GMAT: Data sufficiency 29

WEBVTT
Kind: captions
Language: en

00:00:00.640 --> 00:00:05.480
We're on problem 119.

00:00:05.480 --> 00:00:08.980
Is 2x minus 3y less
than x squared?

00:00:08.980 --> 00:00:17.330
2x minus 3y less than x
squared they ask us.

00:00:17.330 --> 00:00:19.290
All right, let's see if
we can figure it out.

00:00:19.290 --> 00:00:24.130
Statement 1, 2x minus 3y
is equal to minus 2.

00:00:33.530 --> 00:00:35.530
So they're telling us that the
left-hand side of this

00:00:35.530 --> 00:00:37.280
original question is
equal to minus 2.

00:00:37.280 --> 00:00:39.400
So now this question, if we
take statement 1 into

00:00:39.400 --> 00:00:42.680
consideration, it boils
down to is minus

00:00:42.680 --> 00:00:45.780
2 less than x squared?

00:00:45.780 --> 00:00:47.680
So first you might be saying,
oh, I don't know.

00:00:47.680 --> 00:00:48.850
I don't know what x is.

00:00:48.850 --> 00:00:50.060
But think about it.

00:00:50.060 --> 00:00:51.850
Can x be a negative number?

00:00:51.850 --> 00:00:55.400
At worst case, x is 0.

00:00:55.400 --> 00:00:56.990
That's the worst case.

00:00:56.990 --> 00:00:59.940
If x was anything else, x
squared is going to be a

00:00:59.940 --> 00:01:01.880
positive number.

00:01:01.880 --> 00:01:05.590
So we actually know, just from
statement 1, that negative 2

00:01:05.590 --> 00:01:08.040
has to be less than x squared,
unless x was some type of

00:01:08.040 --> 00:01:09.660
weird, imaginary number
or something.

00:01:09.660 --> 00:01:11.730
I think that doesn't
occur on the GMAT.

00:01:11.730 --> 00:01:13.790
So statement 1 alone
is sufficient.

00:01:13.790 --> 00:01:18.200
x squared is going to be at
least 0 or some positive

00:01:18.200 --> 00:01:19.960
number larger than 0.

00:01:19.960 --> 00:01:22.490
So statement 1 is sufficient.

00:01:22.490 --> 00:01:31.790
Statement two, x is greater
than 2 and y is

00:01:31.790 --> 00:01:33.676
greater than 0.

00:01:38.140 --> 00:01:41.620
So let me just try to come up
with two contradictory cases

00:01:41.620 --> 00:01:43.390
using these conditions to see.

00:01:43.390 --> 00:01:46.460
Let's say if x was-- and they
don't tell us that anything is

00:01:46.460 --> 00:01:48.330
an integer here.

00:01:48.330 --> 00:01:55.980
So if x was 2.1, x is equal to
2.1 and y is equal to-- I

00:01:55.980 --> 00:01:58.730
don't know-- y is
greater than 0.

00:01:58.730 --> 00:02:03.250
So let's say that y
is equal to 0.1.

00:02:03.250 --> 00:02:05.300
Let's see what happens here.

00:02:05.300 --> 00:02:07.420
So 2 times 2.1.

00:02:07.420 --> 00:02:11.520
You get 4.2 minus 3 times y.

00:02:11.520 --> 00:02:18.160
So minus 0.3 is less
than x squared.

00:02:18.160 --> 00:02:18.770
It's what?

00:02:18.770 --> 00:02:22.930
It's like 4 point something.

00:02:22.930 --> 00:02:24.990
So it's greater than 2.

00:02:24.990 --> 00:02:26.240
This is interesting.

00:02:33.020 --> 00:02:33.980
Actually this is interesting.

00:02:33.980 --> 00:02:36.840
So actually, you don't have
to try examples out.

00:02:36.840 --> 00:02:37.990
Let's just write the
equation down.

00:02:37.990 --> 00:02:44.080
2x minus 3y is less
than x squared.

00:02:44.080 --> 00:02:47.610
So if y is greater than 0,
which they tell us in

00:02:47.610 --> 00:02:51.660
statement 2, then the quantity
on the left-hand side is

00:02:51.660 --> 00:02:53.620
always going to be 2x.

00:02:53.620 --> 00:02:55.380
It's always going to be
less than 2x, right?

00:02:55.380 --> 00:02:57.070
Because this'll have some
positive value.

00:02:57.070 --> 00:03:00.170
It might have an insignificantly
small value.

00:03:00.170 --> 00:03:03.590
We could make it 0.000001.

00:03:03.590 --> 00:03:05.120
But it's still going to have
some positive value.

00:03:05.120 --> 00:03:07.940
So no matter what y we choose,
as long as it's greater than

00:03:07.940 --> 00:03:12.880
0, 2x minus 3y will be
greater than 2x.

00:03:12.880 --> 00:03:21.660
So we could say that if 2x is
less than x squared for any x

00:03:21.660 --> 00:03:28.580
we pick, than 2x minus 3y is
definitely going to be less

00:03:28.580 --> 00:03:29.440
than x squared.

00:03:29.440 --> 00:03:30.090
Why is that?

00:03:30.090 --> 00:03:33.250
Because minus 3y is going to
subtract from the 2x, because

00:03:33.250 --> 00:03:36.146
we know that y is
greater than 0.

00:03:36.146 --> 00:03:38.230
So let me ask you a question.

00:03:38.230 --> 00:03:41.780
Is 2x always going to be less
than x squared if x is

00:03:41.780 --> 00:03:43.390
greater than 2?

00:03:43.390 --> 00:03:44.050
Sure.

00:03:44.050 --> 00:03:48.100
I mean whatever x is, on the
left-hand side it's going to

00:03:48.100 --> 00:03:54.110
be 2 times-- pick a random
number-- 2 times x.

00:03:54.110 --> 00:03:56.520
It could be 2.5.

00:03:56.520 --> 00:03:58.743
But on the other side, on the
right-hand side, you're going

00:03:58.743 --> 00:04:01.760
to have 2.5 squared.

00:04:01.760 --> 00:04:02.680
So if you think about
it, you're going to

00:04:02.680 --> 00:04:05.200
have 2 times a number.

00:04:05.200 --> 00:04:08.040
That's always going to be less
than that number, which

00:04:08.040 --> 00:04:11.310
happens to be larger
than 2 squared.

00:04:11.310 --> 00:04:17.860
The smallest possible
is 2 times 2.00001.

00:04:17.860 --> 00:04:19.480
You could make a lot
of 0's there.

00:04:19.480 --> 00:04:20.829
But I think you get the point.

00:04:20.829 --> 00:04:26.880
That's still going to be less
than 2.0001 squared.

00:04:26.880 --> 00:04:31.090
Because you only have a 2 here
instead of a 2.0001.

00:04:31.090 --> 00:04:34.440
So actually, statement 2
alone is sufficient.

00:04:34.440 --> 00:04:35.490
Hopefully that made sense.

00:04:35.490 --> 00:04:38.050
You just have to see oh, if y is
greater than 0, then the 3y

00:04:38.050 --> 00:04:40.660
is definitely going to take
away from the 2x.

00:04:40.660 --> 00:04:43.750
Then as long as x is greater
than 2, 2x is always going to

00:04:43.750 --> 00:04:44.910
be less than x squared.

00:04:44.910 --> 00:04:47.120
If that makes sense to you, then
you should realize that

00:04:47.120 --> 00:04:49.650
statement 2 alone is sufficient
for this.

00:04:49.650 --> 00:04:52.430
That was interesting.

00:04:52.430 --> 00:04:54.020
Oh, no sorry.

00:04:54.020 --> 00:04:56.000
Either of them alone
were sufficient.

00:04:56.000 --> 00:04:57.600
We did that in the
first one, right?

00:04:57.600 --> 00:05:00.810
Statement 1 or statement 2,
independently are sufficient

00:05:00.810 --> 00:05:03.300
to answer that question.

00:05:03.300 --> 00:05:08.100
120.

00:05:08.100 --> 00:05:12.480
A report consisting of 2,600
words is divided into 23

00:05:12.480 --> 00:05:13.200
paragraphs.

00:05:13.200 --> 00:05:19.050
So 2,600 words and it
has 23 paragraphs.

00:05:19.050 --> 00:05:22.230
A two-paragraph preface is
then added to the report.

00:05:25.950 --> 00:05:31.510
Is the average number of words
per paragraph for all 25

00:05:31.510 --> 00:05:38.720
paragraphs less than 120?

00:05:38.720 --> 00:05:39.720
So this is interesting.

00:05:39.720 --> 00:05:45.730
So the average number of words
per paragraph for all 25

00:05:45.730 --> 00:05:47.790
paragraphs less than 120.

00:05:47.790 --> 00:05:49.510
So if we knew the total
number of words in the

00:05:49.510 --> 00:05:50.710
document we'd be set.

00:05:50.710 --> 00:05:55.740
We would just take the total
words divided by the total

00:05:55.740 --> 00:05:56.820
paragraphs they have now.

00:05:56.820 --> 00:06:00.240
They have the 23 original plus
the 2 from the preface, you

00:06:00.240 --> 00:06:03.480
have 25 total paragraphs.

00:06:03.480 --> 00:06:06.350
Now it told you the average
words per paragrah.

00:06:06.350 --> 00:06:09.210
Now, we don't know the total
words, because the total is

00:06:09.210 --> 00:06:13.330
going to be equal to the 2,600
words in the body of the

00:06:13.330 --> 00:06:17.840
document plus the words from the
preface-- I'll call that

00:06:17.840 --> 00:06:22.230
words sub preface-- all
of that divided by 25.

00:06:22.230 --> 00:06:23.710
This is the average.

00:06:23.710 --> 00:06:25.760
This is what we really have to
figure out, to figure out if

00:06:25.760 --> 00:06:28.270
it's less than 120.

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That's what they want to know.

00:06:30.170 --> 00:06:32.200
So statement number 1.

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Each paragraph of the preface
has more than 100 words.

00:06:44.670 --> 00:06:47.900
So I guess we could say that
the preface, the words from

00:06:47.900 --> 00:06:53.320
the preface are greater
than 200.

00:06:53.320 --> 00:06:59.230
That's another way of saying
that the total is going to be

00:06:59.230 --> 00:07:03.130
greater than 2,800.

00:07:03.130 --> 00:07:05.800
Now if the total is greater
than 2,800, what does that

00:07:05.800 --> 00:07:10.070
tell us about the total divided
by-- excuse me.

00:07:10.070 --> 00:07:13.320
So then the total divided by 25
is going to be greater than

00:07:13.320 --> 00:07:16.310
2,800 divided by 25.

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What's 2,800 divided by 25?

00:07:18.980 --> 00:07:27.960
Let's see, 25 goes into 2,800.

00:07:27.960 --> 00:07:37.780
1, 25, 30, 1, 1 times
25, 25, 50, 12.

00:07:37.780 --> 00:07:42.190
So it tells us that the
average is going to be

00:07:42.190 --> 00:07:44.150
greater than 112.

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So that doesn't help us.

00:07:45.200 --> 00:07:48.250
If it told us that the average
was going to be greater than

00:07:48.250 --> 00:07:49.440
120, we would be done.

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We would say oh, we have enough
information to answer

00:07:51.400 --> 00:07:52.010
the question.

00:07:52.010 --> 00:07:54.330
Actually, the answer is no, that
the average is going to

00:07:54.330 --> 00:07:56.680
be greater than 120.

00:07:56.680 --> 00:07:58.740
But here, this tells us the
average is greater than 112.

00:07:58.740 --> 00:08:00.610
It could be 113 or
it could be 121.

00:08:00.610 --> 00:08:02.840
So it doesn't answer our
question of whether the

00:08:02.840 --> 00:08:04.990
average is less than 120.

00:08:04.990 --> 00:08:08.310
So statement one alone
is not that useful.

00:08:08.310 --> 00:08:13.230
Statement number 2 tells us each
paragraph of the preface

00:08:13.230 --> 00:08:15.650
has fewer than 100 words.

00:08:15.650 --> 00:08:23.160
So the total preface has
less than 300 words.

00:08:23.160 --> 00:08:25.190
They say each paragraph of the
preface, and there's 2 of

00:08:25.190 --> 00:08:27.310
them, has fewer than
150 words.

00:08:27.310 --> 00:08:29.990
So the total preface has
less than 300 words.

00:08:29.990 --> 00:08:31.725
So we could do the same logic.

00:08:35.054 --> 00:08:41.530
So that means that the total is
going to be less than what?

00:08:41.530 --> 00:08:45.190
The total is going to be less
than the original number of

00:08:45.190 --> 00:08:46.710
words plus the preface.

00:08:46.710 --> 00:08:50.080
So it's going to be less
than 2,600 plus 300.

