GMAT: Math 51

WEBVTT
Kind: captions
Language: en

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We're on problem 237.

00:00:04.390 --> 00:00:08.490
A part-time employee whose
hourly wage was increased by

00:00:08.490 --> 00:00:12.520
25% decided to reduce the number
of hours worked per

00:00:12.520 --> 00:00:15.320
week so that the employee's
total weekly income would

00:00:15.320 --> 00:00:16.630
remain unchanged.

00:00:16.630 --> 00:00:19.110
By what percent should
the number of

00:00:19.110 --> 00:00:21.740
hours worked be reduced?

00:00:21.740 --> 00:00:26.790
So before, he made his
hourly wage times

00:00:26.790 --> 00:00:28.280
hours worked, right?

00:00:28.280 --> 00:00:31.730
This is what he would normally
work in a week, right?

00:00:31.730 --> 00:00:34.730
So his wage per hour times
hours per week.

00:00:34.730 --> 00:00:36.250
This is what he used to make.

00:00:36.250 --> 00:00:40.550
But now what he's done is since
he's making 25% more of

00:00:40.550 --> 00:00:48.200
his wage, he's going to reduce
his hours by some number, by

00:00:48.200 --> 00:00:49.310
some fraction.

00:00:49.310 --> 00:00:52.390
Let's call that x.

00:00:52.390 --> 00:00:56.050
So then the new wage times the
new hours , and they're saying

00:00:56.050 --> 00:00:57.410
that he doesn't want to change
the total amount that

00:00:57.410 --> 00:00:58.430
he makes in a week.

00:00:58.430 --> 00:01:01.780
So the new wage times the new
hours will equal w times h.

00:01:01.780 --> 00:01:04.530
Let's divide both sides by w.

00:01:04.530 --> 00:01:06.320
This goes to 1, that
goes to 1.

00:01:06.320 --> 00:01:08.250
Divide both sides by h.

00:01:08.250 --> 00:01:10.050
That goes to 1, that
goes to 1.

00:01:10.050 --> 00:01:15.640
And you're left with 1 is
equal to 1.25 times x.

00:01:15.640 --> 00:01:18.200
And I view that-- this is easier
to think of as what?

00:01:18.200 --> 00:01:19.780
5/4, right?

00:01:19.780 --> 00:01:21.400
1.25-- right?

00:01:21.400 --> 00:01:24.430
4/4 is 1, and then you
add another 1/4.

00:01:24.430 --> 00:01:26.130
This is 1 and 1/4,
so this is 5/4.

00:01:26.130 --> 00:01:29.350
So let's write that as 5/4x.

00:01:29.350 --> 00:01:33.950
Multiply both sides by 4/5,
you get x is equal to 4/5,

00:01:33.950 --> 00:01:36.320
which is equal to 0.8.

00:01:36.320 --> 00:01:39.610
So another way to view it is he
would reduce-- he's working

00:01:39.610 --> 00:01:46.470
80% of the hours that he used to
work, so he reduced by 20%

00:01:46.470 --> 00:01:47.960
the amount that he worked.

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And that will be choice B.

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Next problem, 238.

00:01:59.280 --> 00:02:03.230
OK, they've drawn us a figure,
so let's draw the figure.

00:02:07.190 --> 00:02:10.550
Let me see if I could
make it thicker.

00:02:10.550 --> 00:02:14.170
OK, so they drew a box in a box,
and there's another box

00:02:14.170 --> 00:02:17.180
in that box, and it looks
something like that.

00:02:17.180 --> 00:02:21.350
And then they shaded it in,
so I'll shade it in.

00:02:23.950 --> 00:02:29.710
And they say that this side up
here is 18, and they say that

00:02:29.710 --> 00:02:33.560
this side over here is 15.

00:02:33.560 --> 00:02:36.300
The shaded region in the figure
above represents a

00:02:36.300 --> 00:02:40.210
rectangular frame with length 18
inches and width 15 inches.

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The frame encloses a rectangular
picture that has

00:02:42.300 --> 00:02:45.730
the same area as this
frame itself.

00:02:45.730 --> 00:02:48.160
So this area is equal
to this area.

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Fascinating.

00:02:51.450 --> 00:02:55.020
If the length and width of the
picture have the same ratio as

00:02:55.020 --> 00:02:59.430
the length and width of the
frame, what is the length of

00:02:59.430 --> 00:03:01.910
the picture in inches?

00:03:01.910 --> 00:03:04.670
So they're saying that this is
the length, so this is l.

00:03:08.360 --> 00:03:09.350
And this is the width.

00:03:09.350 --> 00:03:12.600
And they want us
to solve for l.

00:03:12.600 --> 00:03:14.040
What is the length of
the picture, right?

00:03:14.040 --> 00:03:16.340
They're calling-- I mean, I
would call that width, but

00:03:16.340 --> 00:03:19.390
they originally say the frame
with length 18 inches.

00:03:19.390 --> 00:03:21.630
So they want to know the
length of the picture.

00:03:21.630 --> 00:03:24.310
OK, first of all, they tell us
that the ratios are the same.

00:03:24.310 --> 00:03:28.600
So l:w of the picture is the
same ratio as it is for the

00:03:28.600 --> 00:03:31.782
frame, is 18:15.

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You divide by 3.

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That's the same thing as 6:5,
right? l:w is equal to 6:5.

00:03:36.660 --> 00:03:39.590
And the other thing they told
us is that the area of the

00:03:39.590 --> 00:03:42.000
picture the same as the
area of the frame.

00:03:42.000 --> 00:03:46.000
So the area the picture is
l times w, and what's

00:03:46.000 --> 00:03:47.360
the area the frame?

00:03:47.360 --> 00:03:52.960
What's the area of this whole
thing , which is 15 times 18,

00:03:52.960 --> 00:03:55.560
minus the area of the
picture, right?

00:03:55.560 --> 00:03:57.350
Because the area of the frame
is not this whole rectangle.

00:03:57.350 --> 00:03:59.090
It's just the part that doesn't
have the picture in

00:03:59.090 --> 00:04:02.990
it, so minus l times w.

00:04:02.990 --> 00:04:09.020
So if we add lw to both
sides, we get 2lw is

00:04:09.020 --> 00:04:12.060
equal to 15 times 18.

00:04:12.060 --> 00:04:17.019
I'm just going to leave
that as 15 times 18.

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Let's see, we could already
divide both sides by 2, so you

00:04:19.529 --> 00:04:27.080
get lw is equal to 15 times 9.

00:04:27.080 --> 00:04:29.290
And let's see, we have two
equations with two unknowns.

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Let's see if we can solve.

00:04:30.150 --> 00:04:32.630
So we have l/w is
equal to 6/5.

00:04:32.630 --> 00:04:38.420
We can cross-multiply, so we
get 5l is equal to 6w.

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I ignored the stuff
in the middle.

00:04:40.990 --> 00:04:42.790
And we want to solve
for l, right?

00:04:42.790 --> 00:04:44.160
So let's substitute for w.

00:04:44.160 --> 00:04:52.320
So we get 5/6l is equal to w,
and now let's substitute that

00:04:52.320 --> 00:04:53.760
into this equation.

00:04:53.760 --> 00:05:05.110
So we have l times w, which is
5/6l, is equal to 15 times 9.

00:05:05.110 --> 00:05:09.520
And let's see, let's multiply
both sides by 6/5, and so you

00:05:09.520 --> 00:05:21.210
would get l squared is equal to
15 times 9 times 6 over 5.

00:05:21.210 --> 00:05:23.500
So let's see, we could do
a little simplification.

00:05:23.500 --> 00:05:29.320
This becomes 3, this becomes
1, and then we have-- let's

00:05:29.320 --> 00:05:32.850
see, now we have to
do some math.

00:05:32.850 --> 00:05:35.372
3 times 9 is 27.

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27 times 6 is what?

00:05:41.390 --> 00:05:44.150
7 times 6 is 42.

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2 times 6 is 12,
plus 4 is 161.

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That's a strange number.

00:05:58.190 --> 00:06:00.600
So let's see if I can
simplify this.

00:06:00.600 --> 00:06:02.180
Oh, I'm looking at choices,
and they have all sorts of

00:06:02.180 --> 00:06:03.410
crazy square roots in it.

00:06:03.410 --> 00:06:11.320
So let's just say that l is
equal to the square root of--

00:06:11.320 --> 00:06:13.640
let's see, how can
we rewrite this?

00:06:13.640 --> 00:06:17.820
We could rewrite the 6
as 3 times 2, right?

00:06:17.820 --> 00:06:22.170
So then we get 3 times 9 times
3, that's the same

00:06:22.170 --> 00:06:23.210
thing as 9 times 9.

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That's 81, right?

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81 times 2.

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And we have a 1 in
the denominator.

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So l is equal to 9, and I'll
do one more step, because I

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think this confuses
a lot of people.

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That's equal to the square root
of 81 times the square

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root of 2, which is equal
to 9 square roots of 2,

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which is choice A.

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Problem 239.

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Of the 200 students at College
T majoring in one or more of

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the sciences-- I already feel
a Venn diagram coming on.

00:07:01.630 --> 00:07:05.360
Of the 200 students at College
T majoring in one or more of

00:07:05.360 --> 00:07:09.750
the sciences, 130 are majoring--
so let me draw the

00:07:09.750 --> 00:07:11.460
whole-- well, let me read
the whole problem.

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130 are majoring in
chemistry and 150

00:07:14.200 --> 00:07:15.640
are majoring in biology.

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If at least 30 of the students
are not majoring in either

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chemistry or biology, then the
number of students majoring in

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both chemistry and biology can
be any number from-- OK, let

00:07:24.090 --> 00:07:26.370
me draw the Venn diagram.

00:07:26.370 --> 00:07:31.930
So that's chemistry, that's
biology, and then there's a

00:07:31.930 --> 00:07:33.350
leftover, right?

00:07:33.350 --> 00:07:35.660
This is a whole pool.

00:07:35.660 --> 00:07:38.920
So they tell us there's
200 total, right?

00:07:38.920 --> 00:07:41.010
There's 200 total.

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And they say that 130 are
majoring in chemistry, 150 in

00:07:47.780 --> 00:07:53.530
biology, and then at least 30
of the students are not

00:07:53.530 --> 00:07:57.830
majoring in either chemistry
or biology, so we could say

00:07:57.830 --> 00:08:00.350
greater than or equal to 30.

00:08:00.350 --> 00:08:03.380
So this is driving a little
spin here by making it an

00:08:03.380 --> 00:08:04.240
inequality.

00:08:04.240 --> 00:08:06.910
Then the number of students
majoring in both chemistry and

00:08:06.910 --> 00:08:13.770
biology could be any number
from-- OK, so let's say that

00:08:13.770 --> 00:08:16.120
this is 30, just to simplify
our thinking.

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If this is 30, how many
people are majoring in

00:08:18.850 --> 00:08:21.270
chemistry or biology?

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Well, then it's 170, right?

00:08:24.170 --> 00:08:25.660
So let's think of it this way.

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Let's think of this as the
intercept-- this is both.

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Well, I used B for biology.

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So let's call this-- I don't
know, let's call this-- I used

00:08:33.640 --> 00:08:35.200
C for combined.

00:08:35.200 --> 00:08:38.760
So let's call this I for
the intersection.

00:08:38.760 --> 00:08:44.360
So if 30 people are majoring
in-- well, actually, let's

00:08:44.360 --> 00:08:47.730
just call this x.

00:08:47.730 --> 00:08:50.000
So how many people are majoring
in-- if I wanted to

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add these two numbers up, if I
want to know the people who

00:08:53.040 --> 00:08:56.090
are in chemistry or biology,
what would it be?

00:08:56.090 --> 00:09:04.100
It would be 130 plus 150, and
remember, and we've done this

00:09:04.100 --> 00:09:06.440
a couple of times with these
Venn diagram problems, if I

00:09:06.440 --> 00:09:12.200
counted these 130, and then I
count these 150, I've counted

00:09:12.200 --> 00:09:13.260
this intersection twice.

00:09:13.260 --> 00:09:16.830
I counted it with the 130, and
I counted with the 150.

00:09:16.830 --> 00:09:19.610
So I have to subtract out at
least the intersection once.

00:09:19.610 --> 00:09:21.250
So I subtract it out once.

00:09:21.250 --> 00:09:25.320
So these are the number of
people who are in chemistry or

00:09:25.320 --> 00:09:26.800
biology or both, right?

00:09:26.800 --> 00:09:29.630
So it's the intersection of
chemistry or biology or both.

00:09:29.630 --> 00:09:36.960
And now we know that that has
got to be equal to what?

00:09:36.960 --> 00:09:40.870
Well, 200 minus the people who
are in nothing, right?

00:09:40.870 --> 00:09:43.260
So I'm going to call
that x for now.

00:09:43.260 --> 00:09:46.605
200 minus the people
who are nothing.

