.

00:01:50.390 --> 00:01:53.430
So the least common multiple
is 24, which is B.

00:01:53.430 --> 00:01:58.210
Clearly you can divide a gym
class into 3 groups of 8, or 2

00:01:58.210 --> 00:02:02.170
groups of 12.

00:02:02.170 --> 00:02:07.040
72.

00:02:07.040 --> 00:02:12.610
At least 2/3 of the 40 members
of a committee must vote in

00:02:12.610 --> 00:02:14.595
favor of a resolution
for it to pass.

00:02:24.420 --> 00:02:28.170
What is the greatest number of
members who could vote against

00:02:28.170 --> 00:02:32.490
the resolution and still
have it to pass?

00:02:32.490 --> 00:02:35.030
So essentially they're saying,
what is the least number that

00:02:35.030 --> 00:02:38.120
we need to have it pass, and
then 40 minus that is the

00:02:38.120 --> 00:02:40.220
greatest number that could
vote against it.

00:02:40.220 --> 00:02:42.090
So we have to have at
least 2/3 of 40.

00:02:42.090 --> 00:02:45.450
So what's 2/3 times 40?

00:02:45.450 --> 00:02:50.280
Well that's equal to 80/3.

00:02:50.280 --> 00:02:53.580
That's 3 goes into 80,
let's figure it out.

00:02:53.580 --> 00:02:56.330
3 goes into 8 2 times.

00:02:56.330 --> 00:02:58.890
2 times 3 is 6, 20.

00:02:58.890 --> 00:03:01.640
3 goes into 20 6 times.

00:03:01.640 --> 00:03:04.600
6 times 3 is 18.

00:03:04.600 --> 00:03:08.040
You bring down a
2 and then a 0.

00:03:08.040 --> 00:03:10.460
So it's going to just
keep repeating.

00:03:10.460 --> 00:03:13.440
So you have to have at least
26.6 people vote for it.

00:03:13.440 --> 00:03:18.330
But clearly you can't have
a 0.6 person vote for it.

00:03:18.330 --> 00:03:20.150
26 people isn't going
to be good enough.

00:03:20.150 --> 00:03:27.340
So you need at least
27 people.

00:03:27.340 --> 00:03:28.920
So if 27 are going to
vote for, how many

00:03:28.920 --> 00:03:30.330
going to vote against?

00:03:30.330 --> 00:03:33.620
Well that means 40 minus
27, that means 13

00:03:33.620 --> 00:03:38.440
against, which is E.

00:03:38.440 --> 00:03:39.750
That is the greatest number.

00:03:39.750 --> 00:03:43.090
Because if a larger number voted
against it, you would

00:03:43.090 --> 00:03:45.660
have less people
voting for it.

00:03:45.660 --> 00:03:51.490
Problem 73.

00:03:51.490 --> 00:03:54.480
In the Johnson's monthly budget,
the dollar amounts

00:03:54.480 --> 00:03:58.303
allocated to household expenses,
food-- so I'll say h

00:03:58.303 --> 00:04:02.010
for household expenses, f for
food-- and miscellaneous

00:04:02.010 --> 00:04:10.960
items, are in the ratio of
5:2:1-- fair enough--

00:04:10.960 --> 00:04:11.870
respectively.

00:04:11.870 --> 00:04:16.180
If the total amount allocated
to these three categories is

00:04:16.180 --> 00:04:21.100
$1,800, so $1,800 is the total,
what is the amount

00:04:21.100 --> 00:04:23.280
allocated to food?

00:04:23.280 --> 00:04:26.840
So we could view it this way.

00:04:26.840 --> 00:04:32.890
So food is going to be twice
times miscellaneous, and

00:04:32.890 --> 00:04:35.420
household items is going to
be equal to 5 times the

00:04:35.420 --> 00:04:36.670
miscellaneous.

00:04:41.100 --> 00:04:44.750
So we could say that household
plus food plus miscellaneous

00:04:44.750 --> 00:04:48.830
is going to be equal to $1,800
This ratio tells us that food

00:04:48.830 --> 00:04:51.170
is 2 times miscellaneous,
household is 5 times

00:04:51.170 --> 00:04:51.896
miscellaneous.

00:04:51.896 --> 00:04:54.120
So let's just substitute
that in.

00:04:54.120 --> 00:04:58.020
5 times miscellaneous plus 2
times miscellaneous plus

00:04:58.020 --> 00:05:02.965
miscellaneous is equal to $1,800
Let's see, 5 plus 2 is

00:05:02.965 --> 00:05:04.750
7 plus 1 is 8.

00:05:04.750 --> 00:05:09.710
8 times miscellaneous is equal
to $1,800 So m is equal to

00:05:09.710 --> 00:05:13.780
$1,800 over 8.

00:05:13.780 --> 00:05:16.010
Let's see, what does
that turn into?

00:05:16.010 --> 00:05:24.670
That is equal to 900 over 4,
which is equal to 450 over 2.

00:05:24.670 --> 00:05:27.610
That's how my brain works,
I have to go in steps.

00:05:27.610 --> 00:05:29.110
What's 450 divided by 2?

00:05:29.110 --> 00:05:31.850
That's 225.

00:05:31.850 --> 00:05:33.480
That's miscellaneous.

00:05:33.480 --> 00:05:35.340
They want to know how much
is allocated to food.

00:05:35.340 --> 00:05:36.846
Well, food is 2 times
miscellaneous.

00:05:40.010 --> 00:05:47.590
So 2 times 225 is equal
to, we're back at 450.

00:05:47.590 --> 00:05:49.035
And that is choice D.

00:05:52.100 --> 00:05:58.350
Problem 74.

00:05:58.350 --> 00:06:00.640
There are 4 more women
than men on

00:06:00.640 --> 00:06:03.110
Centerville's Board of Education.

00:06:03.110 --> 00:06:07.740
So 4 more women, so women
is equal to men plus 4.

00:06:07.740 --> 00:06:11.820
If there are 10 members on the
board, how many are women?

00:06:11.820 --> 00:06:18.030
So we know that men plus
women is equal to 10.

00:06:18.030 --> 00:06:19.850
We want to solve for women.

00:06:19.850 --> 00:06:22.580
So let me solve for men here,
then substitute there.

00:06:22.580 --> 00:06:26.000
So you get men is equal
to 10 minus the women.

00:06:26.000 --> 00:06:28.890
We could substitute
that back there.

00:06:28.890 --> 00:06:33.530
We get women is equal to m, or
the men, which we just figured

00:06:33.530 --> 00:06:37.490
out is 10 minus the
women plus 4.

00:06:40.590 --> 00:06:42.800
My brain was jumping ahead.

00:06:42.800 --> 00:06:44.970
So let's add w to both sides.

00:06:44.970 --> 00:06:51.460
So you get 2w is equal to 10
plus 4, which is equal to 14.

00:06:51.460 --> 00:06:53.655
w is equal to 7.

00:06:53.655 --> 00:06:58.130
There are seven women on
the board, so that's D.

00:06:58.130 --> 00:07:00.270
Problem 75.

00:07:00.270 --> 00:07:01.865
After this video, I think I'm
going to call it for a night

00:07:01.865 --> 00:07:03.590
and go watch a movie
or something.

00:07:03.590 --> 00:07:06.620
75.

00:07:06.620 --> 00:07:11.280
Leona bought a 1 year $10,000
certificate of deposit that

00:07:11.280 --> 00:07:14.340
pays interest at an
annual rate of 8%.

00:07:14.340 --> 00:07:20.520
So 1 year, $10,000, and
it paid a rate of 8%.

00:07:23.620 --> 00:07:27.540
Compounded semi-annually, what
was the total amount of

00:07:27.540 --> 00:07:31.280
interest paid on the certificate
at maturity?

00:07:31.280 --> 00:07:34.360
So when you say compound
semi-annually, that means you

00:07:34.360 --> 00:07:39.080
collect half of the interest
every half year.

00:07:39.080 --> 00:07:41.000
That's something I don't know
if the GMAT, they should be

00:07:41.000 --> 00:07:43.010
expecting you to know that, it's
something you probably

00:07:43.010 --> 00:07:44.250
would learn in business
school.

00:07:44.250 --> 00:07:56.020
But anyway, so after 6 months
you're going to get 4% on the

00:07:56.020 --> 00:07:56.800
original amount.

00:07:56.800 --> 00:07:58.840
So you're going to have
$10,000 dollars.

00:07:58.840 --> 00:08:01.720
And you're going to 4%
percent of this.

00:08:01.720 --> 00:08:05.850
So they're going to owe you--
compounded semi-annually, what

00:08:05.850 --> 00:08:07.690
was the total amount of
interest paid on the

00:08:07.690 --> 00:08:09.400
certificate at maturity?

00:08:09.400 --> 00:08:16.890
So they're going to pay you
$10,000 times half of it,

00:08:16.890 --> 00:08:18.980
because only six months
have gone by.

00:08:18.980 --> 00:08:20.330
8% is for the full year.

00:08:20.330 --> 00:08:22.050
So for half the year, you're
going to get times 4%.

00:08:27.440 --> 00:08:30.110
So let's see, $10,000 times
4%, what is that?

00:08:30.110 --> 00:08:37.360
$10,000 times 0.04.

00:08:37.360 --> 00:08:41.879
Let's look at it this way, 4
times $10,000 is $40,000.

00:08:41.879 --> 00:08:49.150
We have two numbers behind the
decimal place, so it's $400.

00:08:49.150 --> 00:08:53.010
So they're going to
pay you $400.

00:08:53.010 --> 00:08:56.480
So then you can view
it essentially,

00:08:56.480 --> 00:08:58.660
they owe you $10,400.