00:08:50.080 --> 00:08:53.480
It's going to be less
than 2,900.

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Then if you divide both sides
by 25 to get the average, 25

00:09:00.000 --> 00:09:03.220
goes into 2,900 really
four more times.

00:09:07.170 --> 00:09:08.420
That's right.

00:09:10.540 --> 00:09:14.700
The average is going to be less
than-- let me make sure

00:09:14.700 --> 00:09:15.860
I'm getting that right.

00:09:15.860 --> 00:09:21.000
So 4, 25 goes into 2,900.

00:09:21.000 --> 00:09:26.435
1, 25, 40, 1, 25.

00:09:26.435 --> 00:09:29.970
Then we have 150.

00:09:29.970 --> 00:09:32.400
25 goes into 150 six times.

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So we have the average
is less than 1/16.

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So statement 2 alone
is sufficient.

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Statement 2 tells us that the
average of the words per

00:09:40.800 --> 00:09:43.110
paragraph is less than
116, which is

00:09:43.110 --> 00:09:44.340
definitely less than 120.

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So statement 2 alone is
sufficient, and statement 1

00:09:47.580 --> 00:09:49.120
doesn't help us much.

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I've run out of time.

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See you in the next video.


GMAT: Data sufficiency 24

WEBVTT
Kind: captions
Language: en

00:00:00.900 --> 00:00:05.920
We're on problem 103.

00:00:05.920 --> 00:00:14.420
And it says, if n and k
are greater than 0,

00:00:14.420 --> 00:00:16.350
is n over k an integer?

00:00:19.550 --> 00:00:22.660
So essentially they're asking,
is k divisible into n.

00:00:22.660 --> 00:00:26.630
So let's see, statement
1 says, n

00:00:26.630 --> 00:00:28.120
and k are both integers.

00:00:33.500 --> 00:00:35.070
And that's good that they told
me that, because I was

00:00:35.070 --> 00:00:36.320
assuming it incorrectly.

00:00:38.510 --> 00:00:40.210
So they're saying n and
k are both integers.

00:00:40.210 --> 00:00:41.780
Well that still doesn't
help me much.

00:00:41.780 --> 00:00:45.240
n could be 2 and
k could be 100.

00:00:45.240 --> 00:00:46.710
And 2 over 100, is 1/50.

00:00:46.710 --> 00:00:47.690
That's not an integer.

00:00:47.690 --> 00:00:50.180
Although n could be 4
and k could be 2.

00:00:50.180 --> 00:00:50.990
And that would be an integer.

00:00:50.990 --> 00:00:51.950
4 over 2 is 2.

00:00:51.950 --> 00:00:55.670
So statement 1 by itself
doesn't help me.

00:00:55.670 --> 00:01:01.500
Statement 2 says n squared and
k squared are both integers.

00:01:08.530 --> 00:01:11.800
Well once again, I don't see
this as helping me much.

00:01:11.800 --> 00:01:15.530
If n and k are both integers, of
course when you square them

00:01:15.530 --> 00:01:16.280
they're going to integers.

00:01:16.280 --> 00:01:18.410
You take any integer and you
square it you get an integer.

00:01:18.410 --> 00:01:20.762
You take any other integer
and you square

00:01:20.762 --> 00:01:21.520
it you get an integer.

00:01:21.520 --> 00:01:28.760
So this actually gives me no new
information relative to 1.

00:01:28.760 --> 00:01:31.050
So, I'm just trying to see
if I'm missing something.

00:01:31.050 --> 00:01:33.330
But as far as I can
tell it's E.

00:01:33.330 --> 00:01:35.360
Both statements together
are not sufficient

00:01:35.360 --> 00:01:37.890
to answer this question.

00:01:37.890 --> 00:01:39.230
I mean, I can give you a case.

00:01:39.230 --> 00:01:43.970
n could be 4, k could be 2.

00:01:43.970 --> 00:01:47.300
And then, n over k would
be an integer.

00:01:47.300 --> 00:01:49.400
And both of these would
satisfy both of these

00:01:49.400 --> 00:01:49.830
conditions.

00:01:49.830 --> 00:01:52.730
Or it could be, 2 and 4.

00:01:52.730 --> 00:01:55.160
In which case, n over
k aren't integers.

00:01:55.160 --> 00:01:56.210
They don't actually
differentiate

00:01:56.210 --> 00:01:57.940
between n and k at all.

00:01:57.940 --> 00:01:59.010
So it's E.

00:01:59.010 --> 00:02:00.940
Next problem.

00:02:00.940 --> 00:02:03.080
104.

00:02:03.080 --> 00:02:07.950
If the average arithmetic mean
of six numbers is 75, how many

00:02:07.950 --> 00:02:13.020
of the numbers are
equal to 75?

00:02:13.020 --> 00:02:15.350
OK, so six numbers
are equal to 75.

00:02:15.350 --> 00:02:22.930
How many of them are
equal to 75?

00:02:22.930 --> 00:02:25.930
Let me go scroll down
a little bit.

00:02:25.930 --> 00:02:29.550
The first statement says,
none of the six numbers

00:02:29.550 --> 00:02:32.810
is less than 75.

00:02:32.810 --> 00:02:40.810
So none less than 75.

00:02:40.810 --> 00:02:42.270
So this is interesting.

00:02:42.270 --> 00:02:43.770
If I have six numbers.

00:02:43.770 --> 00:02:50.170
And their average is 75 and none
of them are less than 75,

00:02:50.170 --> 00:02:58.200
they essentially all
have to be 75.

00:02:58.200 --> 00:03:02.240
Let's say the first
number is 75.

00:03:02.240 --> 00:03:05.340
Now let's just say that I had
some number above 75 in the

00:03:05.340 --> 00:03:08.230
list. Let's just say for
argument that there was a 76

00:03:08.230 --> 00:03:10.060
in the list. It doesn't
have to be an integer.

00:03:10.060 --> 00:03:10.990
They're not assuming that.

00:03:10.990 --> 00:03:14.200
But let's say I had 76 in the
list. In order for the average

00:03:14.200 --> 00:03:17.370
to be 75, I would have to offset
this number that's one

00:03:17.370 --> 00:03:19.130
more than 75 with another
number that's

00:03:19.130 --> 00:03:21.500
one less than 75.

00:03:21.500 --> 00:03:25.480
But they told us that none of
the numbers are less than 75.

00:03:25.480 --> 00:03:28.380
So if I have a number greater
than 75, I have to have a

00:03:28.380 --> 00:03:33.440
corresponding number less than
75, or several of them to

00:03:33.440 --> 00:03:34.820
balance off that number.

00:03:34.820 --> 00:03:36.590
Or you could have several
balancing several.

00:03:36.590 --> 00:03:37.880
It can get complicated.

00:03:37.880 --> 00:03:40.880
But the general idea is, is that
if no numbers are less

00:03:40.880 --> 00:03:42.840
than 75, you can't
have any numbers

00:03:42.840 --> 00:03:44.700
greater than 75 either.

00:03:44.700 --> 00:03:51.290
So this actually tells you
that all six are 75.

00:03:51.290 --> 00:03:54.040
So statement 1 alone
is sufficient.

00:03:54.040 --> 00:03:57.090
Statement 2 says, none
of the six numbers is

00:03:57.090 --> 00:04:00.990
greater than 75.

00:04:00.990 --> 00:04:02.700
Well it's the same argument.

00:04:02.700 --> 00:04:07.450
If I have a number,
let's call it a.

00:04:07.450 --> 00:04:10.120
Let's say it's one of the
numbers that's in my list. And

00:04:10.120 --> 00:04:12.010
it's greater than 75.

00:04:12.010 --> 00:04:14.830
In order to average down to
75, I'm going to have to

00:04:14.830 --> 00:04:18.190
have-- well let's say
a is less than 75.

00:04:18.190 --> 00:04:20.200
Because we're using statement
number 2.

00:04:20.200 --> 00:04:23.040
If a is less than 75--
let's say 75 is here

00:04:23.040 --> 00:04:23.960
in the number line.

00:04:23.960 --> 00:04:26.520
I'm just doing ad hoc
diagrams. So a

00:04:26.520 --> 00:04:27.800
is less than 75.

00:04:27.800 --> 00:04:31.090
In order for the whole group
to average to 75, I have to

00:04:31.090 --> 00:04:34.370
have some number that's bigger
than 75 to balance off the a.

00:04:34.370 --> 00:04:35.700
Let's call that b.

00:04:35.700 --> 00:04:37.410
But they're saying that
we have no numbers

00:04:37.410 --> 00:04:38.330
greater than 75.

00:04:38.330 --> 00:04:40.400
So we have no numbers
greater than 75.

00:04:40.400 --> 00:04:43.020
We can't have any numbers less
than 75 either and all the

00:04:43.020 --> 00:04:44.660
numbers have to be
equal to 75.

00:04:44.660 --> 00:04:45.740
All six of them.

00:04:45.740 --> 00:04:47.530
So once again 2 is
also sufficient.

00:04:47.530 --> 00:04:51.460
So each of these statements,
independently, are sufficient

00:04:51.460 --> 00:04:52.420
to answer this question.

00:04:52.420 --> 00:04:54.800
Actually they both answer the
question that all six are

00:04:54.800 --> 00:04:57.770
equal to 75.

00:04:57.770 --> 00:04:59.020
That was interesting.

00:05:02.790 --> 00:05:07.360
Problem 105.

00:05:07.360 --> 00:05:16.780
Is the absolute value of
x equal to y minus z?

00:05:16.780 --> 00:05:17.440
OK.

00:05:17.440 --> 00:05:22.440
Absolute value of x equal
to y minus z.

00:05:22.440 --> 00:05:22.910
All right.

00:05:22.910 --> 00:05:28.260
So in statement number 1,
they tell us that x plus

00:05:28.260 --> 00:05:32.335
y is equal to z.

00:05:35.250 --> 00:05:37.900
So let's see if we can do
some substitution. z is

00:05:37.900 --> 00:05:39.470
equal to x plus y.

00:05:39.470 --> 00:05:42.490
So if we substitute z into this
top equation we get the

00:05:42.490 --> 00:05:47.015
absolute value of x is equal
to y minus x plus y.

00:05:51.630 --> 00:05:54.090
So that means that the absolute
value of x is equal

00:05:54.090 --> 00:05:58.980
to y minus x minus y.

00:05:58.980 --> 00:06:01.280
And that says that the absolute
value of x is equal

00:06:01.280 --> 00:06:02.460
to minus x.

00:06:02.460 --> 00:06:04.390
Because the y's cancel out.

00:06:04.390 --> 00:06:05.670
Well I don't know if
this is true still.

00:06:05.670 --> 00:06:08.480
This would apply to any
negative number.

00:06:08.480 --> 00:06:10.870
If I have a negative
1, negative 1

00:06:10.870 --> 00:06:11.595
absolute value is 1.

00:06:11.595 --> 00:06:14.020
And negative negative
1 is 1 as well.

00:06:14.020 --> 00:06:16.610
So this would apply if x is
0 or some negative number.

00:06:16.610 --> 00:06:17.850
But they don't tell us that.

00:06:17.850 --> 00:06:20.340
So we don't know if
this is true.

00:06:20.340 --> 00:06:24.520
Statement 2 tells us-- well
there you go-- statement 2

00:06:24.520 --> 00:06:27.660
tells us that x is
less than 0.

00:06:27.660 --> 00:06:30.670
So this tells us x is definitely
a negative number.

00:06:30.670 --> 00:06:35.120
And if you put any negative
number into this, which we got

00:06:35.120 --> 00:06:39.360
from this condition and this
condition, if you put this

00:06:39.360 --> 00:06:43.070
into that, you know this is true
for any negative number.

00:06:43.070 --> 00:06:45.090
The absolute value of any
negative number is the

00:06:45.090 --> 00:06:46.870
opposite of that number.

00:06:46.870 --> 00:06:48.260
So you need both of
these statements.

00:06:48.260 --> 00:06:49.920
And obviously statement
2 alone is useless.

00:06:49.920 --> 00:06:51.810
Because if you just say x is
less than 0, you don't know

00:06:51.810 --> 00:06:55.640
anything about y or z without
this condition right here.

00:06:55.640 --> 00:06:57.710
So both statements together
are sufficient.

00:06:57.710 --> 00:07:02.080
But individually, they are
reasonably useless.

00:07:02.080 --> 00:07:03.900
106.

00:07:03.900 --> 00:07:05.150
We're getting up there.

00:07:07.870 --> 00:07:11.490
What was the total amount of
revenue that a theater

00:07:11.490 --> 00:07:15.120
received from the sale of 400
tickets, some of which were

00:07:15.120 --> 00:07:18.470
sold at x percent of full price
and the rest of which

00:07:18.470 --> 00:07:20.515
were sold at full price?