00:09:46.605 --> 00:09:49.690
And let's see if we can solve
for the intersection, which is

00:09:49.690 --> 00:09:51.810
what they're asking
us in terms of x.

00:09:51.810 --> 00:10:02.260
So this becomes 280 minus I
is equal to 200 minus x.

00:10:02.260 --> 00:10:04.720
And then they tell us to
subtract 200 from both sides.

00:10:04.720 --> 00:10:08.890
You get 80 minus I is
equal to minus x.

00:10:08.890 --> 00:10:10.680
Let's add I to both sides.

00:10:10.680 --> 00:10:17.820
So you get 80 is equal
to I minus x, right?

00:10:17.820 --> 00:10:21.010
Or even better, let's
add x to both sides.

00:10:21.010 --> 00:10:31.380
So you get I is equal
to 80 plus x.

00:10:31.380 --> 00:10:35.680
And so, if x is greater than
or equal to 30-- so we know

00:10:35.680 --> 00:10:39.770
that if x is 30, then
we get what?

00:10:39.770 --> 00:10:45.270
We get 130 plus 80
is 110, right?

00:10:45.270 --> 00:10:47.550
So we know that I is
going to be greater

00:10:47.550 --> 00:10:51.350
than or equal to 110.

00:10:51.350 --> 00:10:55.310
The intersection is
at least 110.

00:10:55.310 --> 00:10:56.750
Now, what's an upper
bound on it?

00:10:56.750 --> 00:10:59.960
How many people can
be studying both?

00:10:59.960 --> 00:11:01.860
And if you look at the choices
already, there's two choices

00:11:01.860 --> 00:11:05.170
that have 110 as the minimum for
the number studying both.

00:11:05.170 --> 00:11:08.010
But what's the maximum that
can be studying both?

00:11:08.010 --> 00:11:09.520
Well, it's 130, right?

00:11:09.520 --> 00:11:12.980
If all the chemistry people
are also studying biology,

00:11:12.980 --> 00:11:17.200
then the intersection
becomes 130, right?

00:11:17.200 --> 00:11:19.490
But you can't have 150 people
studying both, because there's

00:11:19.490 --> 00:11:21.780
only 150 studying chemistry.

00:11:21.780 --> 00:11:25.630
So the intersection is greater
than or equal to 110.

00:11:25.630 --> 00:11:28.300
And it's limited by the number
of people studying chemistry,

00:11:28.300 --> 00:11:32.340
130, which is choice D.

00:11:32.340 --> 00:11:34.770
And I'll see you in
the next video.


GMAT: Math 53

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:04.590
We're on problem 245.

00:00:04.590 --> 00:00:14.410
If x plus y is equal to a, and
x minus y is equal to b, then

00:00:14.410 --> 00:00:19.070
what is-- they want to know
what 2xy is equal to.

00:00:19.070 --> 00:00:21.760
Let's solve for x and y in terms
of a and b, and then

00:00:21.760 --> 00:00:23.520
just figure out what
this equals to.

00:00:23.520 --> 00:00:26.030
So we have two equations
with two unknowns.

00:00:26.030 --> 00:00:28.650
Let's just add them together
to solve for x.

00:00:28.650 --> 00:00:32.470
We get x plus x is 2x-- the
y's cancel out-- is

00:00:32.470 --> 00:00:34.953
equal to a plus b.

00:00:34.953 --> 00:00:39.990
Or x is equal to a
plus b over 2.

00:00:39.990 --> 00:00:44.540
Now if we had x plus
y is equal to a-- I

00:00:44.540 --> 00:00:45.560
just re-wrote this.

00:00:45.560 --> 00:00:48.090
And now if we multiply both
sides of this by negative 1,

00:00:48.090 --> 00:00:52.870
so we get minus x plus y
is equal to minus b.

00:00:52.870 --> 00:00:54.450
And now add these
two equations.

00:00:54.450 --> 00:00:58.570
So I'm essentially subtracting
this equation from that one.

00:00:58.570 --> 00:01:04.970
That cancels out, so I get 2y is
equal to a minus b, or y is

00:01:04.970 --> 00:01:09.650
equal to a minus b over 2.

00:01:09.650 --> 00:01:11.750
And now we can figure out
what 2xy is equal to.

00:01:11.750 --> 00:01:21.090
2xy is equal to 2 times a
plus b over 2, times a

00:01:21.090 --> 00:01:23.530
minus b over 2.

00:01:23.530 --> 00:01:27.060
This 2 will cancel out with
one of these 2's.

00:01:27.060 --> 00:01:29.320
And we're left with--
and what's a plus b

00:01:29.320 --> 00:01:30.850
times a minus b?

00:01:30.850 --> 00:01:36.200
It's a squared minus
b squared over 2.

00:01:36.200 --> 00:01:37.450
Which is choice A.

00:01:40.500 --> 00:01:42.740
Problem 246.

00:01:42.740 --> 00:01:45.540
Let me do it in magenta.

00:01:45.540 --> 00:01:47.940
246.

00:01:47.940 --> 00:01:51.720
A rectangular circuit board is
to have width w inches-- let

00:01:51.720 --> 00:01:53.390
me draw it.

00:01:53.390 --> 00:01:58.710
So let's say it has width
w inches, perimeter of p

00:01:58.710 --> 00:02:02.070
inches-- so let me just put that
at the side right here--

00:02:02.070 --> 00:02:05.790
perimeter of p inches, and
area of k square inches.

00:02:05.790 --> 00:02:08.830
Which of the following equations
must be true?

00:02:08.830 --> 00:02:12.340
And so they want us to
relate this width to

00:02:12.340 --> 00:02:15.260
the area to the perimeter.

00:02:15.260 --> 00:02:16.390
Let me introduce another
variable.

00:02:16.390 --> 00:02:21.650
Let's call this, right here,
let's call this the height of

00:02:21.650 --> 00:02:23.450
the circuit board.

00:02:23.450 --> 00:02:25.010
So now we can do some
interesting things.

00:02:25.010 --> 00:02:27.170
If that's the height, then
that's also the height.

00:02:27.170 --> 00:02:29.620
If that's the width, then
this is also the width.

00:02:29.620 --> 00:02:31.350
So let's see what the
perimeter would be.

00:02:31.350 --> 00:02:38.610
It will be 2 times the width,
plus 2 times the height is

00:02:38.610 --> 00:02:41.490
equal to the perimeter.

00:02:41.490 --> 00:02:42.600
And then we could also
say width times

00:02:42.600 --> 00:02:44.040
height is equal to area.

00:02:44.040 --> 00:02:46.920
But if we can solve for height
in terms of the perimeter and

00:02:46.920 --> 00:02:49.550
the width, then we could use
that to get an expression that

00:02:49.550 --> 00:02:51.300
doesn't involve this variable.

00:02:51.300 --> 00:02:52.710
So let's do that.

00:02:52.710 --> 00:02:56.470
So if you divide both sides of
this by 2, you get width plus

00:02:56.470 --> 00:02:59.960
height is equal to
perimeter over 2.

00:02:59.960 --> 00:03:04.800
And then you get height is
equal to perimeter over 2

00:03:04.800 --> 00:03:06.050
minus width.

00:03:10.180 --> 00:03:13.870
And so the area, k, will
be equal to the

00:03:13.870 --> 00:03:16.550
width times the height.

00:03:16.550 --> 00:03:18.390
Instead of writing an h there,
let's write what we just

00:03:18.390 --> 00:03:19.380
figured out.

00:03:19.380 --> 00:03:23.720
p over 2 minus w.

00:03:27.230 --> 00:03:38.055
And then that is equal to
pw/2 minus w squared.

00:03:38.055 --> 00:03:40.720
Let's see, when I look at the
solution, they don't have any

00:03:40.720 --> 00:03:42.772
fractions in it, so let's
multiple both sides of the

00:03:42.772 --> 00:03:43.210
equation by 2.

00:03:43.210 --> 00:03:46.930
We can ignore this. k is equal
to pw/2 minus w squared.

00:03:46.930 --> 00:03:50.190
Multiply both sides by 2,
you get 2k is equal

00:03:50.190 --> 00:03:53.930
to pw minus w squared.

00:03:53.930 --> 00:03:55.510
Let's add w squared
the both sides.

00:03:55.510 --> 00:04:00.910
You get w squared plus
2k is equal to pw.

00:04:00.910 --> 00:04:03.480
Let's subtract, because all of
the choices have them setting

00:04:03.480 --> 00:04:04.690
equal to 0.

00:04:04.690 --> 00:04:09.490
So then we could subtract pw
from both sides, and you get--

00:04:09.490 --> 00:04:10.900
oh wait, I made a mistake.

00:04:10.900 --> 00:04:14.510
If we multiply both sides of
this by 2, 2 times k is 2k.

00:04:14.510 --> 00:04:16.760
2 times pw/2 is pw.

00:04:16.760 --> 00:04:20.350
2 times minus w squared
is minus 2w squared.

00:04:20.350 --> 00:04:24.010
So in this step we have to add
2w squared to both sides.

00:04:24.010 --> 00:04:25.640
Sorry about that.

00:04:25.640 --> 00:04:30.400
So we have 2w squared plus
2k is equal to pw.

00:04:30.400 --> 00:04:36.080
Subtract pw from both sides, you
get 2w squared minus pw,

00:04:36.080 --> 00:04:40.480
plus 2k is equal to 0.

00:04:40.480 --> 00:04:43.010
And that is choice E, right?

00:04:43.010 --> 00:04:44.770
2w squared minus pw plus 2k.

00:04:44.770 --> 00:04:47.600
That is choice E.

00:04:47.600 --> 00:04:50.450
Next question.

00:04:50.450 --> 00:04:55.710
Problem 247.

00:04:55.710 --> 00:04:58.300
An arithmetic sequence is a
sequence in which each term

00:04:58.300 --> 00:05:01.160
after the first is equal to the
sum of the preceding term

00:05:01.160 --> 00:05:02.930
and a constant.

00:05:02.930 --> 00:05:05.400
If the list of letters shown
above is an arithmetic

00:05:05.400 --> 00:05:10.410
sequence-- so they wrote
p, r, s, t, u.

00:05:10.410 --> 00:05:14.430
So all they're saying is that,
the difference between p and r

00:05:14.430 --> 00:05:15.500
is going to be some number.

00:05:15.500 --> 00:05:16.810
And the difference between
r and s is going to

00:05:16.810 --> 00:05:17.490
be that same number.

00:05:17.490 --> 00:05:18.775
And the difference between
s and t is going to

00:05:18.775 --> 00:05:19.980
be that same number.

00:05:19.980 --> 00:05:22.210
So an example of an arithmetic
sequence, this could

00:05:22.210 --> 00:05:25.220
be 1, 2, 3, 4, 5.

00:05:25.220 --> 00:05:28.550
Because every number is one more
than the one before it.

00:05:28.550 --> 00:05:31.440
So anyway, they say which of the
following must also be an

00:05:31.440 --> 00:05:33.030
arithmetic sequence?

00:05:33.030 --> 00:05:45.240
So choice one, they write
2p, 2r, 2s, 2t, 2u.

00:05:45.240 --> 00:05:46.960
Well, let's just use
our example.

00:05:46.960 --> 00:05:50.960
If this was p, r, s, t, and u,
what is 2 times all of that?

00:05:50.960 --> 00:05:57.230
Well, then it'll be 2, 4-- no
no, sorry-- it'll be, yeah, 2,

00:05:57.230 --> 00:06:00.510
4, 6, 8, 10.

00:06:00.510 --> 00:06:02.765
So now instead of incrementing
by one every time, we're

00:06:02.765 --> 00:06:03.990
incrementing by two
every time.

00:06:03.990 --> 00:06:06.160
But it's still an arithmetic
sequence because the

00:06:06.160 --> 00:06:08.400
difference between each
number and the number

00:06:08.400 --> 00:06:09.410
before it is a constant.

00:06:09.410 --> 00:06:12.280
It's always equal to 2.

00:06:12.280 --> 00:06:13.950
So choice number one
is definitely

00:06:13.950 --> 00:06:16.400
an arithmetic sequence.

00:06:16.400 --> 00:06:17.650
Choice two.

00:06:19.950 --> 00:06:21.560
And if you say, well, that works
for that example, how do

00:06:21.560 --> 00:06:22.690
I know it'll work for
all examples?

00:06:22.690 --> 00:06:24.040
So the other way to think
about is, whatever the

00:06:24.040 --> 00:06:27.130
difference is between p and r,
now you're going to have twice

00:06:27.130 --> 00:06:30.960
the difference between
2p and 2r.

00:06:30.960 --> 00:06:33.070
And it was the same distance
between r and s, now you're

00:06:33.070 --> 00:06:35.600
going to have twice that
distance between 2r and 2s.