00:08:58.660 --> 00:08:59.920
That's essentially how
much they borrowed.

00:08:59.920 --> 00:09:01.190
Because they're not going to
give it to you just then.

00:09:01.190 --> 00:09:03.240
You're going to get all your
money back at the end.

00:09:03.240 --> 00:09:07.710
So at the end, they're going to
have to pay you another 4%.

00:09:07.710 --> 00:09:10.750
But this time, it's not going
to be off of the $10,000.

00:09:10.750 --> 00:09:14.220
It's going to be off
of the $10,400.

00:09:14.220 --> 00:09:19.020
So $10,400 times 0.04.

00:09:19.020 --> 00:09:20.140
4 times 0 is 0.

00:09:20.140 --> 00:09:21.920
4 times 0 is 0.

00:09:21.920 --> 00:09:24.910
4 times 4 is 16.

00:09:24.910 --> 00:09:27.240
4 times 0 is 0 plus 1 is 1.

00:09:27.240 --> 00:09:30.260
4 times 1 is 4.

00:09:30.260 --> 00:09:31.980
Then we have two numbers behind
the decimal point.

00:09:31.980 --> 00:09:37.190
So now they're going to pay you
$416, the second payment.

00:09:37.190 --> 00:09:38.890
What was the total amount
of interest?

00:09:38.890 --> 00:09:51.500
So it's going to be $416 plus
$400, which is $816,

00:09:51.500 --> 00:09:53.120
which is choice C.

00:09:53.120 --> 00:09:55.390
I'm a little surprised that they
expect you to know what

00:09:55.390 --> 00:09:57.110
compounding semi-annually
means.

00:09:57.110 --> 00:09:58.830
But since it's there, I guess
you should know it.

00:09:58.830 --> 00:10:01.380
When it compound semi-annually,
it means that

00:10:01.380 --> 00:10:05.190
each semi-annual point in time,
you divide the annual

00:10:05.190 --> 00:10:08.610
interest rate by 2, and
you get that much.

00:10:08.610 --> 00:10:12.500
But then the next interest you
get is off of, not just the

00:10:12.500 --> 00:10:15.180
initial amount, but the initial
amount plus the

00:10:15.180 --> 00:10:17.330
previous interest, because they
haven't paid you yet.

00:10:17.330 --> 00:10:19.500
But anyway, I hope you don't
find that too confusing.

00:10:19.500 --> 00:10:20.740
You might want to look it
up on the internet.

00:10:20.740 --> 00:10:22.720
You could also compound
monthly, or daily, or

00:10:22.720 --> 00:10:23.180
continuously.

00:10:23.180 --> 00:10:25.350
I actually have a couple of
videos on the Khan Academy.

00:10:25.350 --> 00:10:27.840
But anyway, I'm all out of time,
so I'll see you in the

00:10:27.840 --> 00:10:29.300
next video.


GMAT: Math 11

WEBVTT
Kind: captions
Language: en

00:00:01.510 --> 00:00:04.510
We're on problem 61.

00:00:04.510 --> 00:00:13.930
If 1 kilometer is approximately
0.6 miles, which

00:00:13.930 --> 00:00:16.920
of the following best
approximates the number of

00:00:16.920 --> 00:00:20.270
kilometers in 2 miles?

00:00:20.270 --> 00:00:22.120
So we want to know 2 miles.

00:00:24.840 --> 00:00:25.930
So we could set up a ratio.

00:00:25.930 --> 00:00:35.160
We could say, 0.6 miles are to 2
miles as 1 kilometer is to x

00:00:35.160 --> 00:00:35.972
kilometers.

00:00:35.972 --> 00:00:37.440
And you could cross multiply.

00:00:37.440 --> 00:00:40.960
You could say 0.6
is equal to 2.

00:00:40.960 --> 00:00:45.010
And that x is equal to 2 divided
by 0.6, which is the

00:00:45.010 --> 00:00:49.990
same thing as 20 divided by 6.

00:00:49.990 --> 00:00:51.010
Right?

00:00:51.010 --> 00:00:57.820
20 divided by 6 is
equal to 3 2/6.

00:00:57.820 --> 00:00:58.560
Right?

00:00:58.560 --> 00:00:59.810
3 1/3.

00:01:03.130 --> 00:01:04.930
3 1/3 kilometers.

00:01:04.930 --> 00:01:06.630
And that makes sense, right?

00:01:06.630 --> 00:01:08.520
A mile is longer than
a kilometer.

00:01:08.520 --> 00:01:12.580
So 2 miles is about
3 1/3 kilometers.

00:01:12.580 --> 00:01:14.530
And that's not one of the
choices, but if we wrote this

00:01:14.530 --> 00:01:18.370
as an improper fraction, 3 times
3 is 9, plus 1 is 10.

00:01:18.370 --> 00:01:23.010
So that equals 10/3 kilometers,
which is choice A.

00:01:26.760 --> 00:01:27.850
Let me do a brighter color.

00:01:27.850 --> 00:01:30.490
I don't know if you
can even see this.

00:01:30.490 --> 00:01:33.150
62.

00:01:33.150 --> 00:01:36.290
Lucy invested $10,000 in a
new mutual fund account

00:01:36.290 --> 00:01:37.870
exactly 3 years ago.

00:01:42.080 --> 00:01:44.700
The value of the account
increased by 10% during the

00:01:44.700 --> 00:01:54.080
first year, increased by 5%
during the second year, and

00:01:54.080 --> 00:02:00.290
decreased by 10% during
the third year.

00:02:00.290 --> 00:02:02.450
What is the value of
the account today?

00:02:02.450 --> 00:02:06.400
So you start with $10,000.

00:02:06.400 --> 00:02:09.000
When you grow by 10%, that's
the same thing as

00:02:09.000 --> 00:02:11.370
multiplying by 1.1.

00:02:11.370 --> 00:02:13.080
Right?

00:02:13.080 --> 00:02:16.910
It's like 1 plus 0.1
times whatever.

00:02:16.910 --> 00:02:19.780
So that's multiplying by 1.1.

00:02:19.780 --> 00:02:21.430
And then you grow
by another 5%.

00:02:21.430 --> 00:02:24.800
That's like multiplying
by 1.05.

00:02:24.800 --> 00:02:27.800
And then when you decrease
by 10%, that's like

00:02:27.800 --> 00:02:31.050
multiplying by 0.9.

00:02:31.050 --> 00:02:32.860
So we need to figure
out what this is.

00:02:32.860 --> 00:02:36.500
So this is a little bit
of math for us to do.

00:02:36.500 --> 00:02:38.320
So 1.1 times 10,000.

00:02:38.320 --> 00:02:39.550
That's at least fairly
straightforward.

00:02:39.550 --> 00:02:41.920
That's 11,000.

00:02:41.920 --> 00:02:42.210
Right?

00:02:42.210 --> 00:02:44.270
That's how much we have
after year one.

00:02:44.270 --> 00:02:48.930
11,000 and we have to multiply
that times 1.05.

00:02:48.930 --> 00:02:50.660
And then we lose 10%.

00:02:50.660 --> 00:02:54.940
So 11,000 times 1.05.

00:02:54.940 --> 00:02:56.970
Well, just to make sure I get
right, just so I don't make a

00:02:56.970 --> 00:02:59.210
careless mistake, let's
actually do it.

00:02:59.210 --> 00:03:06.150
11,000 times 1.05.

00:03:06.150 --> 00:03:12.210
So 5 times 11,000 is 55,000.

00:03:12.210 --> 00:03:14.240
And then we should
add two 0's.

00:03:14.240 --> 00:03:17.210
The 0 doesn't matter,
so we add two 0's.

00:03:17.210 --> 00:03:22.676
And then 1 times 11,000
is 11,000.

00:03:22.676 --> 00:03:23.990
You add them up.

00:03:23.990 --> 00:03:28.230
You get 0, 0, 0, 5, 5, 1, 1.

00:03:28.230 --> 00:03:31.980
And we have two digits behind
the decimal point.

00:03:31.980 --> 00:03:34.700
So we got 11,550.

00:03:34.700 --> 00:03:36.460
Which is right.

00:03:36.460 --> 00:03:38.670
It would have been weird
if we got 100,000

00:03:38.670 --> 00:03:39.690
or if we got 1,000.

00:03:39.690 --> 00:03:41.780
We only had a 5% change.

00:03:41.780 --> 00:03:47.120
So then we have 11,550.

00:03:47.120 --> 00:03:49.320
And now it's going to
decrease by video.

00:03:49.320 --> 00:03:50.550
10%.

00:03:50.550 --> 00:03:53.020
We could multiply it by 0.9.

00:03:53.020 --> 00:03:54.890
I don't know, it might be easier
just to take out 10%.

00:03:54.890 --> 00:03:56.140
Well, let's multiply
it by 0.9.

00:04:01.250 --> 00:04:02.310
9 times 0 is 0.

00:04:02.310 --> 00:04:03.650
9 times 0 is 0.

00:04:03.650 --> 00:04:07.170
9 times 5 is 45.

00:04:07.170 --> 00:04:11.670
9 times 1 is 9, plus 4 is 13.

00:04:11.670 --> 00:04:14.160
9 times 1 is 9, plus 1 is 10.

00:04:14.160 --> 00:04:16.899
And we have one digit behind
the decimal point.

00:04:16.899 --> 00:04:18.680
So it's right there.

00:04:18.680 --> 00:04:24.640
So we're left with $10,350,
and that is choice A.

00:04:24.640 --> 00:04:25.890
Next problem.

00:04:29.210 --> 00:04:31.490
63.

00:04:31.490 --> 00:04:33.190
And they give us this table.