00:07:23.040 --> 00:07:27.240
So let's say we have the reduced
price tickets and the

00:07:27.240 --> 00:07:27.900
full price.

00:07:27.900 --> 00:07:31.360
So R is the number of reduced
price tickets and F is the

00:07:31.360 --> 00:07:32.780
number of full price tickets.

00:07:32.780 --> 00:07:34.955
So R plus F.

00:07:34.955 --> 00:07:40.740
So the the total number
of tickets was 400.

00:07:40.740 --> 00:07:42.570
What was the total amount
of revenue?

00:07:42.570 --> 00:07:46.510
And then the total amount of
revenue generated is going to

00:07:46.510 --> 00:07:53.440
be equal to the price
of full price times

00:07:53.440 --> 00:07:54.890
the full price tickets.

00:07:54.890 --> 00:08:00.010
So P times F where P is the
price of full priced.

00:08:00.010 --> 00:08:04.270
Plus the number of reduced
tickets and that's sold at x

00:08:04.270 --> 00:08:08.770
percent of the full
price tickets.

00:08:08.770 --> 00:08:10.760
Whatever x is. x percent.

00:08:10.760 --> 00:08:12.750
we'll convert it to a decimal
at the appropriate time.

00:08:12.750 --> 00:08:16.460
So this is what the initial
problem description tells us.

00:08:16.460 --> 00:08:19.180
That the total number of
tickets is 400 and then

00:08:19.180 --> 00:08:23.360
whatever-- of its x percentage
of P-- so whatever the full

00:08:23.360 --> 00:08:26.230
price is times the full price
tickets plus-- this would be

00:08:26.230 --> 00:08:28.390
the reduced price times the
reduced price tickets-- equals

00:08:28.390 --> 00:08:29.880
the total revenue.

00:08:29.880 --> 00:08:33.640
Now let's see if we can
figure this one out.

00:08:33.640 --> 00:08:37.610
x is equal to 50.

00:08:37.610 --> 00:08:39.770
Well this by itself just
tells us that this is p

00:08:39.770 --> 00:08:40.789
over 2 right here.

00:08:40.789 --> 00:08:42.880
This x is 0.5.

00:08:42.880 --> 00:08:44.290
It's 50%.

00:08:44.290 --> 00:08:45.880
Remember they said x percent.

00:08:45.880 --> 00:08:50.810
So this just makes this
equation, it turns it into,

00:08:50.810 --> 00:08:58.310
0.5 times P times R
plus P times F is

00:08:58.310 --> 00:09:00.780
equal to the revenue.

00:09:00.780 --> 00:09:03.450
And we still have
one, two, three

00:09:03.450 --> 00:09:05.470
unknowns and two equations.

00:09:05.470 --> 00:09:07.220
So that by itself
isn't enough.

00:09:09.860 --> 00:09:11.260
We actually have
four unknowns.

00:09:11.260 --> 00:09:13.230
R, P, F and revenue.

00:09:13.230 --> 00:09:14.340
Four unknowns, two equations.

00:09:14.340 --> 00:09:15.750
Not good enough.

00:09:15.750 --> 00:09:19.370
2, full price tickets
sold for $20 each.

00:09:19.370 --> 00:09:23.390
So the price of a full
price ticket is $20.

00:09:23.390 --> 00:09:24.510
So now, this is interesting.

00:09:24.510 --> 00:09:26.500
Now we could take this
and substitute

00:09:26.500 --> 00:09:27.700
it into this equation.

00:09:27.700 --> 00:09:31.530
Because we now know what the
price is, the P variable.

00:09:31.530 --> 00:09:35.310
And so if we use both of these
conditions, we have 50% of a

00:09:35.310 --> 00:09:38.080
full price-- well, that's $10--
times the number of

00:09:38.080 --> 00:09:42.290
reduced price tickets plus $20,
times the number of full

00:09:42.290 --> 00:09:51.090
price tickets, is equal to
the revenue generated.

00:09:51.090 --> 00:09:57.220
And then we know that a total
of 400 tickets are sold.

00:09:57.220 --> 00:09:59.770
R plus F is equal to 400.

00:09:59.770 --> 00:10:04.080
Well even now, we still just
don't have enough information.

00:10:04.080 --> 00:10:08.350
They would have to tell
us either R or F.

00:10:08.350 --> 00:10:10.800
Or they would have to tell us
the total amount of revenue

00:10:10.800 --> 00:10:13.930
generated in order for us--
well, actually that's what

00:10:13.930 --> 00:10:14.640
they want to figure out.

00:10:14.640 --> 00:10:16.820
They want to know the total
amount of revenue.

00:10:16.820 --> 00:10:21.390
So in order to figure that out,
we would have to have at

00:10:21.390 --> 00:10:23.980
least one more condition
to solve for R.

00:10:23.980 --> 00:10:25.720
And then be able
to solve for F.

00:10:25.720 --> 00:10:27.970
We have to know R or F to
figure out the revenue.

00:10:27.970 --> 00:10:30.640
Let me just make sure I'm not
missing something here.

00:10:30.640 --> 00:10:33.490
Yeah, there's no other way to
just-- you can't just separate

00:10:33.490 --> 00:10:34.520
out an R plus F.

00:10:34.520 --> 00:10:36.810
So I'm going to say that E, both
statements together are

00:10:36.810 --> 00:10:38.060
not sufficient.

00:10:40.190 --> 00:10:41.370
I'm pretty sure I'm right.

00:10:41.370 --> 00:10:43.720
I'm don't think I'm missing
anything right here.

00:10:43.720 --> 00:10:45.830
Some of which were sold at x
percent of full price and the

00:10:45.830 --> 00:10:49.270
rest were sold at full
price, which is $20.

00:10:49.270 --> 00:10:51.110
So R plus F is 40.

00:10:51.110 --> 00:10:54.670
And then we have 10R is
equal to revenue.

00:10:54.670 --> 00:10:56.390
Yeah.

00:10:56.390 --> 00:10:57.790
We have three unknowns and two

00:10:57.790 --> 00:10:59.290
equations, two linear equations.

00:10:59.290 --> 00:11:00.280
Not good enough.

00:11:00.280 --> 00:11:01.560
Next problem.

00:11:01.560 --> 00:11:02.790
Oh, I'm over time.

00:11:02.790 --> 00:11:04.580
See you in the next video.


GMAT: Data sufficiency 26

WEBVTT
Kind: captions
Language: en

00:00:00.700 --> 00:00:03.825
We're on problem 110.

00:00:03.825 --> 00:00:07.830
Let me scroll this up.

00:00:07.830 --> 00:00:10.530
Whenever Martin has a restaurant
bill with an amount

00:00:10.530 --> 00:00:14.440
between $10 and $99 he
calculates the dollar amount

00:00:14.440 --> 00:00:16.500
of the tip as two times
the tens digit of the

00:00:16.500 --> 00:00:17.280
amount of his bill.

00:00:17.280 --> 00:00:18.210
Fair enough.

00:00:18.210 --> 00:00:19.720
So essentially, if there
is a ten digit, he just

00:00:19.720 --> 00:00:21.090
multiplies it by 2.

00:00:21.090 --> 00:00:23.750
If the amount of Martin's most
recent restaurant bill was

00:00:23.750 --> 00:00:27.490
between $10 and $99, was the
tip calculated by Martin on

00:00:27.490 --> 00:00:31.080
his bill greater than 15% of
the amount of the bill?

00:00:34.960 --> 00:00:37.010
That is the question.

00:00:37.010 --> 00:00:40.710
Statement 1 says, the amount
of the bill was

00:00:40.710 --> 00:00:48.150
between $15 and $50.

00:00:48.150 --> 00:00:53.500
So 1 essentially is enough for
this problem, is sufficient,

00:00:53.500 --> 00:00:57.712
if for every bill, based on
his calculation where you

00:00:57.712 --> 00:01:00.650
double the tens digit, it's
going to be greater than 15.

00:01:00.650 --> 00:01:04.019
And I suspect, let's see if we
take the lower end of this, on

00:01:04.019 --> 00:01:06.540
this he'll pay $2.

00:01:06.540 --> 00:01:10.480
He'll pay a $2 tip on $15.

00:01:10.480 --> 00:01:12.160
And what percentage is that?

00:01:12.160 --> 00:01:16.190
15 goes into 2.00.

00:01:16.190 --> 00:01:18.760
1, 15, 50.

00:01:18.760 --> 00:01:21.630
15 goes into 50 3 times.

00:01:21.630 --> 00:01:24.160
3 times 50, 45 and it
just keeps going.

00:01:24.160 --> 00:01:28.890
So that's a 13% tip.

00:01:28.890 --> 00:01:32.770
Well, it's going to be even
lower than that at $16.

00:01:32.770 --> 00:01:34.990
Maybe the bill wasn't $15,
the bill was $16.

00:01:34.990 --> 00:01:38.835
So the tip is, at the lower
end it's 13%, 12%.

00:01:38.835 --> 00:01:47.970
And at the higher end, if the
bill is $40 exactly and he

00:01:47.970 --> 00:01:52.390
pays $8 on that.

00:01:52.390 --> 00:01:55.990
If the bill is $40, then Martin
would pay $8, which

00:01:55.990 --> 00:01:58.190
would be 20%.

00:01:58.190 --> 00:02:00.880
So I can pick different numbers
in this range, and

00:02:00.880 --> 00:02:11.230
based on the way Martin
calculates his tip, he can

00:02:11.230 --> 00:02:14.560
either pay less than 15%
or more than 15%.

00:02:14.560 --> 00:02:17.730
So statement 1 alone
is not sufficient.

00:02:17.730 --> 00:02:19.880
What does statement 2 tell us?

00:02:19.880 --> 00:02:21.480
The tip calculated
by Martin was $8.

00:02:24.510 --> 00:02:26.500
Well this is going to be
2 times the tens digit.

00:02:26.500 --> 00:02:30.650
So that means that the bill
was equal to $40-- I don't

00:02:30.650 --> 00:02:33.170
know, $40-something.

00:02:33.170 --> 00:02:35.860
So let's think about it.

00:02:35.860 --> 00:02:40.150
So the worst case is if the
bill-- if he paid $8 an a $40

00:02:40.150 --> 00:02:43.270
bill, that's definitely
more than 15%.

00:02:43.270 --> 00:02:44.140
That's 20%.

00:02:44.140 --> 00:02:47.220
That's what I just actually
calculated.

00:02:47.220 --> 00:02:50.030
Let's see the worst case
is on a $49 bill.

00:02:50.030 --> 00:02:53.160
That the bill keeps going
up and he just pays $8.

00:02:53.160 --> 00:02:57.820
So is 8 bigger than 15% of 49?

00:02:57.820 --> 00:02:58.230
Well yeah.

00:02:58.230 --> 00:03:03.110
Because 8/50 is equal to what?

00:03:03.110 --> 00:03:06.140
That's equal to 16%.

00:03:06.140 --> 00:03:11.320
So if 8/50 is 16%, 8/49, if we
lower the denominator a little

00:03:11.320 --> 00:03:13.860
bit, that's going to be
greater than 16%.

00:03:13.860 --> 00:03:17.830
So no matter what range in the
forties the bill was, whether

00:03:17.830 --> 00:03:22.500
it's $40 or $49 or anything in
between, an $8 tip is going to

00:03:22.500 --> 00:03:26.200
be more than-- it's actually
going to be more than 16%.

00:03:26.200 --> 00:03:28.330
Not to speak of even 15%.

00:03:28.330 --> 00:03:30.480
So statement number 2
alone is sufficient

00:03:30.480 --> 00:03:31.640
to answer this question.

00:03:31.640 --> 00:03:35.680
And statement number 1
is fairly useless.

00:03:35.680 --> 00:03:39.060
Problem 111.

00:03:39.060 --> 00:03:44.730
The price per share of stock x
increased by 10% over the same

00:03:44.730 --> 00:03:48.500
time period that the price
per share of stock y

00:03:48.500 --> 00:03:51.010
decreased by 10%.

00:03:51.010 --> 00:03:54.280
The reduced price per share of
stock y was what percent of

00:03:54.280 --> 00:03:58.090
the original price per
share of stock x?

00:03:58.090 --> 00:03:59.100
Fascinating.

00:03:59.100 --> 00:04:00.920
So let's do initial and final.

00:04:00.920 --> 00:04:09.730
So x final is equal to an
increase by 10% from the

00:04:09.730 --> 00:04:11.920
initial period.

00:04:11.920 --> 00:04:17.959
OK, so it equals 1.1
times x initial.

00:04:17.959 --> 00:04:19.040
Fair enough.

00:04:19.040 --> 00:04:23.670
And then, over the same time
period y decreased by 10%.