00:06:35.600 --> 00:06:38.640
So here in our particular
example, we went from 1 to 2,

00:06:38.640 --> 00:06:40.940
but it could have been
something else.

00:06:40.940 --> 00:06:45.290
OK, Statement two says, p
minus 3, r minus 3-- so

00:06:45.290 --> 00:06:47.070
they're just shifting
everything; I don't even have

00:06:47.070 --> 00:06:50.470
to write them alll-- all
the way to u minus 3.

00:06:50.470 --> 00:06:52.700
So they just took everything in
this sequence and made them

00:06:52.700 --> 00:06:54.420
three less.

00:06:54.420 --> 00:07:00.650
But if r minus p is equal to
some number, r minus 3, minus

00:07:00.650 --> 00:07:02.640
p minus 3 is going to be
the exact same thing.

00:07:02.640 --> 00:07:04.380
I can even prove that
to you, right?

00:07:04.380 --> 00:07:11.950
r minus p-- sorry, r minus
3, minus p minus 3.

00:07:11.950 --> 00:07:16.940
That's equal to r minus
3, minus p plus 3.

00:07:16.940 --> 00:07:19.920
And so these cancel out.

00:07:19.920 --> 00:07:24.220
So the difference between this
and this ends up to be r minus

00:07:24.220 --> 00:07:25.950
p, the difference between
that and that.

00:07:25.950 --> 00:07:28.850
And that should make sense
intuitively, we're just

00:07:28.850 --> 00:07:30.740
shifting all the numbers
down by three.

00:07:30.740 --> 00:07:31.700
So that shouldn't change the

00:07:31.700 --> 00:07:34.030
difference between the numbers.

00:07:34.030 --> 00:07:35.935
So two is still an arithmetic
sequence.

00:07:38.980 --> 00:07:40.270
Statement three.

00:07:40.270 --> 00:07:44.200
p squared, r squared-- so we're
just squaring all the

00:07:44.200 --> 00:07:46.870
numbers-- t squared,
and u squared.

00:07:46.870 --> 00:07:48.380
So let's just use our
particular example.

00:07:48.380 --> 00:07:53.660
If p was 1, then p squared is
1, 2 squared is 4, s squared

00:07:53.660 --> 00:07:56.690
is 9-- right, 3 squared is
nine, 4 squared is 16.

00:07:56.690 --> 00:07:58.470
Now what's the difference
between the numbers?

00:07:58.470 --> 00:08:00.340
The difference here is three.

00:08:00.340 --> 00:08:01.460
The difference here is five.

00:08:01.460 --> 00:08:04.470
The difference here is seven.

00:08:04.470 --> 00:08:07.920
And this is interesting in and
of itself, that-- well, first

00:08:07.920 --> 00:08:09.460
of all, let's just answer
our question.

00:08:09.460 --> 00:08:11.360
The difference is now
not constant.

00:08:11.360 --> 00:08:13.930
We have a different difference
between each successive

00:08:13.930 --> 00:08:14.890
number, right?

00:08:14.890 --> 00:08:17.800
At the beginning, the difference
is two every time.

00:08:17.800 --> 00:08:19.980
Here it's three, then it changes
to five, then it

00:08:19.980 --> 00:08:21.120
changes to seven.

00:08:21.120 --> 00:08:23.790
So three is not an arithmetic
sequence.

00:08:23.790 --> 00:08:28.760
So the answer is
D, one and two.

00:08:28.760 --> 00:08:29.820
This is something interesting.

00:08:29.820 --> 00:08:31.990
And if you've never experimented
with it, this is

00:08:31.990 --> 00:08:33.289
something to look at.

00:08:33.289 --> 00:08:35.650
I've always been fascinated by
the distance between the

00:08:35.650 --> 00:08:39.440
perfect squares increases by
increasing odd numbers, which

00:08:39.440 --> 00:08:41.200
is just something
to think about.

00:08:41.200 --> 00:08:42.775
Anyway, next problem.

00:08:47.210 --> 00:08:49.350
Actually, I have two problems
left out of all of the

00:08:49.350 --> 00:08:51.880
problem-solving problems, so
instead of just doing one

00:08:51.880 --> 00:08:54.340
problem and going over time, let
me do two of them in the

00:08:54.340 --> 00:08:55.000
the next video.

00:08:55.000 --> 00:08:56.550
See you soon.


GMAT: Math 52

WEBVTT
Kind: captions
Language: en

00:00:00.410 --> 00:00:04.250
We're on problem 240.

00:00:04.250 --> 00:00:09.630
Seed mixture x is 40% rye
grass and 60% bluegrass.

00:00:09.630 --> 00:00:17.240
Let's see, x is 40% rye grass
and 60% bluegrass.

00:00:17.240 --> 00:00:18.070
Fair enough.

00:00:18.070 --> 00:00:26.110
Seed mixture y is 25% rye
grass-- so it's 0.25 rye

00:00:26.110 --> 00:00:31.690
grass-- and 75% fescue.

00:00:31.690 --> 00:00:33.850
So I should look up
what that is.

00:00:33.850 --> 00:00:35.780
75% fescue.

00:00:35.780 --> 00:00:40.650
If a mixture of x and y contain
30% rye grass, what

00:00:40.650 --> 00:00:44.690
percent of the weight
of the mixture is x?

00:00:44.690 --> 00:00:45.310
OK.

00:00:45.310 --> 00:00:51.560
Well, let's say that A is equal
to the percent of weight

00:00:51.560 --> 00:00:56.280
of mixture that is x, what
they're asking for.

00:00:56.280 --> 00:01:02.650
So how much rye grass-- what
percentage of that mixture

00:01:02.650 --> 00:01:05.450
will be rye grass that
comes from x?

00:01:05.450 --> 00:01:11.650
Well, we have A%, or you know,
we could call that-- fraction

00:01:11.650 --> 00:01:14.740
A of the mixture is from x.

00:01:14.740 --> 00:01:17.040
And then x is 40% rye grass.

00:01:17.040 --> 00:01:20.010
So if we multiply the amount
that we're getting from x

00:01:20.010 --> 00:01:25.110
times 40%, times 0.4, this'll
tell us the amount of rye

00:01:25.110 --> 00:01:26.490
grass from x.

00:01:26.490 --> 00:01:30.810
So r from x, or the proportion
of rye grass from x.

00:01:30.810 --> 00:01:33.430
And now, how much rye grass are
we going to get from y?

00:01:33.430 --> 00:01:35.630
So first of all, what's
our proportion of y?

00:01:35.630 --> 00:01:40.870
If this mixture is A of
x, there's going to be

00:01:40.870 --> 00:01:43.450
1 minus A of y.

00:01:43.450 --> 00:01:48.160
If this is 1/4, this is going
to be 3/4, right?

00:01:48.160 --> 00:01:48.930
Makes sense.

00:01:48.930 --> 00:01:53.240
So this is how much y we have,
and y is 25% rye grass.

00:01:53.240 --> 00:01:58.180
So our rye grass from y will
be the amount of y we have

00:01:58.180 --> 00:02:01.630
times how much y is rye grass.

00:02:01.630 --> 00:02:05.920
So this is rye grass from y.

00:02:05.920 --> 00:02:09.580
And they tell us that this
is equal to a mixture.

00:02:09.580 --> 00:02:12.520
The mixture should have
30% rye grass.

00:02:12.520 --> 00:02:14.310
So let's just solve for A.

00:02:14.310 --> 00:02:21.100
We get 0.4 times A plus-- let's
see, multiply-- 0.25

00:02:21.100 --> 00:02:27.780
minus 0.25A-- just distributed
the 0.25-- is equal to 0.30.

00:02:27.780 --> 00:02:34.550
0.4A minus 0.25A-- 40 minus
25-- that's 0.15A.

00:02:34.550 --> 00:02:39.240
And then subtract 0.25 from both
sides, is equal to 0.5.

00:02:39.240 --> 00:02:44.890
So A is equal to 0.5 divided by
0.15, is the same thing as

00:02:44.890 --> 00:02:50.427
5 over 15, which is equal to
1/3, which is equal to 33 and

00:02:50.427 --> 00:02:57.360
1/3%, Which is choice B.

00:02:57.360 --> 00:03:00.260
Next problem.

00:03:00.260 --> 00:03:03.210
Problem 241.

00:03:03.210 --> 00:03:06.560
If the integer n has exactly
three positive divisors,

00:03:06.560 --> 00:03:10.480
including 1 and n-- so it's
divisors are, I don't know, 1,

00:03:10.480 --> 00:03:14.990
some number, and n-- how many
positive divisors does n

00:03:14.990 --> 00:03:16.790
squared have?

00:03:16.790 --> 00:03:18.900
So one thing, I don't know if
you've ever thought about

00:03:18.900 --> 00:03:20.890
this, but how can any
number have an

00:03:20.890 --> 00:03:22.660
odd number of divisors?

00:03:22.660 --> 00:03:23.000
Right?

00:03:23.000 --> 00:03:26.200
Because normally, if you take
a number, let's take the

00:03:26.200 --> 00:03:28.500
number 6-- and you shouldn't
do this on the GMAT, it's a

00:03:28.500 --> 00:03:29.510
waste of time.

00:03:29.510 --> 00:03:33.230
But its divisors are 1 times
6, or 2 times 3.

00:03:33.230 --> 00:03:36.060
So every divisor tends to have
a corresponding divisor.

00:03:36.060 --> 00:03:38.100
So how can you have an odd
number of divisors?

00:03:38.100 --> 00:03:40.790
Well, only if one of the
divisor's corresponding

00:03:40.790 --> 00:03:43.020
divisors is itself.

00:03:43.020 --> 00:03:50.070
If it's 1 times n, and x times
x, which implies that if you

00:03:50.070 --> 00:03:51.590
have an odd number of divisors,
you're dealing with

00:03:51.590 --> 00:03:52.780
a perfect square.

00:03:52.780 --> 00:03:54.810
Anyway, I just wanted
to point that out.

00:03:54.810 --> 00:03:56.840
But that's actually not that
relevant to that problem.

00:03:56.840 --> 00:04:01.350
It's just something, you know,
it is useful sometimes.

00:04:01.350 --> 00:04:02.810
But anyway.

00:04:02.810 --> 00:04:04.490
They just want to know how many
divisors n squared has.

00:04:04.490 --> 00:04:06.180
Let's just find a number
that has this property.

00:04:06.180 --> 00:04:09.180
Well, we know any perfect
square-- well, a small perfect

00:04:09.180 --> 00:04:10.680
square will have
this property.

00:04:10.680 --> 00:04:12.560
So let's see.

00:04:12.560 --> 00:04:14.085
Number 4, it has its property.

00:04:14.085 --> 00:04:17.690
It's factors are 1, 2, and 4.

00:04:17.690 --> 00:04:20.250
So how many factors does
4 squared have?

00:04:20.250 --> 00:04:21.490
Well, 4 squared is 16.

00:04:21.490 --> 00:04:27.250
Its factors are 1 and 16,
2 and 8, and 4 and 4.

00:04:27.250 --> 00:04:31.870
So it has five factors,
and that is choice B.

00:04:31.870 --> 00:04:33.340
And you could do it
mathematically.

00:04:33.340 --> 00:04:34.820
You could say all the
combinations of when I

00:04:34.820 --> 00:04:38.990
multiply all the factors of
this times itself, and you

00:04:38.990 --> 00:04:40.050
could say, oh, they have
five combinations.

00:04:40.050 --> 00:04:42.540
But in this case, it's just way
easier to think of, OK,

00:04:42.540 --> 00:04:44.110
let me think of a small perfect
square that's going to

00:04:44.110 --> 00:04:44.930
have three factors.

00:04:44.930 --> 00:04:46.990
A perfect square just tells you
it has an odd number of

00:04:46.990 --> 00:04:48.690
factors, but a small one
will have three.

00:04:48.690 --> 00:04:50.700
And let me just square it and
just count its factors.

00:04:50.700 --> 00:04:52.550
Fastest way to do that
problem, I think.

00:04:52.550 --> 00:04:54.300
Unless there is-- I
don't know, maybe

00:04:54.300 --> 00:04:55.940
there is a faster one.

00:04:55.940 --> 00:04:58.440
242.

00:04:58.440 --> 00:05:06.340
If n is a positive integer, then
n times n plus 1, times n

00:05:06.340 --> 00:05:09.870
plus 2 is-- OK, they have
a bunch of things.

00:05:09.870 --> 00:05:12.130
What happens when n-- let's see,
even when n is even, the

00:05:12.130 --> 00:05:13.620
even only one is odd,
odd [? 1n ?]

00:05:13.620 --> 00:05:14.670
is odd.

00:05:14.670 --> 00:05:16.080
OK, so they want us to
see what happens when

00:05:16.080 --> 00:05:16.850
n is even or odd.

00:05:16.850 --> 00:05:19.100
So let's see what happens
when n is even.