00:04:33.190 --> 00:04:36.250
They say a computer chip
manufacturer expects the ratio

00:04:36.250 --> 00:04:39.420
of the number of defective chips
to the total number of

00:04:39.420 --> 00:04:43.360
chips in all future shipments
to equal the corresponding

00:04:43.360 --> 00:04:47.050
ratio for shipments
as combined, as

00:04:47.050 --> 00:04:47.760
shown in the table.

00:04:47.760 --> 00:04:50.710
What is the expected number
in a shipment.

00:04:50.710 --> 00:04:53.650
OK, so let me write down what
they wrote, so that we see the

00:04:53.650 --> 00:04:54.130
same thing.

00:04:54.130 --> 00:04:55.380
So shipment.

00:04:57.690 --> 00:05:05.500
And they labeled them
S1, S2, S3, and S4.

00:05:05.500 --> 00:05:13.750
And they need to ask us the
number of defective chips in

00:05:13.750 --> 00:05:14.265
the shipment.

00:05:14.265 --> 00:05:16.610
I know you can't read
my handwriting.

00:05:16.610 --> 00:05:21.760
2, 5, 6, and 4.

00:05:21.760 --> 00:05:26.430
And then they say the total
number of chips in each

00:05:26.430 --> 00:05:38.600
shipment is 5,000, 12,000,
18,000, and 16,000.

00:05:38.600 --> 00:05:39.790
Now let's reread the question.

00:05:39.790 --> 00:05:41.590
Maybe it'll make a little
bit more sense.

00:05:41.590 --> 00:05:43.830
A computer chip manufacturer
expects the ratio of the

00:05:43.830 --> 00:05:48.600
number of defective chips to the
total number of chips --

00:05:48.600 --> 00:05:54.760
so that's defective to total --
in all future shipments to

00:05:54.760 --> 00:05:58.810
equal the corresponding ratio
for shipments S1 through S4

00:05:58.810 --> 00:06:02.150
combined, as shown in
the table above.

00:06:05.120 --> 00:06:07.810
Let me make sure I read that.

00:06:07.810 --> 00:06:11.010
To equal the corresponding ratio
for shipments S1, S2,

00:06:11.010 --> 00:06:14.020
S3, and S4 combined, as shown
in the table above.

00:06:14.020 --> 00:06:15.860
What are the expected number
of defective chips in a

00:06:15.860 --> 00:06:18.430
shipment of 60,000?

00:06:18.430 --> 00:06:21.110
They're saying, essentially,
if we take these shipments

00:06:21.110 --> 00:06:23.530
combined, what percentage
were defective?

00:06:23.530 --> 00:06:25.620
And that's the same number we
would expect to be defective

00:06:25.620 --> 00:06:27.170
in a shipment of 60,000.

00:06:27.170 --> 00:06:29.380
So let's figure out what
percentage are defective.

00:06:29.380 --> 00:06:31.380
So how many total
were defective?

00:06:31.380 --> 00:06:38.350
2 plus 5 is 7, 7 plus 6 is
13, 13 plus 4 is 17.

00:06:38.350 --> 00:06:41.320
And how many total chips
did we ship?

00:06:41.320 --> 00:06:43.670
17,000.

00:06:43.670 --> 00:06:48.410
17 plus 18 is 35.

00:06:48.410 --> 00:06:57.940
35 plus 16 is 41, is equal
to 51,000 chips.

00:06:57.940 --> 00:07:00.850
So we could view it
a couple of ways.

00:07:00.850 --> 00:07:05.100
It's 17 for every 51,000
were defective.

00:07:05.100 --> 00:07:08.030
But actually, if you haven't
realized it already, 51 is

00:07:08.030 --> 00:07:09.380
divisible by 17.

00:07:09.380 --> 00:07:10.750
That's one that a lot
of people miss.

00:07:10.750 --> 00:07:12.340
17 times 3.

00:07:12.340 --> 00:07:15.750
So then if we divide both of
these numbers by 17, we can

00:07:15.750 --> 00:07:23.320
say that 1 chip for every 3,000
is defective, if we take

00:07:23.320 --> 00:07:25.650
shipments S1 through
S4 combined.

00:07:25.650 --> 00:07:28.140
1 chip in every 3,000.

00:07:28.140 --> 00:07:33.390
And so if we have that same
ratio for 60,000 chips, well,

00:07:33.390 --> 00:07:36.090
how many groups of 3,000
are there in 60,000?

00:07:36.090 --> 00:07:37.673
Well, there are 20
of them, right?

00:07:37.673 --> 00:07:44.330
next We could say 1 in 3,000
is equal to x over 60,000.

00:07:44.330 --> 00:07:46.570
And you could eyeball
this to some degree.

00:07:46.570 --> 00:07:49.730
Or you could just say, what
can I multiply both the

00:07:49.730 --> 00:07:52.030
numerator and the denominator
by to get 60,000.

00:07:52.030 --> 00:07:53.855
Well, if I multiply the
numerator and the denominator

00:07:53.855 --> 00:07:57.840
by 20, I get 20/60,000.

00:07:57.840 --> 00:07:58.790
You could cross multiply.

00:07:58.790 --> 00:08:00.720
There's a bunch of ways
you could do this.

00:08:00.720 --> 00:08:02.280
But the bottom line is
you would expect

00:08:02.280 --> 00:08:04.470
20 defective chips.

00:08:04.470 --> 00:08:07.005
And that is choice B.

00:08:12.070 --> 00:08:15.690
Problem 64.

00:08:15.690 --> 00:08:18.080
I'll do it in this color.

00:08:18.080 --> 00:08:21.640
Let's see, they tell us that A
is equal to a set of numbers.

00:08:21.640 --> 00:08:23.020
I don't know what the
context is yet.

00:08:23.020 --> 00:08:26.730
2, 3, 4, and 5.

00:08:26.730 --> 00:08:29.430
And they tell us that B is
equal to another set of

00:08:29.430 --> 00:08:38.230
numbers, 4, 5, 6, 7, and 8.

00:08:38.230 --> 00:08:41.289
2 integers will be randomly
selected from the sets above,

00:08:41.289 --> 00:08:45.800
1 integer from set A and
1 integer from set B.

00:08:45.800 --> 00:08:48.130
What is the probability
that the sum of the 2

00:08:48.130 --> 00:08:50.570
integers will equal 9?

00:08:54.290 --> 00:08:59.480
So let's think about all of the
combinations that equal 9.

00:08:59.480 --> 00:09:00.730
Right?

00:09:12.400 --> 00:09:18.240
If I pick 2 from this, I have
to pick 7 from here, right?

00:09:18.240 --> 00:09:21.110
If I pick 3 from this set, I
have to pick 6 from here.

00:09:21.110 --> 00:09:24.005
If I pick 4 from this set, I
have to pick 5 from here.

00:09:24.005 --> 00:09:29.190
And if I pick 5 from this set,
I have to pick 4 from here.

00:09:29.190 --> 00:09:30.140
Right?

00:09:30.140 --> 00:09:33.910
So no matter what, I'm going to
pick one of these numbers

00:09:33.910 --> 00:09:35.470
from set 1.

00:09:35.470 --> 00:09:36.790
It's going to be 2,
3, or 4 or 5.

00:09:36.790 --> 00:09:40.450
And depending which of these I
pick, I have to pick the exact

00:09:40.450 --> 00:09:43.080
right number from set B.

00:09:43.080 --> 00:09:44.590
So think of it this way.

00:09:44.590 --> 00:09:46.620
I don't know what I've picked
in set A, right?

00:09:46.620 --> 00:09:47.070
I don't know.

00:09:47.070 --> 00:09:48.160
Let's say we've picked
one of them.

00:09:48.160 --> 00:09:49.770
We don't know which of
these we've picked.

00:09:49.770 --> 00:09:53.200
And we know that exactly one
of these is going to be the

00:09:53.200 --> 00:09:54.850
right number to add
to whatever we've

00:09:54.850 --> 00:09:58.160
picked to equal 9.

00:09:58.160 --> 00:10:00.180
And we have to pick that
exactly right one.

00:10:00.180 --> 00:10:02.950
And we're going to be picking it
out of a selection of 1, 2,

00:10:02.950 --> 00:10:04.910
3, 4, 5 numbers.

00:10:04.910 --> 00:10:09.830
So we have a 1 in 5 chance of
having them add up to 9.

00:10:09.830 --> 00:10:13.965
And 1 in 5 is the same thing
as 0.2, which is choice B.

00:10:13.965 --> 00:10:15.330
I hope that makes sense.

00:10:15.330 --> 00:10:17.960
You could say, look, I don't
care what I pick from set 1.

00:10:17.960 --> 00:10:20.830
I could pick any of these, and
in order for it to add up to

00:10:20.830 --> 00:10:27.840
9, no matter what I pick from
here, there's a 1/5 chance

00:10:27.840 --> 00:10:30.960
that I picked the right
corresponding number that adds

00:10:30.960 --> 00:10:31.690
up to 9 there.

00:10:31.690 --> 00:10:34.000
Because each of these
have only one.

00:10:34.000 --> 00:10:37.370
If I pick 3, I have
to pick 5, right?

00:10:37.370 --> 00:10:42.090
So if I pick 2, I
have to pick 7.

00:10:42.090 --> 00:10:44.693
If I pick 3, I have to pick 5.

00:10:52.430 --> 00:10:55.490
If I pick 3, I have to pick 6.

00:10:55.490 --> 00:10:58.010
If I pick 4, I have to pick 5.

00:10:58.010 --> 00:11:01.870
And if I pick 5, I have
to pick 4, right?