00:04:23.670 --> 00:04:28.660
So y final is equal to 10%
less than y initial.

00:04:28.660 --> 00:04:33.180
So that's 0.9 times y initial.

00:04:33.180 --> 00:04:35.660
And what they want to know is
the reduced price per share of

00:04:35.660 --> 00:04:43.810
stock y-- so that's y f-- was
what percent of the original

00:04:43.810 --> 00:04:46.660
price per share of stock x?

00:04:46.660 --> 00:04:49.210
Of x initial?

00:04:49.210 --> 00:04:51.770
So this is what they
want to figure out.

00:04:51.770 --> 00:04:53.090
This as a percentage.

00:04:53.090 --> 00:04:56.140
So let's see if the statements
help us out at all.

00:04:56.140 --> 00:05:01.520
The increased price per share
of stock x was equal to the

00:05:01.520 --> 00:05:04.690
original price per
share of stock y.

00:05:04.690 --> 00:05:07.380
So the increased price
per share of stock

00:05:07.380 --> 00:05:09.670
x, so that's x f.

00:05:09.670 --> 00:05:10.310
That's the final.

00:05:10.310 --> 00:05:11.950
That's the increased
share price.

00:05:11.950 --> 00:05:14.110
It increased from the initial
to the final.

00:05:14.110 --> 00:05:17.670
So the increased price per share
of stock x was equal to

00:05:17.670 --> 00:05:20.150
the original price per
share of stock y.

00:05:20.150 --> 00:05:23.895
So that equals y initial.

00:05:26.990 --> 00:05:29.160
So this is interesting.

00:05:29.160 --> 00:05:31.150
I don't know if it
gets us anywhere.

00:05:31.150 --> 00:05:35.310
This deals with x final
and x initial.

00:05:35.310 --> 00:05:43.600
So I think we can-- so if we
could write all of it in terms

00:05:43.600 --> 00:05:44.600
of y initial.

00:05:44.600 --> 00:05:47.620
So y final equals-- so
let's rewrite this.

00:05:47.620 --> 00:05:53.400
This is equal to-- y final
is 0.9 times y initial.

00:05:53.400 --> 00:05:54.960
That's just from
this equation.

00:05:54.960 --> 00:05:59.420
0.9 times y initial.

00:05:59.420 --> 00:06:02.190
And let's see if we could write
the initial x in terms

00:06:02.190 --> 00:06:05.150
of the initial y.

00:06:05.150 --> 00:06:08.570
So x final is equal
to y initial.

00:06:08.570 --> 00:06:11.380
So that means that y initial
is equal to this.

00:06:11.380 --> 00:06:16.620
So that equals 1.1 x initial.

00:06:16.620 --> 00:06:20.515
And that means that we can
divide both sides of this

00:06:20.515 --> 00:06:22.740
equality by 1.1.

00:06:22.740 --> 00:06:32.300
And we get x initial is equal to
1 over 1.1 times y initial.

00:06:32.300 --> 00:06:33.830
So then we have this.

00:06:33.830 --> 00:06:39.180
1 over 1.1 times y initial.

00:06:39.180 --> 00:06:40.990
And then these two
would cancel out.

00:06:40.990 --> 00:06:42.350
And you would actually
have your answer.

00:06:42.350 --> 00:06:45.020
So statement 1 alone
is sufficient

00:06:45.020 --> 00:06:46.270
to answer the question.

00:06:48.660 --> 00:06:50.370
It wasn't obvious to me at
first, but then you have to

00:06:50.370 --> 00:06:53.440
realize that, the terminology is
confusing but that you can

00:06:53.440 --> 00:06:57.030
actually write both of these
in terms of y initial given

00:06:57.030 --> 00:06:57.770
that information.

00:06:57.770 --> 00:07:01.100
Given the fact that x final
is equal to y initial.

00:07:01.100 --> 00:07:04.180
Let's see what statement
2 does for us.

00:07:04.180 --> 00:07:10.690
The increase in the price per
share of stock x was 10/11 the

00:07:10.690 --> 00:07:13.960
decrease in the price per
share of stock y.

00:07:13.960 --> 00:07:15.280
Let me think about that.

00:07:15.280 --> 00:07:19.470
The increase in the price
per share of stock x.

00:07:19.470 --> 00:07:27.700
So that means that x final minus
x initial-- that's the

00:07:27.700 --> 00:07:36.800
increase-- that this was equal
to 10/11 times the decrease in

00:07:36.800 --> 00:07:38.605
the price per share
of stock y.

00:07:38.605 --> 00:07:40.330
So what was the decrease?

00:07:40.330 --> 00:07:45.935
This was y initial
minus y final.

00:07:49.960 --> 00:07:51.470
Because this was a larger
number and we wanted a

00:07:51.470 --> 00:07:52.290
positive number here.

00:07:52.290 --> 00:07:53.490
Because we're just saying
the decrease.

00:07:53.490 --> 00:07:55.562
We're not saying the
negative increase.

00:07:55.562 --> 00:07:58.360
So let's see if we can
simplify this at all.

00:08:01.140 --> 00:08:11.320
So let's see, you get x final
minus x initial is equal to

00:08:11.320 --> 00:08:22.300
10/11 y initial minus
10/11 y final.

00:08:22.300 --> 00:08:24.010
And remember, the whole time
we just want to figure out

00:08:24.010 --> 00:08:26.940
what y final over
x initial is.

00:08:31.020 --> 00:08:34.309
So let's think about this.

00:08:34.309 --> 00:08:38.880
Let's write x final is equal
to 1.1 times x initial.

00:08:38.880 --> 00:08:47.450
Right So we have 1.1 times x
initial minus x initial is

00:08:47.450 --> 00:08:49.450
equal to-- actually I should
have done that

00:08:49.450 --> 00:08:50.490
in the first step.

00:08:50.490 --> 00:08:51.730
Let's just skip this
right now.

00:08:51.730 --> 00:08:57.740
Let's just write
the 10 over 11.

00:08:57.740 --> 00:08:58.660
What do we want?

00:08:58.660 --> 00:08:59.690
We want y final.

00:08:59.690 --> 00:09:01.585
So we just want to substitute
for y initial.

00:09:06.260 --> 00:09:07.500
I am confusing myself.

00:09:07.500 --> 00:09:11.000
So y initial is going
to be equal to y

00:09:11.000 --> 00:09:13.470
final divided by 0.9.

00:09:13.470 --> 00:09:20.280
So 1 over 0.9 y final.

00:09:20.280 --> 00:09:21.960
I know this is a little
confusing.

00:09:21.960 --> 00:09:23.490
Minus y final.

00:09:23.490 --> 00:09:26.870
I just did a substitution
for y initial.

00:09:26.870 --> 00:09:30.920
And then here, well this is
actually, we know that we can

00:09:30.920 --> 00:09:31.650
solve this problem.

00:09:31.650 --> 00:09:33.090
Although it gets quite hairy.

00:09:33.090 --> 00:09:35.130
Because here, if you think about
it, you're going to get

00:09:35.130 --> 00:09:39.720
some number, well you're going
to get 0.1 x initial is equal

00:09:39.720 --> 00:09:44.860
to-- you're going to get some
constant after you do all this

00:09:44.860 --> 00:09:46.140
math-- times y final.

00:09:48.880 --> 00:09:52.450
And so you can easily figure out
what y final divided by x

00:09:52.450 --> 00:09:55.650
initial is, just by dividing
both sides by x initial and

00:09:55.650 --> 00:09:57.560
then dividing both sides
by a and you would

00:09:57.560 --> 00:09:58.740
have solved the problem.

00:09:58.740 --> 00:10:00.100
And I'm not going to do that
because it's actually kind of

00:10:00.100 --> 00:10:02.860
hairy and I don't have-- 1
divided by 0.9 and then

00:10:02.860 --> 00:10:05.380
multiplying it by 10/11
is a fairly convoluted

00:10:05.380 --> 00:10:06.410
way of doing it.

00:10:06.410 --> 00:10:09.480
But hopefully, you see that
this is solvable.

00:10:09.480 --> 00:10:12.315
And let me just review that
again because I think I did it

00:10:12.315 --> 00:10:13.800
in my own head.

00:10:13.800 --> 00:10:18.340
So the statement itself said the
change, the gain in x-- x

00:10:18.340 --> 00:10:22.710
final minus x initial-- was
10/11 times the loss in y.

00:10:22.710 --> 00:10:25.280
So y initial minus y final.

00:10:25.280 --> 00:10:27.860
Because y final is
the smaller one.

00:10:27.860 --> 00:10:31.160
x final we can rewrite in terms
of x initial just using

00:10:31.160 --> 00:10:33.720
our initial, the fact that
it was 10% more.

00:10:33.720 --> 00:10:34.970
So I just did that here.

00:10:37.940 --> 00:10:42.285
And y initial, we can
rewrite as y final.

00:10:45.100 --> 00:10:46.670
You could say y initial
is equal to y

00:10:46.670 --> 00:10:50.290
final divided by 0.9.

00:10:50.290 --> 00:10:51.590
And that's what we did there.

00:10:51.590 --> 00:10:53.930
And then you could see here,
this will simplify to some

00:10:53.930 --> 00:10:55.170
constant times y final.

00:10:55.170 --> 00:10:56.740
And then you multiply
that times 10/11.

00:10:56.740 --> 00:10:59.450
So you get some constant
times y final.

00:10:59.450 --> 00:11:01.800
And then you have 0.1
times x initial.

00:11:01.800 --> 00:11:03.360
1.1 minus 1.

00:11:03.360 --> 00:11:06.170
And then you can just do some
simple algebra to figure out

00:11:06.170 --> 00:11:10.200
what y final over
x initial is.

00:11:10.200 --> 00:11:12.780
So both statements,
independently, are sufficient

00:11:12.780 --> 00:11:13.670
to solve this problem.

00:11:13.670 --> 00:11:16.080
I think that was the hardest
one we've done so far.

00:11:16.080 --> 00:11:17.950
See you in the next video.


GMAT: Data sufficiency 25

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:06.250
We're on problem 107.

00:00:06.250 --> 00:00:10.550
Any decimal that has only a
finite number of non-zero

00:00:10.550 --> 00:00:13.340
digits is a terminating
decimal.

00:00:13.340 --> 00:00:18.360
For example, 24-- in the example
they give us-- 24,

00:00:18.360 --> 00:00:24.620
0.82, and 5.096.

00:00:24.620 --> 00:00:26.570
So they're saying if you just
have a finite number of these

00:00:26.570 --> 00:00:29.250
non-zero things, at some point
you have to end, and just have

00:00:29.250 --> 00:00:30.350
zeroes just left over.

00:00:30.350 --> 00:00:32.680
So that's what they mean by
a terminating decimal.

00:00:32.680 --> 00:00:44.290
If r and s are positive
integers, and the ratio r

00:00:44.290 --> 00:00:54.210
divided by s is expressed as a
decimal, is r divided by s a

00:00:54.210 --> 00:00:55.460
terminating decimal?

00:01:00.010 --> 00:01:01.880
So essentially it wouldn't
work if r and n--

00:01:01.880 --> 00:01:02.910
that this is 1/3.

00:01:02.910 --> 00:01:03.700
That's not going to work.

00:01:03.700 --> 00:01:05.610
Because you'll have
0.3 forever.

00:01:05.610 --> 00:01:07.830
So they're saying, does
it at some point end?

00:01:07.830 --> 00:01:09.900
This is interesting.

00:01:09.900 --> 00:01:16.740
So statement 1 tells us that
90 is less than r which is

00:01:16.740 --> 00:01:20.040
less than 100.

00:01:20.040 --> 00:01:22.295
That statement by itself
doesn't help me.

00:01:22.295 --> 00:01:32.550
Now let's say that r was--
let me think of a good r.

00:01:32.550 --> 00:01:35.230
Let's say r was 93.

00:01:35.230 --> 00:01:41.930
If r is equal to 93 and then s
is equal to-- well, let's just

00:01:41.930 --> 00:01:46.290
say that s, for the sake of
argument, is 3 times r.

00:01:46.290 --> 00:01:48.180
Actually, I don't have
to pick an r.

00:01:48.180 --> 00:01:52.520
Whatever r is, I can just pick
an s to be 3 times r.

00:01:52.520 --> 00:01:54.600
And I'm not going to get
a terminating decimal.

00:01:54.600 --> 00:01:58.590
On the other hand, if I pick
s to be 2 times r, then I'm

00:01:58.590 --> 00:01:59.650
going to have a terminating
decimal.

00:01:59.650 --> 00:02:02.325
So statement 1 by itself
isn't going to help me.

00:02:05.330 --> 00:02:06.140
I hope you understand that.