00:05:19.100 --> 00:05:22.210
Let's say that n-- if n is even,
that means it's equal to

00:05:22.210 --> 00:05:24.700
2 times some integer k.

00:05:24.700 --> 00:05:27.110
We don't know, some positive
integer k.

00:05:27.110 --> 00:05:28.220
So let's substitute that in.

00:05:28.220 --> 00:05:34.470
So then this breaks down
to 2k times 2k plus 1,

00:05:34.470 --> 00:05:38.330
times 2k plus 2.

00:05:38.330 --> 00:05:39.460
Interesting.

00:05:39.460 --> 00:05:44.190
And let's see, it looks like
this is saying that e should

00:05:44.190 --> 00:05:44.640
be-- right.

00:05:44.640 --> 00:05:46.400
Because let's see, we could
factor 2 out of this one.

00:05:46.400 --> 00:05:53.390
So this becomes 2k times
2k plus 1, times 2,

00:05:53.390 --> 00:05:55.500
times k plus 1.

00:05:55.500 --> 00:05:55.830
Right?

00:05:55.830 --> 00:05:57.330
I just factored the
2 out of there.

00:05:57.330 --> 00:05:58.760
And let's multiply these two.

00:05:58.760 --> 00:06:05.910
So you get 4k times 2k plus
1, times k plus 1.

00:06:05.910 --> 00:06:07.490
So this one is divisible by 4.

00:06:07.490 --> 00:06:09.250
And I just glanced at statement
e, they talk about

00:06:09.250 --> 00:06:12.200
divisibility by 4, so
I think we're done.

00:06:12.200 --> 00:06:16.910
This simplifies to this if we
can assume that n is even.

00:06:16.910 --> 00:06:20.420
So if n is even, then we are
definitely divisible by 4.

00:06:20.420 --> 00:06:23.660
4 can definitely go into
the number evenly.

00:06:23.660 --> 00:06:25.350
So statement E is right.

00:06:25.350 --> 00:06:28.410
Divisible by 4 when n is even.

00:06:28.410 --> 00:06:31.170
Statement E.

00:06:31.170 --> 00:06:32.070
Next problem.

00:06:32.070 --> 00:06:37.130
We're on the last page, 243.

00:06:37.130 --> 00:06:40.720
A straight pipe 1 yard in
length was marked off in

00:06:40.720 --> 00:06:43.950
fourths and also in thirds.

00:06:43.950 --> 00:06:45.770
Maybe I'll give some
dimensionality to

00:06:45.770 --> 00:06:47.150
our straight pipe.

00:06:47.150 --> 00:06:49.730
So let's say the pipe looks
something like that.

00:06:49.730 --> 00:06:51.260
It's a straight pipe, and
it was marked off

00:06:51.260 --> 00:06:52.400
in fourths and thirds.

00:06:52.400 --> 00:06:54.640
So if I mark it off in fourths,
let's see, that's the

00:06:54.640 --> 00:06:57.350
middle, and that's a
fourth, and that's

00:06:57.350 --> 00:06:58.200
another fourth, roughly.

00:06:58.200 --> 00:07:00.130
And if I mark it off
in thirds, it looks

00:07:00.130 --> 00:07:03.130
something like this.

00:07:03.130 --> 00:07:04.040
Right?

00:07:04.040 --> 00:07:05.780
All right.

00:07:05.780 --> 00:07:08.790
If the pipe was then cut into
separate pieces at each of

00:07:08.790 --> 00:07:12.260
these markings, which of the
following gives all the

00:07:12.260 --> 00:07:15.720
different lengths of the pieces
in fraction of a yard?

00:07:15.720 --> 00:07:17.240
Fascinating.

00:07:17.240 --> 00:07:20.590
OK, so we're going to cut it,
actually, at here, and here,

00:07:20.590 --> 00:07:22.955
and here, and here,
and at here.

00:07:22.955 --> 00:07:25.350
And actually, if we go halfway,
then we can just use

00:07:25.350 --> 00:07:27.930
symmetry to say, OK, this piece
is going to be the same

00:07:27.930 --> 00:07:30.180
as this piece, and this piece
is going to be the same as

00:07:30.180 --> 00:07:31.820
this piece, and that piece
is going to be the

00:07:31.820 --> 00:07:33.030
same as that piece.

00:07:33.030 --> 00:07:34.720
So we really just have to
figure out up until the

00:07:34.720 --> 00:07:36.390
halfway point.

00:07:36.390 --> 00:07:38.020
So let's think about it.

00:07:38.020 --> 00:07:41.940
So this whole thing is 1 yard,
so this distance right here,

00:07:41.940 --> 00:07:43.190
that distance right
here is 1/4.

00:07:46.060 --> 00:07:48.620
That distance is 1/4.

00:07:48.620 --> 00:07:50.980
We know that this whole
distance is 1/3.

00:07:50.980 --> 00:07:53.820
This distance is 1/4, so this
distance right here is going

00:07:53.820 --> 00:07:56.570
to be 1/3, because that's
1/3, minus 1/4.

00:08:00.310 --> 00:08:01.790
Common denominator over 12.

00:08:01.790 --> 00:08:07.910
1/3 is 4/12, minus 3/12
is equal to 1/12.

00:08:07.910 --> 00:08:11.290
So this distance is
going to be 1/12.

00:08:11.290 --> 00:08:15.330
And then what's going
to be this length?

00:08:15.330 --> 00:08:16.340
Let me get a different color.

00:08:16.340 --> 00:08:18.540
I want to make sure that
you see that 1/12.

00:08:18.540 --> 00:08:22.960
Well, this distance is 1/2, and
this distance is 1/3, so

00:08:22.960 --> 00:08:27.290
it's going to be 1/2 minus 1/3
is equal to common denominator

00:08:27.290 --> 00:08:32.200
of 6, is equal to 3/6 minus
2/6, is equal to 1/6.

00:08:32.200 --> 00:08:34.080
So this piece is 1/4.

00:08:34.080 --> 00:08:36.090
This piece is 1/12.

00:08:36.090 --> 00:08:37.929
This piece is 1/6.

00:08:37.929 --> 00:08:39.530
And then you could just say, oh,
well, it's going to happen

00:08:39.530 --> 00:08:40.549
the same thing on
the other side.

00:08:40.549 --> 00:08:46.590
This is 1/6, 1/12, and
then this is 1/4.

00:08:46.590 --> 00:08:51.670
And so if I say-- let's see,
1/6, 1/12, and 1/4.

00:08:51.670 --> 00:08:53.460
Right, that is choice D.

00:08:53.460 --> 00:08:56.440
1/6, 1/12, and 1/4.

00:08:56.440 --> 00:08:56.900
Choice D.

00:08:56.900 --> 00:09:01.590
Those are the different
piece sizes we have.

00:09:01.590 --> 00:09:08.970
Problem 245.

00:09:08.970 --> 00:09:25.640
If 0.0015 times 10 to the m,
over 0.03 times 10 to the k,

00:09:25.640 --> 00:09:35.970
is equal to 5 times 10 to the
seventh, then what does m

00:09:35.970 --> 00:09:38.230
minus k equal to?

00:09:38.230 --> 00:09:39.580
And that's important to
read, I was about to

00:09:39.580 --> 00:09:40.800
solve-- m minus k.

00:09:40.800 --> 00:09:44.700
So they want to know
what m minus k.

00:09:44.700 --> 00:09:47.030
So if we immediately divide
these, we should be able to

00:09:47.030 --> 00:09:48.640
come up with something
interesting, right?

00:09:48.640 --> 00:09:58.190
Because this is the same thing
as 0.0015/0.03 times 10 to the

00:09:58.190 --> 00:09:59.970
m divided by 10 to the k.

00:09:59.970 --> 00:10:06.270
Well, that's just times 10 to
the m minus k, is equal to 5

00:10:06.270 --> 00:10:09.470
times 10 to the seventh.

00:10:09.470 --> 00:10:14.050
And I don't know, let's see if
we can do anything interesting

00:10:14.050 --> 00:10:15.800
to this decimal number.

00:10:15.800 --> 00:10:18.100
Let's see, if we were to--
let's just divide it.

00:10:18.100 --> 00:10:21.840
So if we just say 0.03, instead
of multiplying by 10

00:10:21.840 --> 00:10:26.640
and doing-- going into 0.0015.

00:10:26.640 --> 00:10:28.350
Let's add some 0's.

00:10:28.350 --> 00:10:29.260
OK.

00:10:29.260 --> 00:10:32.120
If we take this decimal two to
the right, we're going to take

00:10:32.120 --> 00:10:35.290
this decimal two to the right.

00:10:35.290 --> 00:10:39.900
So then we get 3 goes into 1
zero times, 3 goes into 15

00:10:39.900 --> 00:10:40.880
five times.

00:10:40.880 --> 00:10:42.700
So we get 0.05.

00:10:42.700 --> 00:10:45.230
So this whole thing simplifies
to-- and I'll write it in

00:10:45.230 --> 00:10:53.490
magenta-- so that simplifies
to 0.05 times 10 to the m

00:10:53.490 --> 00:11:00.560
minus k, is equal to 5 times
10 to the seventh.

00:11:00.560 --> 00:11:04.850
So let's divide both
sides by this 0.05.

00:11:04.850 --> 00:11:08.540
What is 0.05 goes into 5?

00:11:08.540 --> 00:11:11.330
Let's add some decimal
points here.

00:11:11.330 --> 00:11:14.200
So if I push this to the right
two, I push this to the right

00:11:14.200 --> 00:11:16.230
two, and this is my
new decimal point.

00:11:16.230 --> 00:11:19.410
So 5 goes into 5-- well,
5 goes into 5 one

00:11:19.410 --> 00:11:21.300
time, so it's 100.

00:11:21.300 --> 00:11:22.070
Right?

00:11:22.070 --> 00:11:24.750
So 5 divided by 0.05 is 100.

00:11:24.750 --> 00:11:31.800
So we get 10 to the m minus k,
is equal to 100-- what's 100?

00:11:31.800 --> 00:11:33.810
That's the same thing
as 10 squared.

00:11:33.810 --> 00:11:35.870
Times 10 to the 7th.

00:11:35.870 --> 00:11:41.680
So 10 to the m minus k is equal
to 10 to the ninth.

00:11:41.680 --> 00:11:45.530
So m minus k must
be equal to 9.

00:11:45.530 --> 00:11:47.300
And that is choice A.

00:11:47.300 --> 00:11:49.360
See you in the next video.


GMAT: Math 54

WEBVTT
Kind: captions
Language: en

00:00:00.570 --> 00:00:05.150
We're on problem 248, truly
the home stretch.

00:00:05.150 --> 00:00:09.740
Right triangle pqr is to be
constructed on the xy plane.

00:00:09.740 --> 00:00:12.710
Let me draw an xy plane,
that seems like

00:00:12.710 --> 00:00:14.370
it should be useful.

00:00:14.370 --> 00:00:20.620
So that's x, and y -- I'm sorry,
that's y and that's x.

00:00:20.620 --> 00:00:22.780
Let me label them since
I said them wrong.

00:00:22.780 --> 00:00:27.170
y and x, that should be second
nature to you at this point.

00:00:27.170 --> 00:00:31.220
If you start the xy plane so the
right angle is at p, and

00:00:31.220 --> 00:00:35.740
pr is parallel to the axis
-- so it's going to look

00:00:35.740 --> 00:00:40.670
something like that, where
that's p and that's r,

00:00:40.670 --> 00:00:43.840
parallel to-- and p is the right
angle, right, so it's

00:00:43.840 --> 00:00:45.040
going to look something
like that.

00:00:45.040 --> 00:00:48.540
So q has to be right below p.

00:00:48.540 --> 00:00:51.770
The x- and y-coordinates of p,
q, and r are to be integers

00:00:51.770 --> 00:00:56.260
that satisfy the inequality
minus 4 is less than or equal

00:00:56.260 --> 00:00:59.530
to x, which is less than
or equal to 5.

00:00:59.530 --> 00:01:04.860
And it tells us that 6 is less
than or equal to y, which is

00:01:04.860 --> 00:01:07.650
less than or equal to 16.

00:01:07.650 --> 00:01:09.900
How many different triangles
with these properties could be

00:01:09.900 --> 00:01:12.140
constructed?

00:01:12.140 --> 00:01:14.840
So let's first draw
this range.

00:01:14.840 --> 00:01:17.525
So x could be between
minus 4 and 5.

00:01:22.040 --> 00:01:24.650
And x and y are always
going to be integers,

00:01:24.650 --> 00:01:26.140
so that's our boundary.

00:01:26.140 --> 00:01:30.470
And it could be minus
4 or 5, right?

00:01:30.470 --> 00:01:32.650
And then y is between
6 -- let's just say

00:01:32.650 --> 00:01:43.350
this is 6 -- and 16.

00:01:43.350 --> 00:01:44.500
So let's think about this.