00:11:01.870 --> 00:11:04.660
And so you could say, well,
the chances of each

00:11:04.660 --> 00:11:07.450
of these are 1/5.

00:11:07.450 --> 00:11:08.600
Actually I'm not going
to go down that road.

00:11:08.600 --> 00:11:12.170
All you have to say is that just
overly complicates it.

00:11:12.170 --> 00:11:13.085
All you have to say is,
look, I'm going

00:11:13.085 --> 00:11:14.130
to pick one of these.

00:11:14.130 --> 00:11:16.930
And once I have one of those
in my hand, there's a 1/5

00:11:16.930 --> 00:11:20.420
chance that I picked the exact
one that adds up to whatever I

00:11:20.420 --> 00:11:21.700
just picked to equal 9.

00:11:21.700 --> 00:11:24.170
And the answer is B.

00:11:24.170 --> 00:11:25.670
And now I'm out of time.

00:11:25.670 --> 00:11:27.310
See you in the


GMAT: Math 12

WEBVTT
Kind: captions
Language: en

00:00:00.730 --> 00:00:05.540
We're on problem 65.

00:00:05.540 --> 00:00:16.340
They wrote 2, 4, 6, 8,
n, 3, 5, 7, and 9.

00:00:16.340 --> 00:00:19.110
And they tell us, in the list
above, if n is an integer

00:00:19.110 --> 00:00:25.090
between 1 and 10, inclusive--
so that means n could be 1,

00:00:25.090 --> 00:00:27.760
and it could be 10, or any
number inbetween, and it's an

00:00:27.760 --> 00:00:34.090
integer-- then the median must
be-- the median, right, not

00:00:34.090 --> 00:00:35.440
the mean, the median.

00:00:35.440 --> 00:00:37.830
So the median means the
middle number, right?

00:00:40.760 --> 00:00:43.520
Let's put all the other
numbers in order.

00:00:43.520 --> 00:01:02.310
So we have 2, 3, 4,
5, 6, 7, 8, 9.

00:01:02.310 --> 00:01:04.470
And they're essentially
saying that n could

00:01:04.470 --> 00:01:05.730
be anywhere in this.

00:01:05.730 --> 00:01:10.960
It could be a 1 here, it could
be right here, it could be

00:01:10.960 --> 00:01:12.400
another 2, it doesn't tell us.

00:01:12.400 --> 00:01:13.930
It could be any number, it could
be 2, could be another

00:01:13.930 --> 00:01:15.090
3, could be 10.

00:01:15.090 --> 00:01:15.540
We don't know.

00:01:15.540 --> 00:01:17.420
But before we stick n in
here, let's figure out

00:01:17.420 --> 00:01:20.250
what the middle is.

00:01:20.250 --> 00:01:23.690
Right here we have eight
numbers, so the middle of the

00:01:23.690 --> 00:01:28.580
range is actually-- there is no
middle number-- but when we

00:01:28.580 --> 00:01:30.130
add n, there will be
a middle number.

00:01:30.130 --> 00:01:31.380
So let's just think about
it for a little bit.

00:01:34.700 --> 00:01:39.380
If n is 5 or less, so n goes
into this bucket, n goes

00:01:39.380 --> 00:01:42.890
someplace here, then
what happens?

00:01:42.890 --> 00:01:45.120
Then what becomes the
middle number?

00:01:45.120 --> 00:01:49.090
If n is 5 or less, then
we'll have n here.

00:01:49.090 --> 00:01:51.235
And n might be 5, n might
go right here.

00:01:51.235 --> 00:01:52.520
But what becomes the
middle number?

00:01:52.520 --> 00:01:54.890
Then we have 1, 2, 3, 4 on
this side of the middle

00:01:54.890 --> 00:01:58.760
number, and we have 1, 2, 3, 4
on that side of the number.

00:01:58.760 --> 00:02:03.980
So then, the median, which is
the middle number, becomes 5.

00:02:03.980 --> 00:02:06.840
That's if n is 5 or less.

00:02:06.840 --> 00:02:10.180
If n is less than or equal to
5, then we know that the

00:02:10.180 --> 00:02:13.220
median will be equal to 5.

00:02:13.220 --> 00:02:15.120
Now let's do the opposite
thought experiment.

00:02:15.120 --> 00:02:17.990
What if n is 6 or more?

00:02:17.990 --> 00:02:20.840
What if n is greater
than or equal to 6?

00:02:20.840 --> 00:02:23.030
So it goes someplace over
here, so n will

00:02:23.030 --> 00:02:23.720
go someplace here.

00:02:23.720 --> 00:02:26.010
Could be 6, I might have
to put it right there.

00:02:26.010 --> 00:02:29.320
But wherever I put it on the
side, I'll have 4 to the right

00:02:29.320 --> 00:02:32.840
of 6, and I'll have 4
to the left of 6.

00:02:32.840 --> 00:02:35.580
n isn't on this side anymore,
4 to the left of 6.

00:02:35.580 --> 00:02:36.830
So then the median would be 6.

00:02:40.500 --> 00:02:43.580
And either of these cases
have to be true for n.

00:02:43.580 --> 00:02:47.520
So the median is either 5 or
6, and that is choice B.

00:02:50.040 --> 00:02:51.670
Problem 66.

00:02:51.670 --> 00:02:53.160
I like this brownish color.

00:02:56.420 --> 00:03:00.240
Reminds me of when I was
in middle school math

00:03:00.240 --> 00:03:01.160
competitions.

00:03:01.160 --> 00:03:11.580
4u7, n23, 162.

00:03:11.580 --> 00:03:18.390
And you add them all together,
you get one 1,222.

00:03:18.390 --> 00:03:21.390
And what they want to know is,
if n and u represent single

00:03:21.390 --> 00:03:24.640
digits in the correctly worked
computation above, what is the

00:03:24.640 --> 00:03:27.640
value of n plus u?

00:03:27.640 --> 00:03:29.830
So the best thing to do is to
try to work these out, and see

00:03:29.830 --> 00:03:30.340
what happens.

00:03:30.340 --> 00:03:35.870
So 7 plus 3 is 10,
plus 2 is 12.

00:03:35.870 --> 00:03:38.340
So you would write a 2 here,
which they already

00:03:38.340 --> 00:03:40.830
wrote, and carry a 1.

00:03:40.830 --> 00:03:45.690
And now we have 1 plus u-- let
me write this down-- 1 plus u

00:03:45.690 --> 00:03:53.150
plus 2 plus 6 is equal to, well,
it's either going to be

00:03:53.150 --> 00:03:55.940
equal to 2, or some
digit and a 2.

00:03:55.940 --> 00:03:58.020
So let's just think about
it a little bit.

00:03:58.020 --> 00:04:04.080
1 plus u plus 2 plus 6, that's
equal to u plus 9.

00:04:04.080 --> 00:04:09.780
u plus 9 is going to have
to equal something.

00:04:09.780 --> 00:04:14.170
So if u is 9, and it has to be
something that ends with a 2.

00:04:14.170 --> 00:04:19.839
And remember, u can only
be between 0 and 9.

00:04:19.839 --> 00:04:22.890
It's a digit, it has to be an
integer, it has to be a digit.

00:04:22.890 --> 00:04:25.220
So let's think about
it a little bit.

00:04:25.220 --> 00:04:26.700
It has to be something
that ends in a 2.

00:04:26.700 --> 00:04:33.180
So the only next thing above
9 that ends as a 2 is 12.

00:04:33.180 --> 00:04:34.140
Because you can't get to 22.

00:04:34.140 --> 00:04:36.390
To get to 22, you would
have to add 13, and

00:04:36.390 --> 00:04:37.810
you can't be 13.

00:04:37.810 --> 00:04:42.510
So this has to be a 12, so
u has to be equal to 3.

00:04:42.510 --> 00:04:44.500
That's the only possibility
that'll give you something

00:04:44.500 --> 00:04:46.110
that ends in a 2.

00:04:46.110 --> 00:04:50.310
So if we assume that u is 3,
then we have 1 plus 3 plus 2

00:04:50.310 --> 00:04:59.510
plus 6, which is 12, carry the
1, you get 1 plus 4 plus n

00:04:59.510 --> 00:05:04.870
plus 1 is equal to 12.

00:05:04.870 --> 00:05:07.250
So you get 1 plus 4 plus 1.

00:05:07.250 --> 00:05:12.450
That's 6, plus n is equal to 12,
and n would be equal to 6.

00:05:12.450 --> 00:05:14.480
And they want to know
what n plus u is.

00:05:14.480 --> 00:05:17.490
So n plus u, 6 plus 3.

00:05:17.490 --> 00:05:19.070
That's equal to 9.

00:05:19.070 --> 00:05:23.135
And that is choice B, 9.

00:05:25.940 --> 00:05:33.270
67.

00:05:33.270 --> 00:05:35.920
Look at that, this is a dense
looking one, but let me write

00:05:35.920 --> 00:05:39.080
down the little equation they
wrote on top. r is equal to

00:05:39.080 --> 00:05:52.620
400 times d plus s minus
p, all of that over p.

00:05:52.620 --> 00:05:56.280
If stock is sold three months
after it is purchased, the

00:05:56.280 --> 00:06:01.210
formula above relates p, d, s,
and r, where p is the purchase

00:06:01.210 --> 00:06:02.030
price of the stock.

00:06:02.030 --> 00:06:04.020
That's the purchase price.

00:06:04.020 --> 00:06:07.080
d is the amount of any
dividend received.

00:06:07.080 --> 00:06:08.380
Fair enough.

00:06:08.380 --> 00:06:12.840
s is the selling price of the
stock, and r is the yield of

00:06:12.840 --> 00:06:15.450
the investment as a percent.