00:02:06.140 --> 00:02:07.850
I can pick any s to make
it terminating

00:02:07.850 --> 00:02:09.360
or not at this point.

00:02:09.360 --> 00:02:11.310
No matter whether
r is constrained

00:02:11.310 --> 00:02:13.330
between 90 and 100.

00:02:13.330 --> 00:02:19.903
Statement 2 tells us that
s is equal to 4b.

00:02:28.330 --> 00:02:30.820
Now, this is interesting
to me.

00:02:30.820 --> 00:02:33.910
So where did this b come
from all of a sudden?

00:02:33.910 --> 00:02:37.280
Any decimal that has only a
finite number of non-zero

00:02:37.280 --> 00:02:39.990
digits is a terminating
decimal.

00:02:39.990 --> 00:02:46.460
If r and s are integers and the
ratio s is equal to 4b.

00:02:46.460 --> 00:02:48.610
Where did this come from?

00:02:48.610 --> 00:02:49.660
Let me look it up.

00:02:49.660 --> 00:02:52.400
What is this?

00:02:52.400 --> 00:02:54.300
I think this is a typo.

00:02:54.300 --> 00:02:59.080
Because where did b come
from all of a sudden?

00:02:59.080 --> 00:03:00.940
Oh, yeah, when I look at
the solution they say

00:03:00.940 --> 00:03:02.650
s is equal to 4.

00:03:02.650 --> 00:03:04.900
So that's definitely a typo.

00:03:04.900 --> 00:03:07.320
4b.

00:03:07.320 --> 00:03:08.180
s is equal to 4.

00:03:08.180 --> 00:03:10.510
OK that makes a lot
more sense.

00:03:10.510 --> 00:03:13.380
All right, so if s
is equal to 4.

00:03:13.380 --> 00:03:16.670
Pretty much any number, when
you divide any number by 4,

00:03:16.670 --> 00:03:18.350
you're going to have a
terminating decimal.

00:03:18.350 --> 00:03:21.720
It's either going to be
divisible by 4 or it's going

00:03:21.720 --> 00:03:25.750
to be-- the worst case, if you
have 1 divided by 4, that

00:03:25.750 --> 00:03:26.390
equals 0.25.

00:03:26.390 --> 00:03:29.750
5 So no matter what, when you
divide something by 4, you're

00:03:29.750 --> 00:03:31.460
always going to have a
terminating decimal.

00:03:31.460 --> 00:03:33.240
It's never going to
repeat forever.

00:03:33.240 --> 00:03:38.560
I mean you can try it out with
every-- no matter what number

00:03:38.560 --> 00:03:41.770
you divide, if you view it as
a fraction, or kind of your

00:03:41.770 --> 00:03:43.600
fourth grade remainder problems,
the remainder is

00:03:43.600 --> 00:03:45.920
either going to be 1, 2 or 3.

00:03:45.920 --> 00:03:48.450
If the remainder is 1, the
decimal is going to be 0.25.

00:03:48.450 --> 00:03:51.120
If the remainder is 2, the
decimal is going to be 0.5.

00:03:51.120 --> 00:03:55.080
And if the remainder is 3, the
decimal is going to be 0.75.

00:03:55.080 --> 00:03:57.600
In any case, as long as
s equals 4, you have a

00:03:57.600 --> 00:03:58.810
terminating decimal.

00:03:58.810 --> 00:04:02.010
So statement 2 alone is
sufficient and statement 1

00:04:02.010 --> 00:04:03.980
really doesn't tell us much.

00:04:03.980 --> 00:04:07.600
And I'm annoyed that they
had that b typo there.

00:04:07.600 --> 00:04:10.340
Next problem.

00:04:10.340 --> 00:04:13.470
108.

00:04:13.470 --> 00:04:20.850
OK, they've drawn a triangle
right there.

00:04:20.850 --> 00:04:22.565
Let me see if I can
draw it properly.

00:04:30.980 --> 00:04:32.800
There you go.

00:04:32.800 --> 00:04:34.600
And let me label it.

00:04:34.600 --> 00:04:36.660
This is B.

00:04:36.660 --> 00:04:38.550
That's A.

00:04:38.550 --> 00:04:39.490
That's C.

00:04:39.490 --> 00:04:41.460
This is y degrees.

00:04:41.460 --> 00:04:45.030
And this is D and this
is x degrees.

00:04:45.030 --> 00:04:48.140
In the figure above, what is
the value of x plus y?

00:04:48.140 --> 00:04:49.970
So x degrees plus y degrees.

00:04:49.970 --> 00:04:52.850
x plus y is equal to what?

00:04:56.470 --> 00:04:57.480
So they don't tell
us anything else.

00:04:57.480 --> 00:04:59.050
They don't tell us if this is
an equilateral triangle.

00:04:59.050 --> 00:05:01.320
They don't tell us that these
angles are equal.

00:05:01.320 --> 00:05:02.230
They don't tell us
it's symmetrical.

00:05:02.230 --> 00:05:05.640
They don't tell us anything
about this triangle so far.

00:05:05.640 --> 00:05:10.570
So statement number 1 tells
us that x is equal to 70.

00:05:10.570 --> 00:05:13.710
Well, just by x equalling 70,
that still doesn't help me.

00:05:13.710 --> 00:05:15.640
I still don't know
what y can be.

00:05:15.640 --> 00:05:18.390
I mean, you could draw this
interior triangle in a bunch

00:05:18.390 --> 00:05:19.950
of different ways and you could
see that the angle could

00:05:19.950 --> 00:05:23.820
change depending on how much you
lift up D or compress D.

00:05:23.820 --> 00:05:27.350
This y angle can change
irrespective of what x is.

00:05:27.350 --> 00:05:30.220
So x is equal to 70 does not
in any way give me any

00:05:30.220 --> 00:05:32.980
information on what y is.

00:05:32.980 --> 00:05:36.090
Statement 2.

00:05:36.090 --> 00:05:50.050
Triangle ABC and triangle
ADC are both isosceles.

00:05:50.050 --> 00:05:57.310
So isosceles actually doesn't
mean necessarily that those

00:05:57.310 --> 00:05:59.650
two sides are the same.

00:05:59.650 --> 00:06:02.940
I mean, that kind of tends
to be someone's immediate

00:06:02.940 --> 00:06:04.030
assumption, when we
say isosceles.

00:06:04.030 --> 00:06:05.480
Oh maybe that side is
equal to that side.

00:06:05.480 --> 00:06:07.980
But no, it just means that two
of the sides are the same.

00:06:07.980 --> 00:06:11.120
So, likewise on this triangle.

00:06:11.120 --> 00:06:16.150
Although you can, at least,
here-- can I make an argument?

00:06:16.150 --> 00:06:18.630
No, you can't make an argument
which two sides are going to

00:06:18.630 --> 00:06:20.490
be the same.

00:06:20.490 --> 00:06:23.430
So, even if you assumed that
both of those sides are the

00:06:23.430 --> 00:06:26.710
same, you're still not going
to-- because you don't know.

00:06:26.710 --> 00:06:28.445
My gut instinct would be to say,
oh, that side's the same

00:06:28.445 --> 00:06:29.020
as that side.

00:06:29.020 --> 00:06:31.030
But no, I can't make
that assumption.

00:06:31.030 --> 00:06:32.980
Because it could be that this
side is equal to that side.

00:06:32.980 --> 00:06:34.090
That would still make
it isosceles.

00:06:34.090 --> 00:06:36.690
And this side is kind of viewed
as like the base side.

00:06:36.690 --> 00:06:38.140
And it's a very big
difference.

00:06:38.140 --> 00:06:41.300
Because if these are the two
equal sides, and if this is x,

00:06:41.300 --> 00:06:43.050
this is going to be x.

00:06:43.050 --> 00:06:46.060
But then if I take the other
scenario, where if these are

00:06:46.060 --> 00:06:48.720
two sides and if this is x, then
both of these are really

00:06:48.720 --> 00:06:52.490
be 180 minus x divided
by 2, right?

00:06:52.490 --> 00:06:55.720
Because this would be-- The
bottom line is, this still

00:06:55.720 --> 00:06:56.460
doesn't get me anywhere.

00:06:56.460 --> 00:06:58.600
Even if I know that this
is 70 degrees.

00:06:58.600 --> 00:07:02.120
So I'm going to go with, E,
not enough information to

00:07:02.120 --> 00:07:04.470
solve this problem.

00:07:04.470 --> 00:07:10.950
109.

00:07:10.950 --> 00:07:14.385
Are positive integers p and
q both greater than n?

00:07:18.560 --> 00:07:21.030
They told us positive
integers.

00:07:21.030 --> 00:07:22.460
OK.

00:07:22.460 --> 00:07:25.290
They say p minus q is
greater than n.

00:07:29.650 --> 00:07:31.710
Well I'll give you a case right
now where that doesn't

00:07:31.710 --> 00:07:32.420
satisfy this.

00:07:32.420 --> 00:07:41.480
What if p is equal to 10,
q is equal to 1, and

00:07:41.480 --> 00:07:44.610
n is equal to 2.

00:07:44.610 --> 00:07:47.540
Then 10 minus 1 is 9 is
definitely greater than 2.

00:07:47.540 --> 00:07:50.990
But look, q is not
greater than 2.

00:07:50.990 --> 00:07:52.270
1 is not greater than 2.

00:07:52.270 --> 00:07:53.700
So q wouldn't be
greater than n.

00:07:53.700 --> 00:08:00.760
Or I could say, it could
be, 110 and 108.

00:08:00.760 --> 00:08:02.420
Would equal-- and when you
subtracted you'd get 2.

00:08:02.420 --> 00:08:05.100
And in this case q
is bigger than 2.

00:08:05.100 --> 00:08:07.130
So this doesn't give me
enough information.

00:08:07.130 --> 00:08:08.800
I can think of two combinations

00:08:08.800 --> 00:08:11.150
of p's q's and n's.

00:08:11.150 --> 00:08:15.110
One that says that q is not
greater than n and one that

00:08:15.110 --> 00:08:17.150
says that q is greater than n.

00:08:17.150 --> 00:08:21.200
So one, by itself,
isn't enough.

00:08:21.200 --> 00:08:22.450
Statement 2.

00:08:25.310 --> 00:08:29.465
q is greater than p.

00:08:33.000 --> 00:08:36.409
That still doesn't help me.

00:08:36.409 --> 00:08:39.799
Both of these statement actually
cannot be true

00:08:39.799 --> 00:08:40.549
simultaneously.

00:08:40.549 --> 00:08:43.299
Because if these are both
positive integers, which they

00:08:43.299 --> 00:08:49.640
told us-- well, greater
than n.

00:08:49.640 --> 00:08:50.510
Both greater than n.

00:08:50.510 --> 00:08:51.190
They didn't tell us

00:08:51.190 --> 00:08:53.770
necessarily that n is positive.

00:08:53.770 --> 00:08:56.200
So n doesn't have
to be positive.

00:08:56.200 --> 00:08:58.590
My logic for statement
1 still holds.

00:08:58.590 --> 00:09:05.660
But let's see, if q is greater
than p, this by itself doesn't

00:09:05.660 --> 00:09:06.210
help me much.

00:09:06.210 --> 00:09:09.050
Because I can think of a similar
combination to this.

00:09:09.050 --> 00:09:17.130
I can say q is equal to 10, p
is equal to 9, and I could

00:09:17.130 --> 00:09:18.970
make n is equal to 2.

00:09:18.970 --> 00:09:24.680
Or I could say n
is equal to 15.

00:09:24.680 --> 00:09:26.780
This in no way constrains
what n is.

00:09:26.780 --> 00:09:28.540
So it, by itself, doesn't
solve it.

00:09:28.540 --> 00:09:31.280
But what if we were to
use both constraints.

00:09:31.280 --> 00:09:33.520
This is the interesting case.

00:09:33.520 --> 00:09:39.500
What if we were to say that p
minus q is greater than n.

00:09:39.500 --> 00:09:43.430
And q is greater than p.

00:09:43.430 --> 00:09:46.520
So, we know that both p
and q are positive.

00:09:46.520 --> 00:09:48.420
They told us that in the
problem statement.

00:09:48.420 --> 00:09:55.620
If p and q are both positive,
and q is greater than p, this

00:09:55.620 --> 00:09:58.780
is going to end up becoming
a negative number.

00:09:58.780 --> 00:10:00.000
These are both positive.

00:10:00.000 --> 00:10:02.800
And this is the larger of the
two positive numbers based on

00:10:02.800 --> 00:10:04.110
the second constraint.

00:10:04.110 --> 00:10:06.500
So this is going to be
a negative number.

00:10:06.500 --> 00:10:11.050
And so if a negative number is
greater than n, then we can be

00:10:11.050 --> 00:10:14.810
sure, we can be positive,
that both p and q are

00:10:14.810 --> 00:10:15.530
greater than n.