00:01:44.500 --> 00:01:47.110
Let's think about where we
can place the point.

00:01:47.110 --> 00:01:50.320
So first of all, how many
different legitimate places

00:01:50.320 --> 00:01:54.050
can we put the point p?

00:01:54.050 --> 00:01:56.210
Let's just kind of figure out
how many different ways we can

00:01:56.210 --> 00:01:57.750
construct this thing.

00:01:57.750 --> 00:02:00.330
So if we have to pick its
x-coordinate, how many

00:02:00.330 --> 00:02:02.160
different x-coordinates
are valid?

00:02:02.160 --> 00:02:08.590
So you have minus 4, minus 3,
minus 2, minus 1, 0, 1,

00:02:08.590 --> 00:02:11.180
2, 3, 4, and 5.

00:02:11.180 --> 00:02:11.520
Right?

00:02:11.520 --> 00:02:13.890
They should be -- 5 minus
5, so it should be 9.

00:02:13.890 --> 00:02:18.930
1, 2, 3, 4, 5, 6, 7, 8, 9 --
oh actually, no, it's 10

00:02:18.930 --> 00:02:22.650
different points, because we
could include minus 4, right?

00:02:22.650 --> 00:02:27.210
So it could be -- x could be
minus 4, minus 2, 3 -- right,

00:02:27.210 --> 00:02:35.720
this is minus 3, minus 2, minus
1, 0, 1, 2, 3, 4, and 5.

00:02:35.720 --> 00:02:36.280
Right?

00:02:36.280 --> 00:02:41.620
So this x value can take on
any of these 10 spots.

00:02:41.620 --> 00:02:45.310
So p can take on 10
different values.

00:02:45.310 --> 00:02:49.080
Well, its x-value could take on
10 different values, right?

00:02:49.080 --> 00:02:51.070
So p's x can take on 10
different values.

00:02:51.070 --> 00:02:54.540
And how many values can
its y take over?

00:02:54.540 --> 00:02:59.240
Well, this top boundary is 16,
this bottom boundary is 6.

00:02:59.240 --> 00:03:01.010
And we can be either
one, right?

00:03:01.010 --> 00:03:08.870
So 16 minus 6 would be 7, 8, 9,
10, 11, 12, 13, 14, 15, 16.

00:03:08.870 --> 00:03:11.160
But we can include
6 as well, right?

00:03:11.160 --> 00:03:14.500
If you just said 16 minus 6,
that would give you 10 spots,

00:03:14.500 --> 00:03:19.450
but since we're including 6, the
y could take on 11 spots.

00:03:19.450 --> 00:03:22.620
You could count them, maybe
it'll be beneficial for you to

00:03:22.620 --> 00:03:24.310
see all the different
y's it could be.

00:03:24.310 --> 00:03:28.410
It could be anything between 6
and 16, including 6 and 16.

00:03:28.410 --> 00:03:31.950
So there's 11 possibilities
for the y.

00:03:31.950 --> 00:03:37.880
So that means that there are
110 different possible p's.

00:03:37.880 --> 00:03:39.792
Let me just draw one of them.

00:03:39.792 --> 00:03:43.080
Let's say that's our p.

00:03:43.080 --> 00:03:45.020
So our p is there.

00:03:45.020 --> 00:03:46.750
For any given p, how
many different

00:03:46.750 --> 00:03:48.480
possible r's are there?

00:03:48.480 --> 00:03:50.950
Well r is in the
same line as p.

00:03:50.950 --> 00:03:55.320
So whatever p's y value is,
r has to be the same.

00:03:55.320 --> 00:03:57.120
But r could be any of the other

00:03:57.120 --> 00:03:59.610
leftover x spaces, right?

00:03:59.610 --> 00:04:01.950
So if p took up one of them, r
could be here, it could be

00:04:01.950 --> 00:04:03.620
here, it could be here.

00:04:03.620 --> 00:04:06.000
r could be in any of
these spots, right?

00:04:06.000 --> 00:04:08.000
So how many left over
x spots are there?

00:04:08.000 --> 00:04:10.890
Well there were 10 x spots,
10 x-coordinates.

00:04:10.890 --> 00:04:12.400
p took up one of them.

00:04:12.400 --> 00:04:19.004
So now r could only be in one
of nine x-coordinates.

00:04:24.590 --> 00:04:26.450
Fair enough.

00:04:26.450 --> 00:04:29.560
And r is limited to its y.

00:04:29.560 --> 00:04:32.350
Once we pick a y coordinate for
p, that's got to be the

00:04:32.350 --> 00:04:36.040
same coordinate as r, right?
r has to be on the same

00:04:36.040 --> 00:04:38.300
y-coordinate as p.

00:04:38.300 --> 00:04:39.500
Because they told us
that this line is

00:04:39.500 --> 00:04:40.850
parallel to the x-axis.

00:04:40.850 --> 00:04:42.200
Fair enough.

00:04:42.200 --> 00:04:45.420
So how many possibilities --
once we've picked a p and an

00:04:45.420 --> 00:04:46.900
r, how many different
possibilities

00:04:46.900 --> 00:04:50.130
do we have for q?

00:04:50.130 --> 00:04:53.390
Well q is going to have the
same x value, because they

00:04:53.390 --> 00:04:55.670
told us that this is a
right angle, and so

00:04:55.670 --> 00:04:57.380
this has to be q.

00:04:57.380 --> 00:05:01.590
So q has to be in the same
vertical line as p.

00:05:01.590 --> 00:05:03.050
It has to have the
same x-value.

00:05:03.050 --> 00:05:06.230
And so on how many different
y-values can it have?

00:05:06.230 --> 00:05:08.550
Well there were a total of -- we
said there were originally

00:05:08.550 --> 00:05:10.910
11 potential y-values, right?

00:05:10.910 --> 00:05:13.450
That's what we said when we
picked our p. p could be

00:05:13.450 --> 00:05:15.820
anywhere between 6 and 16.

00:05:15.820 --> 00:05:18.675
q could be any of those numbers,
but it can't be at

00:05:18.675 --> 00:05:20.030
the same point as p, right?

00:05:20.030 --> 00:05:22.250
This side has to have
some length.

00:05:22.250 --> 00:05:27.580
So if there were 11 original
slots, 11 original y slots, p

00:05:27.580 --> 00:05:29.490
takes one of them up.

00:05:29.490 --> 00:05:35.570
So then q could be any
of one of 10 y slots.

00:05:35.570 --> 00:05:38.820
So if we want to know the total
number of potential

00:05:38.820 --> 00:05:46.390
triangles like this, there are
110 potential places to put p.

00:05:46.390 --> 00:05:50.240
Once we've put p, there are nine
potential places to put

00:05:50.240 --> 00:05:53.680
r, and once we've put p, there's
also 10 potential

00:05:53.680 --> 00:05:56.590
places to put q.

00:05:56.590 --> 00:06:02.310
So this is what, 110 times 90.

00:06:02.310 --> 00:06:05.570
That's the same thing as 11
times 9 with two 0's, right?

00:06:08.350 --> 00:06:10.145
Which is choice c.

00:06:13.730 --> 00:06:16.025
And we're onto our last -- I'm
glad this a new video, that

00:06:16.025 --> 00:06:17.290
took me six minutes.

00:06:17.290 --> 00:06:19.110
Problem 249.

00:06:19.110 --> 00:06:20.445
Hopefully it won't take you
that long on the GMAT.

00:06:20.445 --> 00:06:23.160
It takes less time if you don't
have to explain it.

00:06:23.160 --> 00:06:28.280
If n is a positive integer less
than 200 -- so n is less

00:06:28.280 --> 00:06:32.680
than 200, it's positive and it's
an intiger -- and 14 over

00:06:32.680 --> 00:06:38.465
n -- 14n over 60
is an integer.

00:06:38.465 --> 00:06:42.140
So that means that 14n divided
by 60 -- or 14 is divisible by

00:06:42.140 --> 00:06:47.190
60 then n has how many different
prime factors?

00:06:47.190 --> 00:06:49.030
Let's simplify this first.
Divide the top and

00:06:49.030 --> 00:06:49.880
the bottom by 2.

00:06:49.880 --> 00:06:59.590
You get -- this is also saying
that 7n over 30 is an integer.

00:06:59.590 --> 00:07:03.100
Well multiplying by 7 doesn't
make it any easier to be

00:07:03.100 --> 00:07:05.570
divisible by 30, right?

00:07:05.570 --> 00:07:08.300
Because 7 and 30 share
no common factors.

00:07:08.300 --> 00:07:10.625
14 and 60 did, 2, but
we got rid of it.

00:07:10.625 --> 00:07:15.430
So we have 17 and 30, so n has
to be divisible by 30.

00:07:15.430 --> 00:07:17.610
Right? n has to be divisible
by 30 for

00:07:17.610 --> 00:07:20.250
this to be an integer.

00:07:20.250 --> 00:07:21.970
Well, I don't know, let's just
pick the smallest one.

00:07:21.970 --> 00:07:23.460
I mean, there's a lot of
different candidates.

00:07:23.460 --> 00:07:25.920
n could be 30, or 60,
or 90, or a bunch

00:07:25.920 --> 00:07:26.620
of different numbers.

00:07:26.620 --> 00:07:28.740
But let's just pick
n is equal to 30.

00:07:28.740 --> 00:07:30.720
They just say that n is less
than 200, so let's just say

00:07:30.720 --> 00:07:32.620
that n is equal to 30.

00:07:32.620 --> 00:07:35.430
If n is equal to 30, then they
say, how many different

00:07:35.430 --> 00:07:36.690
positive prime factors?

00:07:36.690 --> 00:07:39.370
Well let's just do a prime
factorization of 30.

00:07:39.370 --> 00:07:44.480
2 times 15, which
is 3 times 5.

00:07:44.480 --> 00:07:47.600
So it has 3 positive
prime factors.

00:07:47.600 --> 00:07:49.740
So that's choice b.

00:07:49.740 --> 00:07:50.540
I don't know, I'm
just curious.

00:07:50.540 --> 00:07:51.560
So let's see if that would've
worked if we

00:07:51.560 --> 00:07:54.320
picked n equals 60.

00:07:54.320 --> 00:07:57.195
If you'd have done the prime
factorization of 60, you'd

00:07:57.195 --> 00:08:02.860
have gotten 2 times 30,
which is 2 times 15,

00:08:02.860 --> 00:08:05.120
which is 3 times 5.

00:08:05.120 --> 00:08:07.330
And yeah, you still have
only three factors.

00:08:07.330 --> 00:08:08.610
You're using one
of them twice.

00:08:08.610 --> 00:08:11.920
So this is the same thing as
2 squared times 3 times 5.

00:08:11.920 --> 00:08:14.220
So you still have actually
three different

00:08:14.220 --> 00:08:15.490
positive prime factors.

00:08:15.490 --> 00:08:18.230
So it would work for any
of the multiples of 30.

00:08:18.230 --> 00:08:19.300
Anyway, choice c.

00:08:19.300 --> 00:08:20.630
And we're all done.

00:08:20.630 --> 00:08:22.780
I don't know what I'm going to
do next, maybe I'll do some

00:08:22.780 --> 00:08:26.130
LSAT videos, or maybe
I'll get back to

00:08:26.130 --> 00:08:27.590
actually teaching something.

00:08:27.590 --> 00:08:30.800
Anyway, see you in a
future play list.


GMAT: Math 49

WEBVTT
Kind: captions
Language: en

00:00:01.180 --> 00:00:03.720
We were on problem 227 when
I got a phone call.

00:00:03.720 --> 00:00:06.790
It was actually from Jonathan
who helps me with the Khan

00:00:06.790 --> 00:00:08.070
Academy, so I thought
it was worth taking.

00:00:08.070 --> 00:00:10.130
He works at LinkedIn and he
wanted let me know about all

00:00:10.130 --> 00:00:12.410
this news that was
occurring there.

00:00:12.410 --> 00:00:14.100
Anyway, I'm getting
distracted.

00:00:14.100 --> 00:00:19.840
Let's go back to the
GMAT problems.

00:00:19.840 --> 00:00:21.480
So problem 227.

00:00:21.480 --> 00:00:23.230
In the coordinate system above,
which of the following

00:00:23.230 --> 00:00:24.990
is an equation of line l?

00:00:24.990 --> 00:00:28.460
And they didn't put this 2 here
and this 3 here, but from

00:00:28.460 --> 00:00:32.439
the drawing you can assume that
this is the point x is

00:00:32.439 --> 00:00:36.340
equal to 3, and this is the
point x is equal to 2.

00:00:36.340 --> 00:00:38.600
And then frankly, you need that
information to figure out

00:00:38.600 --> 00:00:40.070
the equation of this line.

00:00:40.070 --> 00:00:43.900
So, first of all, what's
the slope of the line?

00:00:43.900 --> 00:00:45.730
Make sure my tool is right.