00:06:15.450 --> 00:06:16.540
Fair enough.

00:06:16.540 --> 00:06:21.550
If Rose purchased $400 worth
of stock-- so p is equal to

00:06:21.550 --> 00:06:27.030
$400-- received a $5 dividend--
so d is equal to

00:06:27.030 --> 00:06:35.140
$5-- and sold the stock for
$420, for three months after

00:06:35.140 --> 00:06:37.230
purchasing-- so this formula
applies, because this is the

00:06:37.230 --> 00:06:40.470
formula for selling after three
months-- what was the

00:06:40.470 --> 00:06:42.750
yield of her investment,
according to the formula?

00:06:42.750 --> 00:06:45.370
Assuming she paid
no commissions.

00:06:45.370 --> 00:06:46.480
We just substitute in.

00:06:46.480 --> 00:06:47.500
So let's see.

00:06:47.500 --> 00:06:55.660
The yield would be equal to
400 times 5 plus 420 minus

00:06:55.660 --> 00:07:01.750
400, p is 400, all
of that over 420.

00:07:01.750 --> 00:07:10.170
That is equal to 420 minus
400 is 20, plus 5 is 25.

00:07:10.170 --> 00:07:17.570
400 times 25 over-- this
shouldn't be 420, this is p.

00:07:17.570 --> 00:07:20.290
The price you paid was 400.

00:07:20.290 --> 00:07:24.050
25 over 400.

00:07:24.050 --> 00:07:26.680
I just substituted these values
into this equation.

00:07:26.680 --> 00:07:31.250
This cancels out, and I'm just
left with a yield of 25, and

00:07:31.250 --> 00:07:32.550
it's probably in terms
of percent.

00:07:32.550 --> 00:07:35.350
Yep, 25%.

00:07:35.350 --> 00:07:36.340
E.

00:07:36.340 --> 00:07:38.790
All right, problem 68.

00:07:38.790 --> 00:07:41.770
Let's switch colors.

00:07:41.770 --> 00:07:44.010
68.

00:07:44.010 --> 00:07:47.660
The temperatures in degree
Celsius recorded at 6:00 in

00:07:47.660 --> 00:07:53.140
the morning in various parts of
a certain country were 10

00:07:53.140 --> 00:07:57.610
degrees, I'm not going to write
all of it, 5, minus 2,

00:07:57.610 --> 00:08:03.990
minus 1, minus 5, and 15.

00:08:03.990 --> 00:08:05.880
What is the median of
these temperatures?

00:08:05.880 --> 00:08:07.760
The median just means
the middle.

00:08:07.760 --> 00:08:10.820
Don't confuse that with the
average, which is the mean.

00:08:10.820 --> 00:08:12.160
Or the mean, which
is the average.

00:08:12.160 --> 00:08:13.800
Median means middle, so let's
just put them in order and

00:08:13.800 --> 00:08:14.810
figure out the middle.

00:08:14.810 --> 00:08:16.540
So the smallest of
these numbers is

00:08:16.540 --> 00:08:19.060
minus 5, cross it out.

00:08:19.060 --> 00:08:22.470
Then we have minus
2, cross it out.

00:08:22.470 --> 00:08:25.630
Then we have minus
1, cross it out.

00:08:25.630 --> 00:08:31.410
Then we have 5, cross it out,
then we have 10, cross it out.

00:08:31.410 --> 00:08:35.970
Then we have 15.

00:08:35.970 --> 00:08:38.150
So this is interesting
about median.

00:08:38.150 --> 00:08:40.780
If there is no true middle
number, you have three on this

00:08:40.780 --> 00:08:43.582
side of negative 1, or negative
1 and less, and you

00:08:43.582 --> 00:08:45.100
have three on that side, so
there's no middle number,

00:08:45.100 --> 00:08:46.910
because we have an even
number of numbers.

00:08:46.910 --> 00:08:50.130
So what you want to do is, you
take the two middle numbers,

00:08:50.130 --> 00:08:53.390
which are negative 1 and 5,
and you average them.

00:08:53.390 --> 00:08:58.830
So it's negative 1 plus 5 over
2, which equals 4 over 2,

00:08:58.830 --> 00:09:01.360
which is equal to 2.

00:09:01.360 --> 00:09:05.320
2 degrees Celsius, which
is choice C.

00:09:05.320 --> 00:09:09.640
Problem 69.

00:09:09.640 --> 00:09:20.320
If y times three 3x minus 5 over
2 is equal to y, and y

00:09:20.320 --> 00:09:25.070
does not equal 0, then
x is equal to what?

00:09:25.070 --> 00:09:27.310
Well the simplest thing, since
y doesn't equal 0, we can

00:09:27.310 --> 00:09:29.760
divide both sides of
this equation by y.

00:09:29.760 --> 00:09:32.290
You divide both sides by y.
y divided by y is 1, y

00:09:32.290 --> 00:09:34.300
divided by y is 1.

00:09:34.300 --> 00:09:40.520
So then we're left with 3x minus
5 over 2 is equal to 1.

00:09:40.520 --> 00:09:46.390
Multiply both sides by 2, you
get 3x minus 5 is equal to 2.

00:09:46.390 --> 00:09:50.830
Add 5 to both sides,
3x is equal to 7.

00:09:50.830 --> 00:09:57.540
And you get x is equal to 7
over 3, which is choice C.

00:09:57.540 --> 00:10:00.980
And I'm out of time, so I'll
see you in the next video.


GMAT: Math 10

WEBVTT
Kind: captions
Language: en

00:00:00.830 --> 00:00:05.500
We're on problem 55.

00:00:05.500 --> 00:00:15.050
If y is equal to 4 plus x minus
3 squared, then y is

00:00:15.050 --> 00:00:20.140
lowest when x is equal to-- so
think about when will this

00:00:20.140 --> 00:00:22.950
expression be the lowest
possible number?

00:00:22.950 --> 00:00:25.460
Well, if you think about this
whole term, right here, this x

00:00:25.460 --> 00:00:27.770
minus 3 squared.

00:00:27.770 --> 00:00:30.350
Any number squared, if we're
dealing with real numbers, is

00:00:30.350 --> 00:00:32.210
going to be a positive
number, right?

00:00:32.210 --> 00:00:35.170
So you could say that x minus
3 squared is going to be

00:00:35.170 --> 00:00:37.920
greater than or equal
to 0, right?

00:00:37.920 --> 00:00:39.820
0 is kind of its
minimum point.

00:00:39.820 --> 00:00:43.080
So this whole value is going
to be as small as possible

00:00:43.080 --> 00:00:46.700
when x minus 3 squared is as
small as possible, right?

00:00:46.700 --> 00:00:48.330
Because that's the variable
part of it.

00:00:48.330 --> 00:00:50.790
And this is going to be as small
as possible when x minus

00:00:50.790 --> 00:00:52.470
3 is equal to 0.

00:00:52.470 --> 00:00:54.700
And when is x minus 3 going
to be equal to 0?

00:00:54.700 --> 00:00:55.440
We could write it out.

00:00:55.440 --> 00:00:58.110
When is x minus 3 equal to 0?

00:00:58.110 --> 00:00:59.330
Well, add 3 to both sides.

00:00:59.330 --> 00:01:01.050
It's when x is equal to 3.

00:01:01.050 --> 00:01:05.840
So y is lowest when x minus
3 is equal to 0 or

00:01:05.840 --> 00:01:07.350
x is equal to 3.

00:01:07.350 --> 00:01:08.850
And that's choice D.

00:01:08.850 --> 00:01:11.660
And all you have to recognize is
the lowest value that this

00:01:11.660 --> 00:01:16.360
function can attain is when this
term goes to 0, because

00:01:16.360 --> 00:01:17.720
otherwise it's a
positive term.

00:01:17.720 --> 00:01:19.700
It will only add to the 4.

00:01:19.700 --> 00:01:22.720
Next problem.

00:01:22.720 --> 00:01:24.000
56.

00:01:24.000 --> 00:01:27.720
Which of the following
is not equal to the

00:01:27.720 --> 00:01:28.990
square of an integer?

00:01:32.840 --> 00:01:36.120
So they say the square root
of the square root of 1.

00:01:36.120 --> 00:01:37.520
The square root of 1 is 1.

00:01:37.520 --> 00:01:41.380
And the square root of that
is going to be equal to 1.

00:01:41.380 --> 00:01:42.980
You could have said negative
1, but then that would have

00:01:42.980 --> 00:01:44.170
been undefined.

00:01:44.170 --> 00:01:44.600
Fair enough.

00:01:44.600 --> 00:01:46.700
One of the roots of
the roots is 1.

00:01:46.700 --> 00:01:48.490
And this is the square
of an integer, right?

00:01:48.490 --> 00:01:50.800
This is equal to 1 squared.

00:01:50.800 --> 00:01:51.930
2.

00:01:51.930 --> 00:01:53.660
Square root of 4.

00:01:53.660 --> 00:01:55.800
Square root of 4,
that equals 2.

00:01:55.800 --> 00:01:58.680
Now is that the square
of an integer?

00:01:58.680 --> 00:01:59.870
No.

00:01:59.870 --> 00:02:03.600
That's equal to square root of 2
squared, but this clearly is

00:02:03.600 --> 00:02:05.390
not an integer.

00:02:05.390 --> 00:02:06.180
Right?

00:02:06.180 --> 00:02:07.920
So the choice is 2.

00:02:07.920 --> 00:02:10.850
2 is not equal to the square
of an integer.

00:02:10.850 --> 00:02:13.570
We could look at
the other ones.

00:02:13.570 --> 00:02:14.800
18 divided by 2.