00:10:15.530 --> 00:10:18.700
Because they told us that
p and q are positive.

00:10:18.700 --> 00:10:21.620
So actually both of
these statements

00:10:21.620 --> 00:10:25.310
imply that n is negative.

00:10:25.310 --> 00:10:26.700
Because we have a negative
number here being

00:10:26.700 --> 00:10:27.880
greater than n.

00:10:27.880 --> 00:10:30.460
And if n is negative, then both
p and q are definitely

00:10:30.460 --> 00:10:31.410
greater than n.

00:10:31.410 --> 00:10:34.520
So both statements combined
are sufficient

00:10:34.520 --> 00:10:35.640
to answer this question.

00:10:35.640 --> 00:10:37.760
And the answer is
actually true.

00:10:37.760 --> 00:10:40.000
I'll see you in the
next video.


GMAT: Data sufficiency 23

WEBVTT
Kind: captions
Language: en

00:00:00.570 --> 00:00:04.330
We're on problem 99.

00:00:04.330 --> 00:00:06.990
And I like these that don't have
a lot of words in them. m

00:00:06.990 --> 00:00:08.140
does not equal n.

00:00:08.140 --> 00:00:09.080
We have to prove that.

00:00:09.080 --> 00:00:12.110
Is it true that m does
not equal n?

00:00:12.110 --> 00:00:20.460
Statement number 1 says that
m plus n is less than 0.

00:00:20.460 --> 00:00:22.690
Well, let's see, what
does this tell us?

00:00:22.690 --> 00:00:28.490
This just tells us that m
is less than negative n.

00:00:28.490 --> 00:00:31.800
It still doesn't tell
us anything.

00:00:31.800 --> 00:00:39.810
Maybe negative n is-- well,
let's say, if m is equal to n,

00:00:39.810 --> 00:00:44.380
which is equal to negative
10, then this

00:00:44.380 --> 00:00:45.580
would hold true, right?

00:00:45.580 --> 00:00:48.290
Because negative 10 plus
negative 10 is minus 20, which

00:00:48.290 --> 00:00:49.580
is less than 0.

00:00:49.580 --> 00:00:51.490
So this still doesn't
prove anything.

00:00:51.490 --> 00:00:53.070
Or, of course, I could have
two different numbers.

00:00:53.070 --> 00:00:56.780
I could have m being minus
5, and n being minus 1.

00:00:56.780 --> 00:00:58.300
And when you add them together
you get minus 6,

00:00:58.300 --> 00:00:59.410
both less than 0.

00:00:59.410 --> 00:01:01.280
So it still doesn't tell us
anything about whether m does

00:01:01.280 --> 00:01:02.860
not equal n.

00:01:02.860 --> 00:01:04.440
Statement two.

00:01:04.440 --> 00:01:11.460
m times n is less than 0.

00:01:11.460 --> 00:01:13.640
Now, this is interesting.

00:01:13.640 --> 00:01:15.350
m times n is less than 0.

00:01:15.350 --> 00:01:21.250
So that tells us that one is
positive and one is negative.

00:01:21.250 --> 00:01:24.170
The only way you can multiply
two numbers and get something

00:01:24.170 --> 00:01:34.130
less than 0 is one positive
and one negative.

00:01:34.130 --> 00:01:37.170
And it doesn't say equal 0, so
they both can't equal 0.

00:01:37.170 --> 00:01:39.105
And so, when you multiply two
numbers and you get a negative

00:01:39.105 --> 00:01:41.270
number, they have to be
different numbers, because one

00:01:41.270 --> 00:01:43.430
has to be positive and one
has to be negative.

00:01:43.430 --> 00:01:45.520
Try it out with as many
things as you want.

00:01:45.520 --> 00:01:48.670
But you know from your basic
negative multiplication rules

00:01:48.670 --> 00:01:51.460
that the only way to get a
negative as a product of two

00:01:51.460 --> 00:01:52.840
numbers is one positive,
one negative.

00:01:52.840 --> 00:01:55.860
So this is all we need to know
to know that m and n are

00:01:55.860 --> 00:01:58.520
different, because one's
positive and one's negative.

00:01:58.520 --> 00:02:00.890
I said that about five times.

00:02:00.890 --> 00:02:02.750
Problem 100.

00:02:02.750 --> 00:02:05.460
And you didn't need
statement one.

00:02:05.460 --> 00:02:06.140
Problem 100.

00:02:06.140 --> 00:02:08.960
When a player in a certain game
tossed a coin a number of

00:02:08.960 --> 00:02:12.840
times, four more heads
than tails resulted.

00:02:12.840 --> 00:02:17.620
So heads is equal
to tails plus 4.

00:02:17.620 --> 00:02:19.440
Heads or tails resulted
each time the

00:02:19.440 --> 00:02:20.510
player tossed the coin.

00:02:20.510 --> 00:02:21.470
Fair enough.

00:02:21.470 --> 00:02:24.070
How many times did
heads result?

00:02:24.070 --> 00:02:27.440
So essentially the problem
description just tells us that

00:02:27.440 --> 00:02:29.780
heads is equal to
tails plus 4.

00:02:29.780 --> 00:02:33.750
And that heads plus tails is
just all of the tosses.

00:02:33.750 --> 00:02:36.140
So statement number one
says, the player

00:02:36.140 --> 00:02:38.080
tossed the coin 24 times.

00:02:38.080 --> 00:02:39.000
So that's what I just said.

00:02:39.000 --> 00:02:44.770
Heads plus tails
is equal to 24.

00:02:44.770 --> 00:02:47.190
And so this is enough
information by itself to know

00:02:47.190 --> 00:02:49.030
how many times did
heads result.

00:02:49.030 --> 00:02:53.640
Because we could rewrite this
top equation as heads minus

00:02:53.640 --> 00:02:55.040
tails is equal to 4.

00:02:55.040 --> 00:02:56.580
And if you wanted to solve
it, you'd get 2

00:02:56.580 --> 00:02:58.870
heads is equal to 28.

00:02:58.870 --> 00:03:00.140
Heads is equal to 14.

00:03:00.140 --> 00:03:01.900
All of that would have been a
waste of time as soon as you

00:03:01.900 --> 00:03:04.930
saw that you had two linear
equations and two unknowns.

00:03:04.930 --> 00:03:06.083
You could have said, oh, I have
enough information to

00:03:06.083 --> 00:03:08.460
solve for any of
the variables.

00:03:08.460 --> 00:03:09.830
This is a 4.

00:03:09.830 --> 00:03:13.280
So statement one by
itself is enough.

00:03:13.280 --> 00:03:15.360
Statement two.

00:03:15.360 --> 00:03:18.970
The players received 3 points
each time heads resulted and 1

00:03:18.970 --> 00:03:20.510
point each time tails
resulted, for

00:03:20.510 --> 00:03:22.710
a total of 52 points.

00:03:22.710 --> 00:03:26.990
So he got 3 points for every
head-- that's how many points

00:03:26.990 --> 00:03:30.450
he got for all the heads-- plus
1 point for each tail.

00:03:30.450 --> 00:03:32.750
So that's how many points he
got for all the tails.

00:03:32.750 --> 00:03:35.010
And that equals 52.

00:03:35.010 --> 00:03:36.870
So once again, this is providing
us with another

00:03:36.870 --> 00:03:37.450
linear equation.

00:03:37.450 --> 00:03:40.420
So now we have two linear
equations with two unknowns.

00:03:40.420 --> 00:03:44.050
I'm not even looking at what
they gave us in statement one.

00:03:44.050 --> 00:03:47.030
So just using these two, we
have enough information to

00:03:47.030 --> 00:03:48.250
solve the problem.

00:03:48.250 --> 00:03:49.450
You can do it the
exact same way.

00:03:49.450 --> 00:03:51.480
This is what you learned
in algebra 1.

00:03:51.480 --> 00:03:56.290
So, each statement independently
is sufficient to

00:03:56.290 --> 00:03:58.310
solve the problem.

00:03:58.310 --> 00:04:01.060
Problem 101.

00:04:01.060 --> 00:04:04.920
We've already done 100
problems. 101.

00:04:04.920 --> 00:04:08.270
Once you get going, these
get kind of fun.

00:04:08.270 --> 00:04:14.320
If s is the infinite sequence--
OK, so it's like s1

00:04:14.320 --> 00:04:16.930
is equal to 9.

00:04:16.930 --> 00:04:20.550
s2 is equal to 99.

00:04:20.550 --> 00:04:24.130
s3 is equal to three 9's.

00:04:24.130 --> 00:04:27.090
I get it.

00:04:27.090 --> 00:04:34.010
And the kth s is equal to
10 to the k minus 1.

00:04:34.010 --> 00:04:34.630
This is the third one.

00:04:34.630 --> 00:04:37.210
10 to the third is
1000 minus 1.

00:04:37.210 --> 00:04:38.790
10 squared is 100 minus 1.

00:04:38.790 --> 00:04:39.020
Right.

00:04:39.020 --> 00:04:40.260
So it all works.

00:04:40.260 --> 00:04:42.740
All right, that's what
they told us.

00:04:42.740 --> 00:04:47.485
Is every term in s divisible
by the prime number, p?

00:04:54.770 --> 00:04:57.440
Well, it depends what p is.

00:04:57.440 --> 00:05:01.290
And frankly, if just the first
term is divisible by p, all of

00:05:01.290 --> 00:05:02.770
them are going to be
divisible by p.

00:05:02.770 --> 00:05:03.920
Why is that?

00:05:03.920 --> 00:05:06.120
Because all of the terms
are divisible by the

00:05:06.120 --> 00:05:08.170
first term, or 9.

00:05:08.170 --> 00:05:11.100
So if p goes into 9, it's going
to go into all of these

00:05:11.100 --> 00:05:14.170
terms, because 9 goes
into all of them.

00:05:14.170 --> 00:05:16.520
So we just have to say,
does p go into 9?

00:05:16.520 --> 00:05:19.830
It's a much simpler way of
thinking about the problem.

00:05:19.830 --> 00:05:24.500
Statement number one says,
p is greater than 2.

00:05:24.500 --> 00:05:29.110
So does every prime number
greater than 2 go into 9?

00:05:29.110 --> 00:05:29.470
Well, no.

00:05:29.470 --> 00:05:31.060
5, 7.

00:05:31.060 --> 00:05:32.440
These don't go into 9.

00:05:32.440 --> 00:05:33.400
3 goes into 9.

00:05:33.400 --> 00:05:36.690
So we still don't know whether
p goes into 9.

00:05:36.690 --> 00:05:38.720
Statement two.

00:05:38.720 --> 00:05:41.790
At least one term in
the sequence, s, is

00:05:41.790 --> 00:05:43.355
divisible by p.

00:05:54.330 --> 00:05:56.540
If we knew that it was this
term, if we knew that the

00:05:56.540 --> 00:06:00.780
first term was divisible by
p, we would be all set.

00:06:00.780 --> 00:06:04.950
But we don't know whether it's
just the first term.

00:06:04.950 --> 00:06:07.510
For example, p could be 11.

00:06:07.510 --> 00:06:10.010
What if p is 11?

00:06:10.010 --> 00:06:13.700
If p is 11, then it goes
into this term.

00:06:13.700 --> 00:06:16.060
It goes into the 99.

00:06:16.060 --> 00:06:17.430
But it won't go into
the first term.

00:06:17.430 --> 00:06:21.410
It won't go into 9.

00:06:21.410 --> 00:06:26.850
So 11 is an example where it
holds for case two, but it

00:06:26.850 --> 00:06:28.360
doesn't hold for the
whole question.

00:06:28.360 --> 00:06:30.140
It's not divisible
into every term.

00:06:30.140 --> 00:06:35.030
Or we could say that if p was
equal to 3-- well, of course,

00:06:35.030 --> 00:06:36.030
that'll go into everyone.

00:06:36.030 --> 00:06:39.570
So statement two by itself
actually doesn't help us any.

00:06:39.570 --> 00:06:41.940
And actually, both of these
numbers satisfy both

00:06:41.940 --> 00:06:42.860
statements.

00:06:42.860 --> 00:06:45.810
And so, if you pick 11,
it doesn't work.

00:06:45.810 --> 00:06:47.600
If you pick 3, it does work.

00:06:47.600 --> 00:06:51.190
So both statements combined
still do not give us enough

00:06:51.190 --> 00:06:52.440
information.

00:06:54.350 --> 00:06:57.890
Problem 102.

00:06:57.890 --> 00:07:00.200
I have got to do some drawing.

00:07:00.200 --> 00:07:03.650
OK, so I have a quadrilateral
here.