00:00:45.730 --> 00:00:51.250
The slope is equal to change
in y over change in x.

00:00:51.250 --> 00:00:52.790
See, when you go from this point
to this point, what's

00:00:52.790 --> 00:00:54.030
the change in y?

00:00:54.030 --> 00:00:58.950
It's 0 minus 2, which makes
sense, because we went down by

00:00:58.950 --> 00:01:03.420
2, and the change in
x is 3 minus 0.

00:01:03.420 --> 00:01:06.250
Whenever you do slope, it's
important remember, if I'm

00:01:06.250 --> 00:01:09.580
taking this as the first point
on the y side, so 0 minus 2, I

00:01:09.580 --> 00:01:12.270
have to do the same on the
bottom, 3 minus 0.

00:01:12.270 --> 00:01:14.290
Otherwise, we'll get the
negative of the slope.

00:01:14.290 --> 00:01:18.220
Anyway, this is equal to minus
2/3, and what's the

00:01:18.220 --> 00:01:18.910
y-intercept?

00:01:18.910 --> 00:01:20.250
Well, it's pretty obvious.

00:01:20.250 --> 00:01:24.460
When x is equal to 0,
y is equal to 2.

00:01:24.460 --> 00:01:27.370
So we could say, y of
0 is equal to 2.

00:01:27.370 --> 00:01:30.820
So the equation of this line,
at least the mx plus b form

00:01:30.820 --> 00:01:35.880
that you learned in school, is y
is equal to minus 2/3 of the

00:01:35.880 --> 00:01:39.970
slope times x plus
the y-intercept.

00:01:39.970 --> 00:01:41.270
And that's not one
of the choices.

00:01:41.270 --> 00:01:43.340
They've written it in
a different form.

00:01:43.340 --> 00:01:46.470
They call it the ax plus by
equals c form, so let's see if

00:01:46.470 --> 00:01:47.810
we can get there.

00:01:47.810 --> 00:01:50.130
Let's get rid of this 3 in the
denominator, so let's multiply

00:01:50.130 --> 00:01:52.010
both sides of this
equation by 3.

00:01:52.010 --> 00:01:53.160
I'll switch colors.

00:01:53.160 --> 00:02:04.030
You get 3y minus 2x-- no, 3y is
equal to-- sorry-- minus 2x

00:02:04.030 --> 00:02:05.430
plus 6, right?

00:02:05.430 --> 00:02:07.310
I just multiplied
everything by 3.

00:02:07.310 --> 00:02:09.590
3y is equal to minus
2x plus 6.

00:02:09.590 --> 00:02:15.550
Now let's add 2x to both sides,
and you get 2x plus 3y

00:02:15.550 --> 00:02:22.170
is equal to 6, which
is choice B.

00:02:22.170 --> 00:02:24.580
Next problem.

00:02:24.580 --> 00:02:27.020
Problem 200.

00:02:27.020 --> 00:02:28.010
No, what is this?

00:02:28.010 --> 00:02:33.600
Problem 228.

00:02:33.600 --> 00:02:36.920
If a two-digit positive
integer has its digits

00:02:36.920 --> 00:02:40.330
reversed, the resulting integer
differs from the

00:02:40.330 --> 00:02:43.110
original by 27.

00:02:43.110 --> 00:02:45.140
So let's say I had AB.

00:02:45.140 --> 00:02:46.700
That's a two-digit number.

00:02:46.700 --> 00:02:49.980
And I'm going to subtract
BA from it, and so the

00:02:49.980 --> 00:02:51.960
difference is 27.

00:02:51.960 --> 00:02:55.590
Since I'm assuming a positive
difference, AB has got to be a

00:02:55.590 --> 00:02:57.530
bigger number than BA.

00:02:57.530 --> 00:02:59.410
So at least the way I've
written it, what do

00:02:59.410 --> 00:03:00.110
we know about it?

00:03:00.110 --> 00:03:01.730
Well A has to be greater
than B, right?

00:03:01.730 --> 00:03:06.730
If AB is greater than BA, A has
got to be-- well, right.

00:03:06.730 --> 00:03:09.050
A has got to be greater
than B.

00:03:09.050 --> 00:03:11.770
I was going to say A could be
greater than or equal to B,

00:03:11.770 --> 00:03:13.580
but if A was equal to B,
then this thing right

00:03:13.580 --> 00:03:15.180
here would be 0.

00:03:15.180 --> 00:03:19.610
So if we assume that AB minus B
is a positive 27, then that

00:03:19.610 --> 00:03:24.180
tells us that A is greater than
B, or B is less than A.

00:03:24.180 --> 00:03:26.820
So if B is less than A, when
we're doing the subtraction

00:03:26.820 --> 00:03:29.110
problem, we're going to have
to-- when we do this part,

00:03:29.110 --> 00:03:31.896
when we do the ones place, if B
is less than A, we're going

00:03:31.896 --> 00:03:33.750
to have to borrow, right?

00:03:33.750 --> 00:03:40.230
So if we borrow, this A becomes
A minus 1 and the B

00:03:40.230 --> 00:03:45.830
becomes B plus 10, and then
we'd be ready to subtract.

00:03:45.830 --> 00:03:47.300
So what could we say?

00:03:47.300 --> 00:03:57.090
We could say that B plus 10
minus A is equal to 7, which

00:03:57.090 --> 00:04:04.030
tells us that B minus A
is equal to minus 3.

00:04:04.030 --> 00:04:05.490
And that's essentially what
they're asking for.

00:04:05.490 --> 00:04:08.360
They want to know by how much
to do the two digits differ.

00:04:08.360 --> 00:04:11.960
Well, B minus A is equal to
minus 3, that's saying that A

00:04:11.960 --> 00:04:14.045
minus B is equal to
positive 3, right?

00:04:14.045 --> 00:04:16.760
You just multiply both
sides by negative 1.

00:04:16.760 --> 00:04:19.430
Or you could say that the
absolute value of B minus A,

00:04:19.430 --> 00:04:22.730
or A minus B, or how much they
differ is equal to 3, right?

00:04:22.730 --> 00:04:25.670
The absolute value of
B minus A is plus 3.

00:04:25.670 --> 00:04:30.260
And just to make sure that this
all works out, if we do

00:04:30.260 --> 00:04:37.166
it with the tens place, A minus
1 minus B is equal to 2.

00:04:37.166 --> 00:04:38.780
Let's add 1 to both sides.

00:04:38.780 --> 00:04:42.740
You get A minus B is equal
to 3, so it works out.

00:04:42.740 --> 00:04:45.510
A and B differ from each
other by exactly 3, and

00:04:45.510 --> 00:04:48.040
that's choice A.

00:04:48.040 --> 00:04:58.520
Problem 229 The circle-- OK, let
me see if I can draw this.

00:04:58.520 --> 00:05:02.220
So I have one line, I have
another line, and

00:05:02.220 --> 00:05:04.670
then I have a circle.

00:05:04.670 --> 00:05:09.420
It starts right there, so it
looks something like that.

00:05:09.420 --> 00:05:10.706
There's a tangent.

00:05:10.706 --> 00:05:14.940
It has center c right there.

00:05:14.940 --> 00:05:17.630
And it says the circle with
center c shown above is

00:05:17.630 --> 00:05:20.720
tangent to both axes.

00:05:20.720 --> 00:05:23.760
If the distance from o to c
is equal to k-- I'll get a

00:05:23.760 --> 00:05:24.940
different color.

00:05:24.940 --> 00:05:27.280
So this is from the
origin to c.

00:05:27.280 --> 00:05:29.540
So they label the origin as o.

00:05:29.540 --> 00:05:34.470
But if that is equal to k,
what is the radius of the

00:05:34.470 --> 00:05:36.880
circle in terms of k?

00:05:36.880 --> 00:05:38.830
Let's think about this.

00:05:38.830 --> 00:05:42.290
So this is-- this is going to
deal with triangles, and how

00:05:42.290 --> 00:05:45.610
can we use the radius and relate
it to this right here?

00:05:45.610 --> 00:05:48.660
Well, the first thing that might
come to mind is if I

00:05:48.660 --> 00:05:54.970
just drop a line straight down
from here, that's equal to the

00:05:54.970 --> 00:05:57.130
radius, right?

00:05:57.130 --> 00:05:59.640
That's equal to the radius,
because it is a 90-degree

00:05:59.640 --> 00:06:00.880
angle right here, right?

00:06:00.880 --> 00:06:02.840
It touches that line.

00:06:02.840 --> 00:06:06.780
So if we could figure out this
distance right here, then we

00:06:06.780 --> 00:06:09.360
could use the Pythagorean
theorem to maybe figure out

00:06:09.360 --> 00:06:10.420
what the radius is.

00:06:10.420 --> 00:06:12.610
And luckily enough, this
distance is also the radius.

00:06:12.610 --> 00:06:14.490
And if that's not obvious
to you, think about it.

00:06:14.490 --> 00:06:17.740
The distance from here to here
is exactly the same thing as

00:06:17.740 --> 00:06:20.240
the distance from here
to there, right?

00:06:20.240 --> 00:06:22.510
And from here to here is the
radius of the circle.

00:06:22.510 --> 00:06:24.460
So this is also r.

00:06:24.460 --> 00:06:26.980
So now we can use the
Pythagorean theorem.

00:06:26.980 --> 00:06:32.590
r squared plus r squared
is equal to k squared.

00:06:32.590 --> 00:06:36.210
Or 2r squared is equal
to k squared.

00:06:36.210 --> 00:06:38.600
They wanted radius in
terms of k, right.

00:06:38.600 --> 00:06:44.580
So you get r squared is equal
to k squared over 2.

00:06:44.580 --> 00:06:48.870
Take the square root of both
sides. r is equal to k over

00:06:48.870 --> 00:06:50.340
the square root of 2.

00:06:50.340 --> 00:06:51.575
Do they want us to
rational-- nope,

00:06:51.575 --> 00:06:52.280
that's one of the choices.

00:06:52.280 --> 00:06:53.773
Sometimes they want you
to get the square

00:06:53.773 --> 00:06:54.890
root of 2 in the numerator.

00:06:54.890 --> 00:06:57.750
At least when I used to take
Algebra, they used to harp on

00:06:57.750 --> 00:06:58.410
that little bit.

00:06:58.410 --> 00:07:02.140
But anyway, this is choice B.

00:07:02.140 --> 00:07:12.120
Next question, problem 230.

00:07:12.120 --> 00:07:15.500
In an electric circuit, two
resistors with the resistances

00:07:15.500 --> 00:07:18.700
x and y are connected
in parallel.

00:07:18.700 --> 00:07:20.490
This is reminding me of
the Physics videos.

00:07:20.490 --> 00:07:21.760
So they're connected
in parallel.

00:07:25.920 --> 00:07:31.060
And this resistance is
x and resistance y.

00:07:31.060 --> 00:07:34.270
In this case, if r is the
combined resistance of these

00:07:34.270 --> 00:07:37.140
two resistors, then the
reciprocal of r is equal to

00:07:37.140 --> 00:07:38.900
the sum of the reciprocals
of x and y, and that's

00:07:38.900 --> 00:07:39.420
what they teach you.

00:07:39.420 --> 00:07:43.080
So if you want to know the
combined resistance of this,

00:07:43.080 --> 00:07:45.640
and let's say that's r, they
say 1 over the combined

00:07:45.640 --> 00:07:48.700
resistance is equal
to 1/x x plus 1/y.

00:07:48.700 --> 00:07:51.220
And if you took basic circuits,
this is one of the

00:07:51.220 --> 00:07:54.290
fundamental things about
parallel resistances.

00:07:54.290 --> 00:08:00.970
And then they want to know what
is r in terms of x and y?

00:08:00.970 --> 00:08:04.370
So let's see if we
can solve for r.

00:08:04.370 --> 00:08:07.040
So 1/r will be equal to--
let's get a common

00:08:07.040 --> 00:08:10.550
denominator, xy.

00:08:10.550 --> 00:08:13.190
1/x x is y/xy.

00:08:13.190 --> 00:08:16.380
1/y is x/xy, right?

00:08:16.380 --> 00:08:18.110
And then we can take the
reciprocal of both sides.

00:08:18.110 --> 00:08:24.970
So then r/1, or r, is equal
to xy over x plus y.

00:08:24.970 --> 00:08:27.200
I just switched those
two around.

00:08:27.200 --> 00:08:33.100
And that is -- xy over x plus
y-- that is choice D.

00:08:33.100 --> 00:08:36.360
Problem 231.

00:08:36.360 --> 00:08:37.730
Let me do it in this
brown color.

00:08:37.730 --> 00:08:40.830
231.

00:08:40.830 --> 00:08:47.370
Xavier, Yvonne and Zelda, who
happen to go by X, Y and Z, at

00:08:47.370 --> 00:08:49.530
least in my world, each try

00:08:49.530 --> 00:08:51.750
independently to solve a problem.