00:02:14.800 --> 00:02:15.070
Yes.

00:02:15.070 --> 00:02:16.510
9 is the square of 3.

00:02:16.510 --> 00:02:17.820
41 minus 25.

00:02:17.820 --> 00:02:18.820
That's 16.

00:02:18.820 --> 00:02:19.460
36.

00:02:19.460 --> 00:02:21.660
So all of the other ones are
squares of integers.

00:02:21.660 --> 00:02:22.190
That's a fairly

00:02:22.190 --> 00:02:25.318
straightforward problem, I think.

00:02:25.318 --> 00:02:30.140
We're on problem 57.

00:02:30.140 --> 00:02:32.890
Fermat primes are prime numbers
that can be written in

00:02:32.890 --> 00:02:38.890
the form 2 to the K plus 1,
where K is an integer and a

00:02:38.890 --> 00:02:40.140
power of 2.

00:02:53.530 --> 00:02:56.800
Which of the following is
not a Fermat prime?

00:02:56.800 --> 00:02:58.210
So A, 3.

00:02:58.210 --> 00:02:59.445
Well 3 is equal to what?

00:02:59.445 --> 00:03:04.050
It's equal to 2 to
the 1 plus 1.

00:03:04.050 --> 00:03:06.270
Right?

00:03:06.270 --> 00:03:08.750
And in this case K is 1,
which is a power of 2.

00:03:08.750 --> 00:03:10.880
That's 2 to the 0.

00:03:10.880 --> 00:03:14.180
B is 5.

00:03:14.180 --> 00:03:15.100
Well, 5 is what?

00:03:15.100 --> 00:03:19.030
That equals 2 squared plus 1.

00:03:19.030 --> 00:03:19.800
4 plus 1.

00:03:19.800 --> 00:03:22.020
And this is definitely
a power of 2.

00:03:22.020 --> 00:03:23.190
2 is a power of 2.

00:03:23.190 --> 00:03:23.600
2

00:03:23.600 --> 00:03:25.180
to the 1st. C.

00:03:25.180 --> 00:03:27.850
17.

00:03:27.850 --> 00:03:30.640
That's 2 to the 4th plus 1.

00:03:30.640 --> 00:03:30.900
Right?

00:03:30.900 --> 00:03:34.350
2 to the 4th is 16 plus
1 and 4 is 2 squared.

00:03:34.350 --> 00:03:36.530
So that's a power of 2.

00:03:36.530 --> 00:03:38.330
Choice D.

00:03:38.330 --> 00:03:43.120
31.

00:03:43.120 --> 00:03:45.710
The closest power, if we
subtract 1 from it.

00:03:50.330 --> 00:03:53.960
2 to something does not
equal 30, right?

00:03:53.960 --> 00:03:56.510
That would have to be true
if 2 to the K plus

00:03:56.510 --> 00:03:57.720
1 is equal to 31.

00:03:57.720 --> 00:04:00.060
Then 2 to the K would
have to equal 30.

00:04:00.060 --> 00:04:02.250
And I can't think of an integer
where I take 2 to some

00:04:02.250 --> 00:04:03.110
power and get 30.

00:04:03.110 --> 00:04:04.800
So the choice is D.

00:04:04.800 --> 00:04:06.120
D is not a Fermat prime.

00:04:06.120 --> 00:04:08.725
And if you wanted to make
sure that it's not E.

00:04:08.725 --> 00:04:10.400
E is 257.

00:04:10.400 --> 00:04:13.120
Well that's just 2 to
the 8th plus 1.

00:04:13.120 --> 00:04:15.570
2 to the 8th is 256.

00:04:15.570 --> 00:04:18.120
And that's 257.

00:04:18.120 --> 00:04:20.589
So the answer is D.

00:04:20.589 --> 00:04:25.720
58.

00:04:25.720 --> 00:04:37.440
If x squared is equal to 2y to
the third, and 2y is equal to

00:04:37.440 --> 00:04:46.500
4, they want to know what x
squared plus y is equal to.

00:04:46.500 --> 00:04:48.730
OK, x squared plus y.

00:04:48.730 --> 00:04:49.900
Well, they tell us
that x squared is

00:04:49.900 --> 00:04:51.055
equal to y to the third.

00:04:51.055 --> 00:04:53.320
So let's just substitute that.

00:04:53.320 --> 00:04:53.640
Right?

00:04:53.640 --> 00:04:59.720
So then we get 2y to the third
plus y, using this information

00:04:59.720 --> 00:05:01.170
and that information.

00:05:01.170 --> 00:05:02.810
And they tell us 2y
is equal to 4.

00:05:02.810 --> 00:05:06.360
Well, just divide both sides by
2, you get y is equal to 2.

00:05:06.360 --> 00:05:08.730
So let's substitute
that into this.

00:05:08.730 --> 00:05:10.500
What's 2 to the third power?

00:05:10.500 --> 00:05:15.300
Well, that's 8 plus 2.

00:05:15.300 --> 00:05:17.360
So I don't want to divide.

00:05:17.360 --> 00:05:21.800
So that equals 16 plus 2,
which is equal to 18.

00:05:21.800 --> 00:05:24.440
Which is choice E.

00:05:24.440 --> 00:05:28.180
Next problem.

00:05:28.180 --> 00:05:31.290
59.

00:05:31.290 --> 00:05:40.270
A glucose solution contains 15
grams of glucose per 100 cubic

00:05:40.270 --> 00:05:41.690
centimeters of solution.

00:05:50.140 --> 00:05:54.120
If 45 cubic centimeters of the
solution were poured into an

00:05:54.120 --> 00:05:56.770
empty container, how many grams
of glucose would be in

00:05:56.770 --> 00:05:58.140
the container?

00:05:58.140 --> 00:05:59.090
So we can just set up a ratio.

00:05:59.090 --> 00:06:02.500
We have 15 grams per 100, so how
many grams are we going to

00:06:02.500 --> 00:06:10.000
have per 45 centimeters cubed?

00:06:10.000 --> 00:06:11.230
How many grams, right?

00:06:11.230 --> 00:06:12.550
So they still want to
know grams. All the

00:06:12.550 --> 00:06:14.150
units are the same.

00:06:14.150 --> 00:06:16.820
And so let's see if we
can cross multiply.

00:06:16.820 --> 00:06:20.950
We could say 15 times 45 is
equal to 100 times x.

00:06:20.950 --> 00:06:29.820
So 15 times 45 is
equal to 100x.

00:06:29.820 --> 00:06:31.140
And just to make the
math easy, let's

00:06:31.140 --> 00:06:32.240
divide by some numbers.

00:06:32.240 --> 00:06:34.930
Let's divide both sides by 5.

00:06:34.930 --> 00:06:39.395
So then this becomes 20
and this becomes 9.

00:06:39.395 --> 00:06:42.420
We could divide both sides by 5
again and then this becomes

00:06:42.420 --> 00:06:45.430
4 and this becomes 3.

00:06:45.430 --> 00:06:47.080
And now the numbers are
easy to deal with.

00:06:47.080 --> 00:06:52.750
3 times 9 is 27 is
equal to 4x.

00:06:52.750 --> 00:06:53.860
Divide both sides by 4.

00:06:53.860 --> 00:06:59.970
You get x is equal to 27/4.

00:06:59.970 --> 00:07:02.540
27/4 and 4 goes into 27.

00:07:02.540 --> 00:07:02.990
what is that?

00:07:02.990 --> 00:07:10.590
That is equal to and 6 and 3/4,
and all their numbers are

00:07:10.590 --> 00:07:13.160
in decimals, so that's 6.75.

00:07:13.160 --> 00:07:14.860
Which is E.

00:07:14.860 --> 00:07:15.080
Right?

00:07:15.080 --> 00:07:17.120
4 times 6 is 24, and you
have 3 left over.

00:07:17.120 --> 00:07:19.120
Right.

00:07:19.120 --> 00:07:20.150
Next problem.

00:07:20.150 --> 00:07:25.790
Problem 60.

00:07:25.790 --> 00:07:29.500
In the figure of P, Q, R,
S is a parallelogram.

00:07:29.500 --> 00:07:30.480
Let me draw this.

00:07:30.480 --> 00:07:32.680
This looks interesting.

00:07:32.680 --> 00:07:35.046
So I have to draw a
couple of lines.

00:07:35.046 --> 00:07:37.480
That's one line.

00:07:37.480 --> 00:07:39.260
And they have another
line that looks

00:07:39.260 --> 00:07:40.510
something like that.

00:07:43.700 --> 00:07:44.475
It's a parallelogram.

00:07:44.475 --> 00:07:47.076
Let me connect the lines.

00:07:47.076 --> 00:07:48.570
It looks like that.

00:07:52.125 --> 00:07:54.880
Let's see, this line actually
keeps going.

00:07:54.880 --> 00:07:56.880
Let me draw that in.

00:07:56.880 --> 00:07:58.330
They tell us, this is P.

00:07:58.330 --> 00:07:59.970
This is Q.

00:07:59.970 --> 00:08:02.000
This is R.

00:08:02.000 --> 00:08:04.165
And this is S.

00:08:04.165 --> 00:08:10.720
And they tell us that
this is 140 degrees.

00:08:10.720 --> 00:08:12.460
They tell us that this is 2y.

00:08:15.960 --> 00:08:19.730
And they tell us
that this is x.

00:08:19.730 --> 00:08:21.700
And then they say, in
the figure above,

00:08:21.700 --> 00:08:25.080
what is y minus x?