00:07:03.650 --> 00:07:04.060
Let's see.

00:07:04.060 --> 00:07:06.810
That's RU.

00:07:06.810 --> 00:07:08.625
And then go up there.

00:07:08.625 --> 00:07:10.950
And then go flat to there.

00:07:10.950 --> 00:07:13.560
And then come down like that.

00:07:13.560 --> 00:07:17.690
And then they draw
an altitude here.

00:07:17.690 --> 00:07:19.490
All righty.

00:07:19.490 --> 00:07:22.190
OK, so this an R.

00:07:22.190 --> 00:07:24.140
This is a W.

00:07:24.140 --> 00:07:25.920
This is a U.

00:07:25.920 --> 00:07:27.600
A T.

00:07:27.600 --> 00:07:28.750
And an S.

00:07:28.750 --> 00:07:31.690
They're saying the height
of this is 60 meters.

00:07:31.690 --> 00:07:34.410
This length is 45 meters.

00:07:34.410 --> 00:07:36.170
And they're saying this
right here, this

00:07:36.170 --> 00:07:38.450
length is 15 meters.

00:07:38.450 --> 00:07:40.400
Fair enough.

00:07:40.400 --> 00:07:45.110
Quadrilateral RSTU, shown above,
is a site plan for a

00:07:45.110 --> 00:07:50.760
parking lot, in which side RU is
parallel to side ST. OK, so

00:07:50.760 --> 00:07:54.010
this and this are parallel.

00:07:54.010 --> 00:07:57.460
What is the area of
the parking lot?

00:07:57.460 --> 00:07:59.970
So, immediately I can figure
out the area of

00:07:59.970 --> 00:08:00.740
this triangle, right?

00:08:00.740 --> 00:08:01.940
Base times height, times 1/2.

00:08:01.940 --> 00:08:04.670
So I can figure out this
area immediately.

00:08:04.670 --> 00:08:11.040
I can immediately figure out
this square region right here.

00:08:11.040 --> 00:08:13.260
Because I know it's 60 by 45.

00:08:13.260 --> 00:08:15.130
And so the question is, can I
figure out this triangular

00:08:15.130 --> 00:08:16.890
region right here?

00:08:16.890 --> 00:08:18.850
Well, I don't know what
this distance is.

00:08:18.850 --> 00:08:20.870
If I knew what this distance
is, then I could say base

00:08:20.870 --> 00:08:22.940
times 60, times 1/2, and
figure this out.

00:08:22.940 --> 00:08:25.920
So this right here
is what matters.

00:08:25.920 --> 00:08:28.410
That's the crux of the
issue right there.

00:08:28.410 --> 00:08:34.679
So statement number one tells
us that RU is 80 meters.

00:08:34.679 --> 00:08:36.679
RU is equal to 80.

00:08:36.679 --> 00:08:38.720
I think this gets
us there, right?

00:08:38.720 --> 00:08:45.340
Because think about it, if this
whole thing is 80 meters,

00:08:45.340 --> 00:08:46.350
I can figure out that.

00:08:46.350 --> 00:08:47.250
How can I figure out that?

00:08:47.250 --> 00:08:48.710
Because I have 15 here.

00:08:48.710 --> 00:08:51.930
I have this length is 45.

00:08:51.930 --> 00:08:55.710
So this length is going to
be 80 minus 45, minus 15.

00:08:55.710 --> 00:08:56.140
And what is that?

00:08:56.140 --> 00:08:56.660
60.

00:08:56.660 --> 00:08:57.550
So 80 minus 60.

00:08:57.550 --> 00:08:59.450
So this will be 20.

00:08:59.450 --> 00:09:01.700
And so just with statement one,
I can figure out this

00:09:01.700 --> 00:09:03.180
length right here.

00:09:03.180 --> 00:09:05.920
And I'm done because this
triangle is this base times

00:09:05.920 --> 00:09:07.390
this height, times 1/2.

00:09:07.390 --> 00:09:10.640
This rectangle is this base
times this height.

00:09:10.640 --> 00:09:14.000
And then this triangle is
20 times 60, times 1/2.

00:09:14.000 --> 00:09:15.980
So I have enough information
to figure out the area just

00:09:15.980 --> 00:09:18.200
with statement one.

00:09:18.200 --> 00:09:20.830
Now statement two.

00:09:20.830 --> 00:09:35.370
TU is equal to 20 square
roots of 10 meters.

00:09:35.370 --> 00:09:36.740
Well, this is enough
information, too.

00:09:36.740 --> 00:09:37.280
Think about it.

00:09:37.280 --> 00:09:39.900
This is a right triangle
right here.

00:09:39.900 --> 00:09:41.450
This height is 60.

00:09:41.450 --> 00:09:43.720
And remember, if we can figure
out-- let me switch colors--

00:09:43.720 --> 00:09:46.260
if we figure out the base,
we're going to be set.

00:09:46.260 --> 00:09:47.830
So we could do Pythagorean
Theorem.

00:09:47.830 --> 00:09:53.100
So we could say, the based
squared plus 60 squared is

00:09:53.100 --> 00:09:55.000
equal to this number squared.

00:09:55.000 --> 00:09:56.690
And that number squared
is what?

00:09:56.690 --> 00:10:00.920
400 times 10.

00:10:00.920 --> 00:10:03.000
So it's 4,000.

00:10:03.000 --> 00:10:06.030
So you get B squared is equal
to 4,000 minus 3,600, which

00:10:06.030 --> 00:10:07.470
equals 400.

00:10:07.470 --> 00:10:09.360
So B is equal to 20 again.

00:10:09.360 --> 00:10:12.220
So this actually also gives you
the information that this

00:10:12.220 --> 00:10:13.510
base right here is
equal to 20.

00:10:13.510 --> 00:10:16.430
And then, like I showed in the
previous statement, that's all

00:10:16.430 --> 00:10:18.070
you need to figure out
the area of the

00:10:18.070 --> 00:10:19.550
entire parking lot.

00:10:19.550 --> 00:10:22.230
So statement two alone
is also sufficient.

00:10:22.230 --> 00:10:25.370
So either of these statements
alone are sufficient to tell

00:10:25.370 --> 00:10:26.780
us the area of the
parking lot.

00:10:26.780 --> 00:10:28.610
See you in the next video.


GMAT: Data sufficiency 21

WEBVTT
Kind: captions
Language: en

00:00:00.440 --> 00:00:05.320
We're on problem 91.

00:00:05.320 --> 00:00:08.590
By what percent did the median
household-- so median is

00:00:08.590 --> 00:00:12.600
middle-- by what percent did the
median household income in

00:00:12.600 --> 00:00:17.540
country Y decrease from
1970 to 1980?

00:00:17.540 --> 00:00:18.790
So they want a percentage.

00:00:23.770 --> 00:00:24.350
All right.

00:00:24.350 --> 00:00:29.430
Statement number one tells us in
1970, the median household

00:00:29.430 --> 00:00:35.270
income in country Y was 2/3
of the median household

00:00:35.270 --> 00:00:37.190
income in country X.

00:00:37.190 --> 00:00:42.885
So let's write Y in 1970-- let's
just write '70, because

00:00:42.885 --> 00:00:44.950
the 19 is redundant.

00:00:44.950 --> 00:00:51.950
The median income in country Y
in 1970 is equal to 2/3 of the

00:00:51.950 --> 00:00:57.150
median income of country
X in 1970.

00:00:57.150 --> 00:00:59.250
That's what statement
one tells us.

00:00:59.250 --> 00:01:02.180
But one again, we know nothing
still about what happened in

00:01:02.180 --> 00:01:04.310
1980 in country Y.

00:01:04.310 --> 00:01:06.390
So we still can't answer
the question.

00:01:06.390 --> 00:01:08.390
Statement number two.

00:01:08.390 --> 00:01:23.050
In 1980, the median household
income in country Y was 1/2

00:01:23.050 --> 00:01:29.000
the median household income
in country X in 1980.

00:01:29.000 --> 00:01:31.930
Now, you might be tempted to
say, oh, two linear equations

00:01:31.930 --> 00:01:34.650
and two unknowns, maybe I can
solve for it, et cetera.

00:01:34.650 --> 00:01:35.020
But no.

00:01:35.020 --> 00:01:37.640
There's actually two
linear equations in

00:01:37.640 --> 00:01:39.800
four unknowns, right?

00:01:39.800 --> 00:01:43.250
Y in 1970 is different
than Y in 1980.

00:01:43.250 --> 00:01:46.310
And X in 1970 is different
than X in 1980.

00:01:46.310 --> 00:01:47.910
So there's actually
four variables.

00:01:47.910 --> 00:01:48.840
But you say, oh no, no.

00:01:48.840 --> 00:01:50.860
But we don't need to figure out
all the variables, we just

00:01:50.860 --> 00:01:53.160
need to figure out the
percent decline.

00:01:53.160 --> 00:01:53.400
Right?

00:01:53.400 --> 00:01:56.300
They just say by what percent
did the median household

00:01:56.300 --> 00:02:01.350
income in country Y decrease
from 1970 to 1980?

00:02:01.350 --> 00:02:12.790
So essentially if we could
figure out this, Y80 over Y70,

00:02:12.790 --> 00:02:14.830
we'll know what the percent
decline was.

00:02:14.830 --> 00:02:15.380
Right?

00:02:15.380 --> 00:02:18.830
If this number is 0.8, then
it would be a 20% decline.

00:02:18.830 --> 00:02:21.950
If this number was 0.5, then
it would be a 50% decline.

00:02:21.950 --> 00:02:25.140
So whatever this number is,
that's essentially 1 minus

00:02:25.140 --> 00:02:26.030
that is the percent decline.

00:02:26.030 --> 00:02:29.410
So maybe we just have
to figure out this.

00:02:29.410 --> 00:02:29.720
But look.

00:02:29.720 --> 00:02:31.790
I can prove to you
mathematically that we still

00:02:31.790 --> 00:02:33.210
can't figure it out
without this.

00:02:33.210 --> 00:02:39.460
Because Y80 divided by Y70,
that's equal to 2/3X-- oh no,

00:02:39.460 --> 00:02:41.060
sorry, Y80.

00:02:41.060 --> 00:02:51.570
So Y80, that's 1/2X in 1980
divided by 2/3X in 1970.

00:02:51.570 --> 00:02:51.890
Right?

00:02:51.890 --> 00:02:52.350
And then let's see.

00:02:52.350 --> 00:02:57.360
If we could take this 3/2
up, we get, let's

00:02:57.360 --> 00:02:59.080
see-- divide by 1/3.

00:02:59.080 --> 00:03:02.870
3 becomes 3/2.

00:03:02.870 --> 00:03:09.250
So it becomes 3/4X80 over X70.

00:03:09.250 --> 00:03:12.290
They never told us what the
median household income in

00:03:12.290 --> 00:03:13.560
country X was in any year.

00:03:13.560 --> 00:03:15.450
So we still can't solve
this problem.

00:03:15.450 --> 00:03:18.650
So there's not enough
information given.

00:03:18.650 --> 00:03:22.610
Next problem, 92.

00:03:22.610 --> 00:03:26.140
A certain group of car
dealerships agreed to donate x

00:03:26.140 --> 00:03:30.810
dollars to a Red Cross chapter
for each car sold during a

00:03:30.810 --> 00:03:31.970
30-day period.

00:03:31.970 --> 00:03:34.875
What was the total amount that
was expected to be donated?

00:03:38.810 --> 00:03:40.880
So the total amount--
let's see.

00:03:40.880 --> 00:03:47.930
Donation is going to be equal
to x dollars times

00:03:47.930 --> 00:03:50.500
the number of cars.

00:03:50.500 --> 00:03:51.720
And this is what we need
to figure out.

00:03:51.720 --> 00:03:54.640
We need to figure out what the
donations are equal to, or the

00:03:54.640 --> 00:03:56.170
expected donations.

00:03:56.170 --> 00:03:58.810
It says a total of 500 cars
were expected to be sold.

00:03:58.810 --> 00:04:02.150
So it's essentially telling
us that C is equal to 500.

00:04:02.150 --> 00:04:04.090
We still can't figure out what D
is because we don't know how

00:04:04.090 --> 00:04:07.330
many dollars are we getting
for each car.

00:04:07.330 --> 00:04:10.720
So that is not enough
information by itself.

00:04:10.720 --> 00:04:12.390
Statement two.

00:04:12.390 --> 00:04:15.470
60 more cars were sold
than expected.

00:04:15.470 --> 00:04:21.410
So the total amount actually
donated was $28,000.

00:04:21.410 --> 00:04:22.120
Interesting.

00:04:22.120 --> 00:04:29.260
So essentially it's saying that
C plus-- so if you had an

00:04:29.260 --> 00:04:32.530
extra 60 cars than
expected, right?