00:08:51.750 --> 00:08:54.880
If their individual
probabilities for success are

00:08:54.880 --> 00:09:02.070
1/4, 1/2, and 5/8, respectively,
what is the

00:09:02.070 --> 00:09:09.290
probability that Xavier and
Yvonne but not Zelda will

00:09:09.290 --> 00:09:10.720
solve the problem?

00:09:10.720 --> 00:09:13.100
So Xavier and Yvonne,
but not Zelda.

00:09:13.100 --> 00:09:14.920
So that's the case we're
looking for.

00:09:14.920 --> 00:09:16.030
So we're looking
for that case.

00:09:16.030 --> 00:09:20.020
So there's a 1/4 probability
that Xavier solves it, and

00:09:20.020 --> 00:09:22.750
then there's a 1/2 probability
that Yvonne does, but the

00:09:22.750 --> 00:09:26.560
probability that both of them
do is 1/4 times 1/2.

00:09:26.560 --> 00:09:28.630
That's the problem that
they both solve it.

00:09:28.630 --> 00:09:33.130
And then we want that case
and-- not or-- and

00:09:33.130 --> 00:09:34.560
Zelda can't solve it.

00:09:34.560 --> 00:09:36.390
So what's the probability that
Zelda doesn't solve it?

00:09:36.390 --> 00:09:40.830
5/8 is the probability that she
does solve it, so what's 1

00:09:40.830 --> 00:09:41.430
minus this?

00:09:41.430 --> 00:09:44.770
So there's a 3/8 probability
that Zelda does not solve the

00:09:44.770 --> 00:09:46.670
problem, right?

00:09:46.670 --> 00:09:47.780
And what does this
come out to?

00:09:47.780 --> 00:09:51.590
This is equal to 3 over--
4 times 2 is 8.

00:09:51.590 --> 00:09:58.020
8 times 8 is 64, which
is choice E.

00:09:58.020 --> 00:09:59.250
And I'm out of time.

00:09:59.250 --> 00:10:01.430
I'll see you in the
next video. video.


GMAT: Math 48

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:04.400
We're on problem 226.

00:00:04.400 --> 00:00:07.450
In the figure above-- let me
draw the figure above.

00:00:07.450 --> 00:00:12.200
So I have a line there, then I
have another line that's like

00:00:12.200 --> 00:00:17.030
that, and then this is a
triangle like that, and then

00:00:17.030 --> 00:00:20.470
they draw another line that goes
straight down like that.

00:00:20.470 --> 00:00:25.500
And they call this right here z
degrees, this is y degrees,

00:00:25.500 --> 00:00:27.440
this is x degrees.

00:00:27.440 --> 00:00:29.350
They tell us that these
are right angles.

00:00:29.350 --> 00:00:30.370
Fair enough.

00:00:30.370 --> 00:00:33.260
In the figure above, if z is
equal to 50, so that is equal

00:00:33.260 --> 00:00:39.570
to 50 degreeS, then x plus
y is equal to what?

00:00:39.570 --> 00:00:42.430
Well if z is 50-- well, first
of all, we know since these

00:00:42.430 --> 00:00:46.380
are both right angles, both of
these lines are going to be

00:00:46.380 --> 00:00:48.140
parallel, right?

00:00:48.140 --> 00:00:49.710
Both of those lines
are parallel.

00:00:49.710 --> 00:00:52.300
And so you can view this
green line as a

00:00:52.300 --> 00:00:56.140
transversal of the parallel.

00:00:56.140 --> 00:00:59.330
And so, z and y are
corresponding angles, so y is

00:00:59.330 --> 00:01:00.260
also going to be 50.

00:01:00.260 --> 00:01:02.250
That should make a little
intuitive sense, but you could

00:01:02.250 --> 00:01:04.510
watch the Khan Academy geometry
videos if that

00:01:04.510 --> 00:01:05.150
doesn't make sense.

00:01:05.150 --> 00:01:07.230
But just eyeballing it looks
right, too, but that's a

00:01:07.230 --> 00:01:10.170
property of transversals
and parallel lines.

00:01:10.170 --> 00:01:14.560
And if that's true, then what
is this angle right here?

00:01:14.560 --> 00:01:22.150
Well, 50 plus 90 plus this angle
is equal to 180, right?

00:01:22.150 --> 00:01:28.740
So we could say 50 plus 90 plus
theta is equal to 180.

00:01:28.740 --> 00:01:34.040
So you get 140 plus theta
is equal to 180.

00:01:34.040 --> 00:01:38.460
Subtract 140 from both
sides, so theta

00:01:38.460 --> 00:01:40.430
is equal to 40 degrees.

00:01:40.430 --> 00:01:42.960
So this angle right here
is 40 degrees.

00:01:42.960 --> 00:01:44.300
What's x?

00:01:44.300 --> 00:01:45.300
Well, they're supplementary.

00:01:45.300 --> 00:01:46.820
They have to add up.

00:01:46.820 --> 00:01:49.610
They have to add up
to be 180, right?

00:01:49.610 --> 00:01:51.260
This whole angle's 180.

00:01:51.260 --> 00:01:55.040
So that whole angle is 180, this
is 40, then x has to be

00:01:55.040 --> 00:01:57.580
140 degrees.

00:01:57.580 --> 00:02:00.180
So they wanted to know
what x plus y is?

00:02:00.180 --> 00:02:06.750
Well x is 140, y is 50, so 140
plus 50 is 190 degrees.

00:02:06.750 --> 00:02:09.330
And that is not one
of the choices.

00:02:09.330 --> 00:02:13.080
So I must have -- oh,
I see my mistake.

00:02:13.080 --> 00:02:15.020
This angle right here,
actually, we're still

00:02:15.020 --> 00:02:15.780
completely fine.

00:02:15.780 --> 00:02:18.870
This angle right here isn't y.

00:02:18.870 --> 00:02:20.730
This angle right here is y.

00:02:20.730 --> 00:02:22.780
But everything we did
so far still holds.

00:02:22.780 --> 00:02:25.950
If this angle is 50, this angle
is still 50 since it's a

00:02:25.950 --> 00:02:27.750
corresponding angle, right?

00:02:27.750 --> 00:02:32.590
And if that's 50, this is 90,
then this is 40, x is 140.

00:02:32.590 --> 00:02:34.840
Now we just have to figure
out what y is.

00:02:34.840 --> 00:02:38.820
Well, y is supplementary with
this angle right here, right?

00:02:38.820 --> 00:02:43.650
So y plus this angle that I used
to think was y until I

00:02:43.650 --> 00:02:47.350
looked closely at the drawing,
y plus 50 has to be equal to

00:02:47.350 --> 00:02:48.970
180 degrees, right?

00:02:48.970 --> 00:02:52.240
Because it's complementary with
this 50 degree angle.

00:02:52.240 --> 00:02:55.330
So y is equal to 130.

00:02:55.330 --> 00:03:03.880
So x plus y is equal to 140 plus
130, which is equal to

00:03:03.880 --> 00:03:06.670
270 degrees, and that's
choice D.

00:03:09.310 --> 00:03:12.968
Problem 227.

00:03:12.968 --> 00:03:14.840
Looks like they've drawn
another coordinate

00:03:14.840 --> 00:03:17.790
axis, which I'll draw.

00:03:17.790 --> 00:03:20.620
Nope, that's not what
I want to draw with.

00:03:20.620 --> 00:03:24.790
I'll draw with that.

00:03:24.790 --> 00:03:29.160
OK, and then they have a
line that comes down

00:03:29.160 --> 00:03:33.380
something like that.

00:03:33.380 --> 00:03:35.160
And they mark it off.

00:03:35.160 --> 00:03:38.140
They say that this is-- let me
see how they mark it off.

00:03:38.140 --> 00:03:44.220
They say that this is the point
1, this is the point 2.

00:03:44.220 --> 00:03:45.560
They don't write the 2 there.

00:03:45.560 --> 00:03:46.720
They call this line l.

00:03:46.720 --> 00:03:48.350
This is the origin.

00:03:48.350 --> 00:03:51.720
This is the x-axis and
that is the y-axis.

00:03:51.720 --> 00:03:54.250
And they say in the coordinate
system above, which of the

00:03:54.250 --> 00:04:00.100
following is the equation
of line l?

00:04:00.100 --> 00:04:01.810
Well, if we just eyeball it--
I mean, they don't say it

00:04:01.810 --> 00:04:04.450
explicitly, but it looks like
this is intersecting at y is

00:04:04.450 --> 00:04:06.890
equal to 2, and this
is intersecting at

00:04:06.890 --> 00:04:08.800
y is equal to 3.

00:04:08.800 --> 00:04:11.740
I guess that's a safe
assumption.

00:04:11.740 --> 00:04:13.330
So how do we set up
this equation?

00:04:13.330 --> 00:04:14.920
Well, you just have to figure
out the slope of the

00:04:14.920 --> 00:04:16.209
y-intercept.

00:04:16.209 --> 00:04:18.220
We already know the y-intercept,
right?

00:04:18.220 --> 00:04:23.330
It intersects-- when
x is 0-- so y of 0.

00:04:23.330 --> 00:04:28.470
When x is 0, y is equal to 2, so
that's the y-intercept, and

00:04:28.470 --> 00:04:30.930
now we just have to figure
out the slope.

00:04:30.930 --> 00:04:32.370
Well, let's think
about the slope.

00:04:32.370 --> 00:04:36.940
If we take this point--
well, I'll do it

00:04:36.940 --> 00:04:37.850
the formal way, right?

00:04:37.850 --> 00:04:43.570
The slope is equal to change
in y over change in x.

00:04:43.570 --> 00:04:44.830
So let's take this
as the end point.

00:04:44.830 --> 00:04:48.310
This is 3 comma 0,
[PHONE RINGS]

00:04:48.310 --> 00:04:50.660
and let's see who's
on the phone.

00:04:50.660 --> 00:04:53.310
If it's someone-- oh,
I'll take that call.

00:04:53.310 --> 00:04:55.750
I'll continue this in
the next video.


GMAT: Math 45

WEBVTT
Kind: captions
Language: en

00:00:00.850 --> 00:00:05.090
We're on problem 214.

00:00:05.090 --> 00:00:08.950
Of the 50 researchers in a
work group, 40% will be

00:00:08.950 --> 00:00:11.070
assigned to team A.

00:00:11.070 --> 00:00:14.400
So let's call that team A.

00:00:14.400 --> 00:00:17.350
Of the 50 researchers working,
40% percent will be

00:00:17.350 --> 00:00:19.120
assigned to team A.

00:00:19.120 --> 00:00:24.240
So 40% of 50, that's equal
to 20 go to team A.

00:00:24.240 --> 00:00:26.870
And the remaining 60%
go to team B.

00:00:26.870 --> 00:00:30.370
So B gets the remaining 60%,
which is 30 people, right?

00:00:30.370 --> 00:00:33.020
60% percent of 50 is 30.

00:00:33.020 --> 00:00:36.690
However, 70% of the researchers
prefer team A, and

00:00:36.690 --> 00:00:39.600
30% prefer team B.

00:00:39.600 --> 00:00:50.250
So 70%, which is what,
35, prefer A, and

00:00:50.250 --> 00:00:51.750
30% prefer team B.

00:00:51.750 --> 00:01:01.210
So the remainder, which is 15,
right, or 30% of 50, prefer B.

00:01:01.210 --> 00:01:04.650
What is the lowest possible
number of researchers who will

00:01:04.650 --> 00:01:08.740
not be assigned to the
team they prefer?

00:01:08.740 --> 00:01:11.390
So there's a lot of
pseudo-double negatives here.

00:01:11.390 --> 00:01:15.350
What is the lowest possible
number of researchers who will

00:01:15.350 --> 00:01:21.060
not be assigned to the team
that they prefer?

00:01:21.060 --> 00:01:23.620
So this is -- I have to read
that a couple of times.

00:01:23.620 --> 00:01:27.130
What is the lowest number of
researchers who will not be

00:01:27.130 --> 00:01:32.050
assigned to the team
they prefer?

00:01:32.050 --> 00:01:34.360
So essentially they're saying
this is the case where most

00:01:34.360 --> 00:01:36.880
people get the team they
prefer, right?

00:01:36.880 --> 00:01:39.210
Where as many people as possible
to get the team they

00:01:39.210 --> 00:01:42.960
prefer, and then we want the
lowest number of people who

00:01:42.960 --> 00:01:45.280
didn't get the team
they prefer.

00:01:45.280 --> 00:01:46.420
So what's the situation?

00:01:46.420 --> 00:01:51.190
Well, the best situation is --
let's see, 35 prefer A, so

00:01:51.190 --> 00:01:53.125
let's say that 20
of them got A.

00:01:56.410 --> 00:02:01.590
And then 15 fall into
this upset category.