00:08:25.080 --> 00:08:27.110
So since we know this is a
parallelogram, we know that

00:08:27.110 --> 00:08:29.720
this line is parallel to this
line, and we know that this

00:08:29.720 --> 00:08:31.910
line is parallel to that line.

00:08:31.910 --> 00:08:34.280
That actually tells us a lot of
information, especially if

00:08:34.280 --> 00:08:35.770
we continue the lines over.

00:08:35.770 --> 00:08:38.000
Then everything we learned in
geometry about parallel lines

00:08:38.000 --> 00:08:40.250
starts to hold.

00:08:40.250 --> 00:08:42.110
Let me draw it in a
different color.

00:08:42.110 --> 00:08:46.300
So if this line, in green, is
parallel to this line, then

00:08:46.300 --> 00:08:47.940
you can view this line right
here as a bit of a

00:08:47.940 --> 00:08:49.410
transversal.

00:08:49.410 --> 00:08:52.480
And 140 degrees and 2y are
corresponding angles.

00:08:52.480 --> 00:08:54.030
So they're actually going
to equal each other.

00:08:54.030 --> 00:08:55.840
And you can even eyeball it and
think about, well, that

00:08:55.840 --> 00:08:56.320
make sense.

00:08:56.320 --> 00:08:57.970
Those lines are parallel.

00:08:57.970 --> 00:09:01.090
So 140 degrees is equal to 2y.

00:09:01.090 --> 00:09:03.630
y is equal to 70.

00:09:03.630 --> 00:09:04.880
Fair enough.

00:09:06.960 --> 00:09:12.400
And now let's consider-- let me
switch colors-- that this

00:09:12.400 --> 00:09:17.510
line right here, this magenta
line and this magenta line,

00:09:17.510 --> 00:09:18.860
those two are parallel.

00:09:18.860 --> 00:09:21.720
And we can now view this
as a transversal.

00:09:21.720 --> 00:09:23.700
Right?

00:09:23.700 --> 00:09:27.730
If this is a transversal, then
the 70 degrees and this angle

00:09:27.730 --> 00:09:30.370
are corresponding angles, so
they're going to be equal.

00:09:30.370 --> 00:09:32.600
So that's 70.

00:09:32.600 --> 00:09:34.910
And then this angle up here,
that 70 degrees that I just

00:09:34.910 --> 00:09:38.160
drew, and the x angle, they're
supplementary, right?

00:09:38.160 --> 00:09:39.670
They add up to 180.

00:09:39.670 --> 00:09:44.830
So you have x plus 70
is equal to 180.

00:09:44.830 --> 00:09:51.210
So you get x is equal
to 110 degrees.

00:09:51.210 --> 00:09:51.860
Oh, no, no, sorry.

00:09:51.860 --> 00:09:52.690
I made a mistake.

00:09:52.690 --> 00:09:54.100
I made a mistake.

00:09:54.100 --> 00:09:57.030
So this angle isn't 70.
y is equal to 70.

00:09:57.030 --> 00:10:00.450
But this angle is 2y, so
this is 140 degrees.

00:10:00.450 --> 00:10:00.810
Right?

00:10:00.810 --> 00:10:03.800
We figured out that this is 140
degrees, so this has to be

00:10:03.800 --> 00:10:05.230
140 degrees.

00:10:05.230 --> 00:10:07.020
And what my brain caught, I was
like, boy, that doesn't

00:10:07.020 --> 00:10:08.360
look like 70 degrees.

00:10:08.360 --> 00:10:09.900
70 degrees would be
a lot narrower.

00:10:09.900 --> 00:10:10.990
That looks more like 140.

00:10:10.990 --> 00:10:12.720
But anyway, this is 140.

00:10:12.720 --> 00:10:15.640
So if this is 140, the
corresponding angle up here is

00:10:15.640 --> 00:10:18.830
also going to be 140 degrees.

00:10:18.830 --> 00:10:21.550
And so, I did that wrong.

00:10:21.550 --> 00:10:26.210
x plus 140, right? x plus
this 140 degrees.

00:10:26.210 --> 00:10:27.260
The logic is still the same.

00:10:27.260 --> 00:10:28.570
They're supplementary.

00:10:28.570 --> 00:10:29.970
Equals 180.

00:10:29.970 --> 00:10:33.080
So x is equal to 40 degrees.

00:10:33.080 --> 00:10:34.520
And they wanted to know what?

00:10:34.520 --> 00:10:36.670
They wanted to know
what y minus x is.

00:10:36.670 --> 00:10:37.680
So that's 30.

00:10:37.680 --> 00:10:39.310
70 minus 40 is 30.

00:10:39.310 --> 00:10:42.030
And that's choice A.

00:10:42.030 --> 00:10:43.960
See you in the next video.


GMAT: Math 9

WEBVTT
Kind: captions
Language: en

00:00:00.920 --> 00:00:09.600
We're on problem 49.

00:00:09.600 --> 00:00:15.010
And it says, what is the square
root of 7 plus the

00:00:15.010 --> 00:00:18.210
square root of 7, and
all of that squared.

00:00:18.210 --> 00:00:20.230
So this is really just a little
bit of simplification.

00:00:20.230 --> 00:00:23.275
So if I have two of something,
in this case, I have 2 square

00:00:23.275 --> 00:00:26.880
roots of 7, if I add them
together, I get 2 of it, so I

00:00:26.880 --> 00:00:31.300
get 2 square roots of 7,
and I'm squaring that.

00:00:31.300 --> 00:00:33.960
And 2 square roots of 7 squared,
that's equal to 2

00:00:33.960 --> 00:00:38.070
squared times the square root
of 7 squared, right?

00:00:38.070 --> 00:00:41.270
That's just your exponent
properties, so that is equal

00:00:41.270 --> 00:00:44.490
to 4 times-- what's the square
root of 7 squared?

00:00:44.490 --> 00:00:47.100
Well, it's just 7, right?

00:00:47.100 --> 00:00:50.310
So it's 4 times 7, which
is equal to 28,

00:00:50.310 --> 00:00:53.120
which is choice C.

00:00:53.120 --> 00:00:54.160
Next problem.

00:00:54.160 --> 00:00:56.350
50.

00:00:56.350 --> 00:01:00.220
In a certain population, there
are three times as many people

00:01:00.220 --> 00:01:03.140
aged 21 or under as there
are people over 21.

00:01:03.140 --> 00:01:11.770
OK, so let's say that x is equal
to under 21 and y is

00:01:11.770 --> 00:01:14.300
equal to over 21.

00:01:14.300 --> 00:01:16.820
So in a certain population,
there are three times as many

00:01:16.820 --> 00:01:26.620
people aged 21 or under as
there are people over 21.

00:01:26.620 --> 00:01:28.960
So this is the number of people
under 21 and there are

00:01:28.960 --> 00:01:34.050
three times as many as
there are over 21.

00:01:34.050 --> 00:01:40.750
The ratio of those 21 or under
to the total population is?

00:01:40.750 --> 00:01:45.360
So they want to know the ratio
of x, 21 or under, to the

00:01:45.360 --> 00:01:50.765
total population, not just to
the over 21 population.

00:01:50.765 --> 00:01:52.890
So what's the total
population?

00:01:52.890 --> 00:01:57.240
That's everyone, right? x plus
y is equal to total.

00:01:57.240 --> 00:01:59.675
So what they want is the
ratio of x to x plus y.

00:02:06.400 --> 00:02:10.460
And then we could do a little
bit of substitution.

00:02:10.460 --> 00:02:12.420
We know x is equal
to 3y, so let's

00:02:12.420 --> 00:02:13.450
substitute that into this.

00:02:13.450 --> 00:02:15.370
Remember, this is the ratio
they're trying to figure out:

00:02:15.370 --> 00:02:19.030
the ratio of 21 or under to
the total population.

00:02:19.030 --> 00:02:23.470
So x is equal to 3y
over 3y plus y.

00:02:23.470 --> 00:02:26.280
And I just did that because,
wow, if we do that then it

00:02:26.280 --> 00:02:28.470
looks like we could be able
to cancel out all the y's.

00:02:28.470 --> 00:02:31.950
So we get 3y over what?

00:02:31.950 --> 00:02:33.700
What's 3y plus another y?

00:02:33.700 --> 00:02:35.210
Well, it's 4y.

00:02:35.210 --> 00:02:36.460
The y's cancel out.

00:02:36.460 --> 00:02:37.950
You get 3/4.

00:02:37.950 --> 00:02:40.020
And that is choice E, 3:4.

00:02:43.240 --> 00:02:45.530
Next question.

00:02:45.530 --> 00:02:49.930
51.

00:02:49.930 --> 00:02:51.370
And actually, you know, you
didn't even have to do it

00:02:51.370 --> 00:02:52.040
algebraically.

00:02:52.040 --> 00:02:53.710
If you just think about question
50, you could have

00:02:53.710 --> 00:02:54.540
just played with numbers.

00:02:54.540 --> 00:02:56.490
You can say, OK, there are three
times as many people

00:02:56.490 --> 00:02:59.110
aged 21 or under as there
are people over 21.

00:02:59.110 --> 00:03:01.330
So you just say, OK, if there's
one person over 21,

00:03:01.330 --> 00:03:04.300
there'd be three people under
21, and there'd be a total of

00:03:04.300 --> 00:03:05.900
four people, so it
would be 3:4.

00:03:05.900 --> 00:03:09.640
But anyway, either way it
didn't take us too long.

00:03:09.640 --> 00:03:12.510
So they've drawn
a figure here.

00:03:12.510 --> 00:03:15.520
Let me draw it as well.

00:03:15.520 --> 00:03:19.450
So they have two lines that
intersect something like that.

00:03:19.450 --> 00:03:25.700
And they say that this angle
right here is 3x degrees.