00:04:32.530 --> 00:04:34.440
500 were expected to be sold.

00:04:34.440 --> 00:04:39.120
Actually we could just say 500
were expected to be sold.

00:04:39.120 --> 00:04:41.245
60 more cars were sold
than expected.

00:04:44.010 --> 00:04:46.950
So this is the actual number
that were sold.

00:04:46.950 --> 00:04:49.620
And then that times the
amount donated per

00:04:49.620 --> 00:04:53.380
car is equal to $28,000.

00:04:53.380 --> 00:04:57.760
Well, now we do have enough
information to figure out--

00:04:57.760 --> 00:04:58.580
well, let's think about it.

00:04:58.580 --> 00:04:59.950
We have enough information
from this to

00:04:59.950 --> 00:05:01.770
figure out x, right?

00:05:05.250 --> 00:05:07.220
Well, we definitely have enough
information now to

00:05:07.220 --> 00:05:09.510
figure out x if we use
statement number one.

00:05:09.510 --> 00:05:11.510
I just want to be careful to
make sure that we can't solve

00:05:11.510 --> 00:05:14.250
this just with statement
number two.

00:05:14.250 --> 00:05:21.550
If I just said 560x is equal to
$28,000, then you get x is

00:05:21.550 --> 00:05:27.850
equal to 28,000 over 560.

00:05:27.850 --> 00:05:30.720
So then the amount that was
expected to be donated would

00:05:30.720 --> 00:05:36.650
be 28,000 over 560-- that's
what x is, whatever that

00:05:36.650 --> 00:05:40.090
number is-- times the number
of cars that were

00:05:40.090 --> 00:05:41.550
expected to be sold.

00:05:41.550 --> 00:05:43.380
Times 500.

00:05:43.380 --> 00:05:46.450
And actually, yeah, you have to
have statement one there,

00:05:46.450 --> 00:05:49.910
because statement two-- 60
more cars were sold.

00:05:49.910 --> 00:05:50.880
Actually, let me think
about that.

00:05:50.880 --> 00:05:54.320
So both combined, when I use
both of the information, it

00:05:54.320 --> 00:05:55.130
definitely works.

00:05:55.130 --> 00:05:57.780
So let me see if I can figure
it out just using

00:05:57.780 --> 00:05:58.870
statement two alone.

00:05:58.870 --> 00:06:01.710
I don't think I can, but I have
a nagging feeling that

00:06:01.710 --> 00:06:04.510
they may be giving more
information than I'm-- so let

00:06:04.510 --> 00:06:07.900
me say that the cars
expected is C.

00:06:07.900 --> 00:06:09.940
So this is what statement two
actually is telling us.

00:06:09.940 --> 00:06:12.740
I assumed the 500, which
I shouldn't have done.

00:06:12.740 --> 00:06:16.480
So statement two is actually
telling, when I have 60 more

00:06:16.480 --> 00:06:20.120
than the cars expected
to be sold

00:06:20.120 --> 00:06:25.840
times x, I raised $28,000.

00:06:25.840 --> 00:06:26.230
Right.

00:06:26.230 --> 00:06:30.160
This alone is not-- you don't
know what x or C is.

00:06:30.160 --> 00:06:34.310
Because at the end of the
day you need to know

00:06:34.310 --> 00:06:35.910
what x times C is.

00:06:35.910 --> 00:06:37.510
x times C is our goal.

00:06:37.510 --> 00:06:43.700
So if you distributed this out,
you get xC plus 60x is

00:06:43.700 --> 00:06:46.890
equal to $28,000.

00:06:46.890 --> 00:06:53.270
And you get xC is equal
to 28,000 minus 60x.

00:06:53.270 --> 00:06:55.830
So this is as much information
as you can glean just from

00:06:55.830 --> 00:06:56.800
statement number two.

00:06:56.800 --> 00:06:58.910
So that alone is not enough.

00:06:58.910 --> 00:07:00.750
If you could figure out what
x is, you're done.

00:07:00.750 --> 00:07:03.110
You actually don't need
to know the expected

00:07:03.110 --> 00:07:04.100
number of cars sold.

00:07:04.100 --> 00:07:06.350
You would just know.

00:07:06.350 --> 00:07:07.800
Well actually, that's true
with statement one.

00:07:07.800 --> 00:07:09.220
So you need both of
these statements

00:07:09.220 --> 00:07:10.230
to solve the problem.

00:07:10.230 --> 00:07:12.120
Anyway, as you can see,
I haven't done

00:07:12.120 --> 00:07:12.970
these problems before.

00:07:12.970 --> 00:07:15.420
So sometimes I'm not sure.

00:07:15.420 --> 00:07:18.300
And sometimes I might
even get them wrong.

00:07:18.300 --> 00:07:23.100
Problem 93.

00:07:23.100 --> 00:07:25.660
While driving on the expressway,
did Robin ever

00:07:25.660 --> 00:07:29.000
exceed the 55 mile an
hour speed limit?

00:07:29.000 --> 00:07:30.230
Well, who knows?

00:07:30.230 --> 00:07:31.430
Statement one.

00:07:31.430 --> 00:07:36.190
Robin drove 100 miles.

00:07:36.190 --> 00:07:38.250
Well, that doesn't tell me
whether she ever went more

00:07:38.250 --> 00:07:39.830
than-- I'm assuming
it's a she.

00:07:39.830 --> 00:07:41.960
I guess it's an androgynous
sounding name.

00:07:41.960 --> 00:07:43.800
That still doesn't tell
me whether she

00:07:43.800 --> 00:07:46.640
went over 100 miles.

00:07:46.640 --> 00:07:47.700
Two.

00:07:47.700 --> 00:07:51.690
Robin drove for 2 hours
on the expressway.

00:07:51.690 --> 00:07:55.320
So time is equal to 2 hours.

00:07:55.320 --> 00:07:57.560
So each of these independently
give me no information about

00:07:57.560 --> 00:07:58.690
how fast she went.

00:07:58.690 --> 00:08:00.790
But if I use both of
them, I can figure

00:08:00.790 --> 00:08:02.480
out her average speed.

00:08:02.480 --> 00:08:04.990
I can say, well, she went
100 miles in 2 hours.

00:08:04.990 --> 00:08:11.690
Average speed is equal
to 50 miles per hour.

00:08:11.690 --> 00:08:13.940
Now, the question is,
did Robin ever

00:08:13.940 --> 00:08:16.090
exceed the speed limit?

00:08:16.090 --> 00:08:16.780
Well, I don't know.

00:08:16.780 --> 00:08:19.500
It's completely possible
that she just went up

00:08:19.500 --> 00:08:21.590
to 50 miles an hour.

00:08:21.590 --> 00:08:25.120
Well, we don't know how fast
her car accelerates.

00:08:25.120 --> 00:08:29.250
She might just gone-- she
accelerated really fast, got

00:08:29.250 --> 00:08:32.600
to 55, stayed there or went down
a little bit and ended up

00:08:32.600 --> 00:08:33.570
averaging at 55.

00:08:33.570 --> 00:08:34.760
She's never exceeded it.

00:08:34.760 --> 00:08:37.650
But she could have easily gone
80 miles an hour at some

00:08:37.650 --> 00:08:39.360
point, and then slowed
down and taken a

00:08:39.360 --> 00:08:40.480
break, and had a picnic.

00:08:40.480 --> 00:08:41.500
We don't know.

00:08:41.500 --> 00:08:45.080
So this by itself is not enough
information to figure

00:08:45.080 --> 00:08:47.360
out if she ever exceeded
the speed limit.

00:08:47.360 --> 00:08:51.680
If her average speed was 56
miles per hour, then we'd know

00:08:51.680 --> 00:08:53.640
that she had to exceed
the speed limit.

00:08:53.640 --> 00:08:58.030
Because, well, we can assume
that at some some point she

00:08:58.030 --> 00:08:59.845
was going at least 56
miles per hour.

00:08:59.845 --> 00:09:02.180
And especially if we can assume
that she started at a

00:09:02.180 --> 00:09:04.250
standstill, because then you'd
have to go even faster than

00:09:04.250 --> 00:09:06.850
the average to make up for the
time that you're going slower.

00:09:06.850 --> 00:09:09.370
But anyway, there's not enough
information here to figure it

00:09:09.370 --> 00:09:14.760
out, just knowing that her
average speed was 50.

00:09:14.760 --> 00:09:16.010
Next problem.

00:09:18.760 --> 00:09:20.500
94.

00:09:20.500 --> 00:09:24.740
In Jefferson School, 300
students study French or

00:09:24.740 --> 00:09:28.010
Spanish or both.

00:09:28.010 --> 00:09:28.250
OK.

00:09:28.250 --> 00:09:29.960
This sounds like
a Venn Diagram.

00:09:29.960 --> 00:09:32.800
French or Spanish or both.

00:09:32.800 --> 00:09:36.222
So this is French,
this is Spanish.

00:09:40.110 --> 00:09:43.490
And this right here is both,
in the intersection.

00:09:43.490 --> 00:09:48.080
If 100 of these students do not
study French-- OK, they

00:09:48.080 --> 00:09:49.710
study French or Spanish
or both.

00:09:49.710 --> 00:09:51.940
There's not an option
to do neither.

00:09:51.940 --> 00:09:55.160
If 100 of these students do not
study French, how many of

00:09:55.160 --> 00:09:57.950
these students study both
French and Spanish?

00:09:57.950 --> 00:10:00.090
So when they tell us that 100 of
these students do not study

00:10:00.090 --> 00:10:03.220
French, that tells us that this
area-- let me color it in

00:10:03.220 --> 00:10:08.550
a suitably garish color.

00:10:08.550 --> 00:10:09.320
Oh, no.

00:10:09.320 --> 00:10:10.570
That's not what I want to do.

00:10:13.380 --> 00:10:19.220
That tells us that this area
right here is 100.

00:10:19.220 --> 00:10:22.160
So essentially, the people who
are studying Spanish but not

00:10:22.160 --> 00:10:24.550
French is 100.

00:10:24.550 --> 00:10:25.050
Right?

00:10:25.050 --> 00:10:27.030
And they're asking, how many of
these students study both

00:10:27.030 --> 00:10:28.190
French and Spanish?

00:10:28.190 --> 00:10:31.030
So they essentially want to
know the intersection of

00:10:31.030 --> 00:10:32.150
French and Spanish.

00:10:32.150 --> 00:10:34.820
That purple area is what
the question asks.

00:10:34.820 --> 00:10:38.070
So let's explore
the statements.

00:10:38.070 --> 00:10:43.210
Statement number one tells us,
of the 300 students, 60 do not

00:10:43.210 --> 00:10:44.070
study Spanish.

00:10:44.070 --> 00:10:48.350
60 no Spanish.

00:10:48.350 --> 00:10:52.750
So that's essentially telling
us this area.

00:10:52.750 --> 00:10:54.780
Not this, just this.

00:10:54.780 --> 00:10:57.620
So that tells us how many
study French only.

00:10:57.620 --> 00:10:59.250
That's 60.

00:10:59.250 --> 00:11:02.560
It still doesn't help us to
know the intersection.

00:11:02.560 --> 00:11:09.260
Statement number two says, a
total of 240 of the students

00:11:09.260 --> 00:11:10.510
study Spanish.

00:11:14.460 --> 00:11:17.140
Well, I think this alone is
enough information, right?

00:11:17.140 --> 00:11:19.720
Because they're telling us that
this purple area plus

00:11:19.720 --> 00:11:21.690
this yellow area is
equal to 240.

00:11:21.690 --> 00:11:26.940
We want to figure out the
purple area, right?

00:11:26.940 --> 00:11:30.490
So the total number of people
who study Spanish-- it's the

00:11:30.490 --> 00:11:33.010
people who study French and
Spanish, which is this purple

00:11:33.010 --> 00:11:36.520
area-- plus the people who only
study Spanish, which they

00:11:36.520 --> 00:11:38.480
gave us in the problem
was 100.

00:11:38.480 --> 00:11:40.090
And then statement number
two says that

00:11:40.090 --> 00:11:42.400
that is equal to 240.

00:11:42.400 --> 00:11:45.340
So the people who study French
and Spanish has to be the

00:11:45.340 --> 00:11:48.830
purple area, which is 240
minus 100, which is 140.

00:11:48.830 --> 00:11:50.290
Which we don't have to figure
out the number, we just have

00:11:50.290 --> 00:11:54.300
to know that two gives us enough
information, by itself,

00:11:54.300 --> 00:11:55.740
to solve the problem.

00:11:55.740 --> 00:12:01.360
And we don't even need
statement number one.

00:12:01.360 --> 00:12:02.300
and I'm out of time.

00:12:02.300 --> 00:12:04.000
See you in the next video.