00:02:01.590 --> 00:02:06.380
And likewise, out of these 15
that prefer B, well, I don't

00:02:06.380 --> 00:02:08.919
know, let's say that
all of them got B.

00:02:18.720 --> 00:02:21.310
All of these got B, but then we
have to put another 15 in

00:02:21.310 --> 00:02:23.480
B, and that's these 15 people.

00:02:23.480 --> 00:02:27.320
So the best case scenario in
which all of these people get

00:02:27.320 --> 00:02:32.300
B, and 20 of these people get
A, but then you've got to

00:02:32.300 --> 00:02:35.330
stick 15 people of these in B,
so those 15 people are going

00:02:35.330 --> 00:02:36.570
to be upset.

00:02:36.570 --> 00:02:39.000
And so that is the lowest
possible number of researchers

00:02:39.000 --> 00:02:41.680
who will not be assigned to
the team they prefer, so

00:02:41.680 --> 00:02:44.930
that's these 15.

00:02:44.930 --> 00:02:46.180
And that's choice A.

00:02:48.800 --> 00:02:53.240
Problem 215.

00:02:53.240 --> 00:02:56.780
If m is the average of the first
ten positive multiples

00:02:56.780 --> 00:03:02.850
of 5, m is equal to average of,
I don't know, let's call

00:03:02.850 --> 00:03:07.840
it multiples of 5, and M is the
median of the first ten --

00:03:07.840 --> 00:03:15.390
and this is the first ten --
and M-- big M-- is equal to

00:03:15.390 --> 00:03:22.430
the median of the same thing,
what is the value of big M

00:03:22.430 --> 00:03:23.180
minus small m?

00:03:23.180 --> 00:03:24.460
So let's just write them out.

00:03:24.460 --> 00:03:25.690
I think that's the simplest
way to do it.

00:03:25.690 --> 00:03:28.580
The first ten multiples of 5.

00:03:28.580 --> 00:03:36.130
5, 10 -- the first ten positive
multiples of 5.

00:03:36.130 --> 00:03:38.070
Right, so we won't count 0.

00:03:38.070 --> 00:03:45.760
5, 10, 15, 20, 25, 30, 35 --
actually, let me write it

00:03:45.760 --> 00:03:47.620
another way, I know this
is a little confusing.

00:03:47.620 --> 00:04:02.930
So this is 5, 10, 15, 20, 25,
30, 35, 40, 45, and 50.

00:04:02.930 --> 00:04:05.920
And I just thought of writing
it that way for a reason.

00:04:05.920 --> 00:04:09.660
So, first of all, they want a
little m, which is the mean.

00:04:09.660 --> 00:04:12.390
Little m is equal to the
average of this.

00:04:12.390 --> 00:04:13.130
Let me ask you a question.

00:04:13.130 --> 00:04:15.740
If you average-- so I paired
these numbers from the lowest

00:04:15.740 --> 00:04:19.230
to the highest, second lowest to
second highest. If you take

00:04:19.230 --> 00:04:21.110
the sum of this one and
this one, you get 55.

00:04:21.110 --> 00:04:22.850
This one and this
one, you get 55.

00:04:22.850 --> 00:04:25.000
This one and this
one, you get 55.

00:04:25.000 --> 00:04:26.250
So I think you get the point.

00:04:26.250 --> 00:04:28.960
The sum of any two
of them are 55.

00:04:28.960 --> 00:04:31.540
So if you take the average of
any of these, the average of 5

00:04:31.540 --> 00:04:36.840
and 50 is 27.5.

00:04:36.840 --> 00:04:38.850
And that's going to actually be
the average for the whole

00:04:38.850 --> 00:04:40.700
set, because you can
pair them up.

00:04:40.700 --> 00:04:42.950
The average of 25
and 30, 27.5.

00:04:42.950 --> 00:04:46.650
The average of 20
and 35 is 27.5.

00:04:46.650 --> 00:04:48.630
And if you don't believe me, I
mean, there's a bunch of ways

00:04:48.630 --> 00:04:49.470
you can think about this.

00:04:49.470 --> 00:04:53.160
You could say, oh, this is
the same thing as 55.

00:04:53.160 --> 00:04:55.470
If you wanted to figure out the
sum of this, you can say

00:04:55.470 --> 00:04:58.680
if I sum these, it would
be 55 times 5.

00:04:58.680 --> 00:05:01.990
So you'd have-- the sum of all
of them would be 55 times 5

00:05:01.990 --> 00:05:07.140
divided by the total of all of
them, which is 10, which is 55

00:05:07.140 --> 00:05:09.490
times 1/2, which is 27.5.

00:05:09.490 --> 00:05:11.300
Anyway, there's a bunch of ways
to think about it, but I

00:05:11.300 --> 00:05:12.870
just wanted to show you a quick
way of figuring out the

00:05:12.870 --> 00:05:16.940
average of the first
ten multiples of 5.

00:05:16.940 --> 00:05:18.790
And then they want to know
what is the median of the

00:05:18.790 --> 00:05:21.650
first ten positive
multiples of 5?

00:05:21.650 --> 00:05:23.660
So the middle numbers--
so there's two middle

00:05:23.660 --> 00:05:25.860
numbers, these two.

00:05:25.860 --> 00:05:28.010
So when you have two middle
numbers, you take the average

00:05:28.010 --> 00:05:29.250
of them to get the median.

00:05:29.250 --> 00:05:30.160
Well, guess what?

00:05:30.160 --> 00:05:33.410
The average of those
two is 27.5.

00:05:33.410 --> 00:05:38.440
So big M is equal to 27.5.

00:05:38.440 --> 00:05:45.930
So big m minus small m is
0, and that is choice B.

00:05:45.930 --> 00:05:52.040
Next question, 216.

00:05:52.040 --> 00:06:01.530
If m is greater than 0, and x is
m% of y-- so x is equal to

00:06:01.530 --> 00:06:04.260
m/100 times y, right?

00:06:04.260 --> 00:06:09.430
If m is 6%-- and this'll
turns into 0.06, right?

00:06:09.430 --> 00:06:21.090
x is m% of y, then in terms of
m, y is what percent of x?

00:06:21.090 --> 00:06:24.520
OK, so let's multiply both
sides of this by 100/m.

00:06:24.520 --> 00:06:31.230
So you get 100/m x, and 100/m
times m/100 is just 1 is equal

00:06:31.230 --> 00:06:33.950
to y, right?

00:06:33.950 --> 00:06:37.450
Let me switch the order to so it
makes a little more-- y is

00:06:37.450 --> 00:06:44.080
equal to 100/m times x.

00:06:44.080 --> 00:06:48.880
So if I wanted to write this
as a percentage, this right

00:06:48.880 --> 00:06:51.620
here is going to be some
type of decimal number.

00:06:51.620 --> 00:06:55.330
And so if I have a decimal and
I want to multiply, and if I

00:06:55.330 --> 00:06:58.090
want to express it as a
percentage, I mean, if this

00:06:58.090 --> 00:07:00.900
right here is 1, if I wanted
express it as a percentage, it

00:07:00.900 --> 00:07:02.330
would be 100%.

00:07:02.330 --> 00:07:05.755
If this right here ends up being
0.2, I would multiply it

00:07:05.755 --> 00:07:07.690
by 100 and get 20%.

00:07:07.690 --> 00:07:09.730
So to express this as
a percentage, I'd

00:07:09.730 --> 00:07:11.270
multiply it by 100.

00:07:11.270 --> 00:07:18.400
So 100/m times 100 is
equal to 10,000/m.

00:07:18.400 --> 00:07:21.380
And that is choice E.

00:07:21.380 --> 00:07:24.040
10,000 over m%, which
is the same thing

00:07:24.040 --> 00:07:28.260
as 100/m as a decimal.

00:07:28.260 --> 00:07:32.870
Next question, 217.

00:07:32.870 --> 00:07:34.120
I'll use green.

00:07:37.830 --> 00:07:41.660
A certain junior class has 1,000
students, so the junior

00:07:41.660 --> 00:07:45.550
class has 1,000 students,
and a certain senior

00:07:45.550 --> 00:07:47.570
class has 800 students.

00:07:47.570 --> 00:07:49.820
So some people dropped out.

00:07:49.820 --> 00:07:50.350
Maybe they didn't.

00:07:50.350 --> 00:07:52.610
Maybe it started bigger
or smaller.

00:07:52.610 --> 00:07:56.250
Among these students there
60 sibling pairs.

00:07:56.250 --> 00:08:00.220
60 siblings-- I already sense
a Venn diagram coming-- each

00:08:00.220 --> 00:08:03.080
consisting of 1 junior
and 1 senior.

00:08:07.220 --> 00:08:10.050
If one student is to be selected
at random from each

00:08:10.050 --> 00:08:14.880
class, what is the probability
that the two students selected

00:08:14.880 --> 00:08:18.330
will be a sibling pair?

00:08:18.330 --> 00:08:20.980
If one student is to be selected
at random from each

00:08:20.980 --> 00:08:24.340
class, what is the probability
that the two students will be

00:08:24.340 --> 00:08:25.630
a sibling pair?

00:08:25.630 --> 00:08:28.220
OK, so how many sibling
pair members are

00:08:28.220 --> 00:08:29.090
there in each class?

00:08:29.090 --> 00:08:31.460
Well, there have to be
30 in each class.

00:08:31.460 --> 00:08:34.990
So there's 30 sibling pair
members in that class and

00:08:34.990 --> 00:08:38.400
there's 30 sibling pair
members in that class.

00:08:38.400 --> 00:08:41.610
OK, so if one student is to be
selected at random from each

00:08:41.610 --> 00:08:44.320
class, what is the probability
that two students will be a

00:08:44.320 --> 00:08:45.040
sibling pair?

00:08:45.040 --> 00:08:48.690
OK, so let's say we pick a
student from the junior class

00:08:48.690 --> 00:08:50.150
first, right?

00:08:50.150 --> 00:08:53.570
So first of all, what's the
chances that they're even part

00:08:53.570 --> 00:08:54.820
of a sibling pair?

00:08:59.010 --> 00:09:01.710
Well, that's going to be--
there's 30 of them that are

00:09:01.710 --> 00:09:03.910
part of a pair, and there's
1,000 in the class, so the

00:09:03.910 --> 00:09:08.740
probability of that happening is
30/1,000, which is the same

00:09:08.740 --> 00:09:13.250
thing as 3/100, right?

00:09:13.250 --> 00:09:17.610
That's the probability that
we got a part of a pair.

00:09:17.610 --> 00:09:23.810
Now we're going to go and pick
someone from the senior class.

00:09:23.810 --> 00:09:26.390
If we want to find this guy's
sibling, we can't just find

00:09:26.390 --> 00:09:28.630
another sibling pair, we've
got to find this

00:09:28.630 --> 00:09:30.350
guy's actual sibling.

00:09:30.350 --> 00:09:33.070
So actually, only one person in
the entire senior class is

00:09:33.070 --> 00:09:36.510
going to be-- whoever this
person we pick from the junior

00:09:36.510 --> 00:09:39.300
class, if we did happen to pick
one, the only way that we

00:09:39.300 --> 00:09:41.990
got an actual sibling pair is if
we pick that one person in

00:09:41.990 --> 00:09:44.620
the senior class who is
this person's sibling.

00:09:44.620 --> 00:09:47.340
So there's actually only
a 1 in 800 chance

00:09:47.340 --> 00:09:49.000
that we picked them.

00:09:49.000 --> 00:09:52.530
So if we multiply that out,
that is equal to 3 over--

00:09:52.530 --> 00:09:54.050
let's see, what is it?

00:09:54.050 --> 00:09:56.160
80,000?

00:09:56.160 --> 00:10:01.570
3/80,000, which is not
one of the choices.

00:10:01.570 --> 00:10:02.820
So what did I do wrong?

00:10:05.500 --> 00:10:06.580
Here.

00:10:06.580 --> 00:10:10.520
So I see 3/40,000, and for some
reason, I think maybe I'm

00:10:10.520 --> 00:10:14.520
not counting two scenarios.

00:10:14.520 --> 00:10:16.310
There's probably two scenarios
in which is

00:10:16.310 --> 00:10:18.360
this can occur, right?

00:10:18.360 --> 00:10:24.150
I could have picked-- if I go to
the junior class first and

00:10:24.150 --> 00:10:27.620
there's a 30 in 1,000 chance
that I pick the correct

00:10:27.620 --> 00:10:34.020
sibling, so that's 3 in 100, and
then the odds that I take

00:10:34.020 --> 00:10:40.120
his or her sibling from the
senior class is 1 in 800.

00:10:40.120 --> 00:10:42.960
But maybe then-- let me see if
I'm missing some logic here.

00:10:42.960 --> 00:10:46.470
Maybe I could have picked--
well, instead of me stumbling

00:10:46.470 --> 00:10:48.600
because I'm already over time,
let me continue this in the

00:10:48.600 --> 00:10:50.150
next video.