00:03:25.700 --> 00:03:29.510
This angle is y plus 30 degrees,
and they say this

00:03:29.510 --> 00:03:33.130
angle is 2x degrees.

00:03:33.130 --> 00:03:37.030
And they say, in the figure
above, the value of y is what?

00:03:37.030 --> 00:03:39.090
Well, there's a bunch of
ways you can do it.

00:03:39.090 --> 00:03:41.220
The way this pops out to me is
we could figure out x because

00:03:41.220 --> 00:03:45.850
we know that this angle plus
this angle is equal to 180

00:03:45.850 --> 00:03:48.530
degrees, because they
are supplementary.

00:03:48.530 --> 00:03:51.060
They go all the way halfway
around a circle.

00:03:51.060 --> 00:03:57.010
So we know that if we add 3x
plus 2x, that should equal 180

00:03:57.010 --> 00:04:01.330
degrees, or 5x is
equal to 180.

00:04:01.330 --> 00:04:03.330
Or that x is equal to what?

00:04:05.836 --> 00:04:09.870
Let's see, 30 times 5 is 150,
then you have 30 left over, so

00:04:09.870 --> 00:04:12.120
it's 36 degrees, right?

00:04:12.120 --> 00:04:15.090
36 times 5 is, yep, 180.

00:04:15.090 --> 00:04:20.610
And now we know if x is 36
degrees, what is this angle?

00:04:20.610 --> 00:04:22.200
Well, this angle is going
to be 72 degrees.

00:04:22.200 --> 00:04:23.920
It's 2 times x.

00:04:23.920 --> 00:04:24.920
72 degrees.

00:04:24.920 --> 00:04:28.030
And then this angle and this
angle are opposite angles.

00:04:28.030 --> 00:04:31.570
And you could do the angle game
module on Khan Academy,

00:04:31.570 --> 00:04:33.810
if that doesn't ring a bell,
but that should ring a bell

00:04:33.810 --> 00:04:34.440
from geometry.

00:04:34.440 --> 00:04:35.270
And there's another way
you could do it.

00:04:35.270 --> 00:04:39.020
You could say that this angle
plus this angle have to equal

00:04:39.020 --> 00:04:39.990
180, either way.

00:04:39.990 --> 00:04:40.590
You could do it either way.

00:04:40.590 --> 00:04:43.180
But the easiest way is to say
that this angle and this angle

00:04:43.180 --> 00:04:45.680
are equal, because they're
opposite angles.

00:04:45.680 --> 00:04:50.210
So we know that y plus
30 has to equal this

00:04:50.210 --> 00:04:54.190
angle, equals 72.

00:04:54.190 --> 00:04:57.330
Subtract 30 from both sides,
you get y is equal to 42

00:04:57.330 --> 00:05:02.170
degrees, which is choice E.

00:05:02.170 --> 00:05:04.480
Next problem.

00:05:04.480 --> 00:05:07.600
Let me make it a different
color now.

00:05:07.600 --> 00:05:09.440
52.

00:05:09.440 --> 00:05:12.560
Kelly and Chris packed several
boxes with books.

00:05:12.560 --> 00:05:28.220
If Chris packed 60% of the total
number of boxes, what

00:05:28.220 --> 00:05:32.420
was the ratio of the number of
boxes Kelly packed to the

00:05:32.420 --> 00:05:35.130
number of boxes Chris packed?

00:05:35.130 --> 00:05:38.865
So they want to know the ratio
of Kelly to Chris, right?

00:05:38.865 --> 00:05:42.640
Well, if Chris packed 60% of the
total, we could say, let C

00:05:42.640 --> 00:05:45.030
be the number that Chris packed,
so that'll be equal to

00:05:45.030 --> 00:05:47.660
0.6 of the total.

00:05:47.660 --> 00:05:49.480
Well, then that means that
Kelly packed the

00:05:49.480 --> 00:05:50.330
rest of them, right?

00:05:50.330 --> 00:05:54.090
So, I'm assuming it's a she,
Kelly would have packed the

00:05:54.090 --> 00:05:58.630
remainder, which is
40% of the total.

00:05:58.630 --> 00:06:01.800
So the ratio of the number
that Chris-- what do

00:06:01.800 --> 00:06:02.730
they want to know?

00:06:02.730 --> 00:06:05.190
What was the ratio of the number
of boxes Kelly packed

00:06:05.190 --> 00:06:08.170
to the number of boxes
Chris packed.

00:06:08.170 --> 00:06:09.990
So the want to know the
ratio of K to C.

00:06:09.990 --> 00:06:15.770
Well, K is 0.4T and C is 0.6T.

00:06:15.770 --> 00:06:17.170
T's cancel out.

00:06:17.170 --> 00:06:20.350
You get, essentially, 4/6,
which is 2/3, right?

00:06:20.350 --> 00:06:22.150
If you multiply the top and the
bottom by 10, it becomes

00:06:22.150 --> 00:06:29.450
4/6, so you get 2:3, and
that is choice E.

00:06:32.220 --> 00:06:37.270
Problem 53.

00:06:37.270 --> 00:06:44.070
Of the following, which is the
closest approximation of 50.2

00:06:44.070 --> 00:06:49.100
times 0.49 over 199.8?

00:06:49.100 --> 00:06:51.220
So I haven't looked at the
choices yet, but if I had to

00:06:51.220 --> 00:06:54.120
approximate what this is, I
would say, well, that's close

00:06:54.120 --> 00:06:56.210
to 50, right?

00:06:56.210 --> 00:07:01.700
50.2 is really close to 50
times-- 0.49 is really close

00:07:01.700 --> 00:07:05.920
to 0.5, all of that over--
199.8 is really

00:07:05.920 --> 00:07:09.870
close to 200, right?

00:07:09.870 --> 00:07:12.215
So you could view this
as being equal to

00:07:12.215 --> 00:07:17.620
-- let's see, 25/200.

00:07:17.620 --> 00:07:22.540
And 25/200, you could divide the
top and the bottom by 25.

00:07:22.540 --> 00:07:26.030
You get 1 over-- 25 goes into
100 four times, goes into

00:07:26.030 --> 00:07:27.850
200-- eight times.

00:07:27.850 --> 00:07:30.190
And that is one of our choices,
so I'll go with that.

00:07:30.190 --> 00:07:31.730
B.

00:07:31.730 --> 00:07:34.150
1/8.

00:07:34.150 --> 00:07:40.980
Problem 54.

00:07:40.980 --> 00:07:49.800
The average of 10, 30, and 50.

00:07:49.800 --> 00:07:54.550
So the average is going to
be 10 plus 30 plus 50.

00:07:54.550 --> 00:07:59.280
So the average of those three
is that, divided by 3.

00:07:59.280 --> 00:08:00.300
First of all, what is that?

00:08:00.300 --> 00:08:02.730
Well, it looks like it
should be 30, right?

00:08:02.730 --> 00:08:06.020
Because you get 60 plus
30/3, so that's 90.

00:08:06.020 --> 00:08:14.630
So the average of 10, 30, and 50
is 5 more than the average

00:08:14.630 --> 00:08:25.570
of 20, 40, and one of
the choices, and x.

00:08:25.570 --> 00:08:28.060
So to write this, we say, OK,
we figured out that the

00:08:28.060 --> 00:08:32.950
average-- oh, sorry, the average
here isn't-- sorry,

00:08:32.950 --> 00:08:34.520
let me redo this for you.

00:08:34.520 --> 00:08:37.210
So they say the average of 10,
30, and 50, and we already

00:08:37.210 --> 00:08:39.960
figured out 10 plus
30 plus 50.

00:08:39.960 --> 00:08:45.120
If you average that, divided by
3, you get 90 divided by 3

00:08:45.120 --> 00:08:45.950
is equal to 30.

00:08:45.950 --> 00:08:47.740
And you actually didn't even
have to do the math.

00:08:47.740 --> 00:08:49.620
You could have said, oh, we'll
have 30 in the middle.

00:08:49.620 --> 00:08:51.990
50 is 20 more than 30.

00:08:51.990 --> 00:08:53.360
10 is 20 less than 30.

00:08:53.360 --> 00:08:54.220
So the average is
going to be 30.

00:08:54.220 --> 00:08:55.850
But this didn't take
you much time.

00:08:55.850 --> 00:08:57.520
So the average is 30.

00:08:57.520 --> 00:09:02.030
And they say that that is 5 more
than the average of 20,

00:09:02.030 --> 00:09:03.900
40, and another number.

00:09:03.900 --> 00:09:08.080
So 30 is equal to 5
plus the average

00:09:08.080 --> 00:09:09.590
of those three numbers.

00:09:09.590 --> 00:09:15.260
So the average of those three
numbers is 20 plus 40 plus x,

00:09:15.260 --> 00:09:18.130
over 3, right?

00:09:18.130 --> 00:09:19.805
So let's just simplify this.

00:09:19.805 --> 00:09:21.600
Let's subtract 5 from
both sides.

00:09:21.600 --> 00:09:28.745
You get 25 is equal to 20
plus 40 plus x, over 3.

00:09:28.745 --> 00:09:31.760
So you multiply both
sides by 3.

00:09:31.760 --> 00:09:39.190
You get 75 is equal
to 60 plus x.

00:09:39.190 --> 00:09:41.250
And then you subtract
60 from both sides.

00:09:41.250 --> 00:09:46.060
You get x is equal to 15,
and that is choice A.

00:09:46.060 --> 00:09:47.815
And I'm almost out of
time, so I'll see

00:09:47.815 --> 00:09:48.690
you in the next video.

00:09:48.690 --> 00:09:50.100
See you soon.