GMAT: Data sufficiency 11

WEBVTT
Kind: captions
Language: en

00:00:00.600 --> 00:00:02.640
Problem 51.

00:00:02.640 --> 00:00:07.390
Actually, let me scroll all
the way up, problem 51.

00:00:07.390 --> 00:00:09.620
They drew a little triangle
here, which I assume I need,

00:00:09.620 --> 00:00:11.660
so I'll draw it as well.

00:00:11.660 --> 00:00:17.970
That side is flat and that side
goes down like that, and

00:00:17.970 --> 00:00:20.640
then they draw some angles.

00:00:20.640 --> 00:00:27.390
This is being angle x, this is
angle y, this is angle z.

00:00:27.390 --> 00:00:29.990
And they say, what is
the value of z in

00:00:29.990 --> 00:00:31.280
the triangle above?

00:00:31.280 --> 00:00:32.820
Fair enough.

00:00:32.820 --> 00:00:42.410
Statement number one is x
plus y is equal to 139.

00:00:42.410 --> 00:00:44.325
Well, as soon as you see a
triangle and you have to

00:00:44.325 --> 00:00:45.320
figure out one side, you should
always remember that

00:00:45.320 --> 00:00:48.530
the sum of the angles of a
triangle add up to 180.

00:00:48.530 --> 00:00:54.590
So we know that x plus y
plus z is equal to 180.

00:00:54.590 --> 00:00:58.690
Statement one just told us that
x plus y is equal to 139.

00:00:58.690 --> 00:01:02.180
So we know from statement
one that this is 139.

00:01:02.180 --> 00:01:05.330
So that would just make
this equation 139 plus

00:01:05.330 --> 00:01:07.700
z is equal to 180.

00:01:07.700 --> 00:01:09.050
Which is very easy to solve.

00:01:09.050 --> 00:01:12.190
Subtract 39 from both sides
which you get z is equal to 41

00:01:12.190 --> 00:01:12.990
or something like that.

00:01:12.990 --> 00:01:14.800
It doesn'nt matter, you don't
have to get the answer.

00:01:14.800 --> 00:01:16.560
You just have to know that
you can get the answer.

00:01:16.560 --> 00:01:19.270
So statement one, alone,
is enough.

00:01:19.270 --> 00:01:21.990
Now what do they give us in
statement number two?

00:01:21.990 --> 00:01:27.840
Statement two, y plus
z is equal to 108.

00:01:27.840 --> 00:01:30.790
This statement alone
is useless.

00:01:30.790 --> 00:01:32.290
We don't know what y is.

00:01:32.290 --> 00:01:34.210
So we can't figure it out.

00:01:34.210 --> 00:01:37.610
I mean, one thing is true,
if you had both of these

00:01:37.610 --> 00:01:39.460
statements, then you can figure
out all of the angles

00:01:39.460 --> 00:01:40.030
of the triangle.

00:01:40.030 --> 00:01:42.930
Because you know that z is 41
then you could figure out y,

00:01:42.930 --> 00:01:45.370
then once you know y you
could figure out x.

00:01:45.370 --> 00:01:47.340
But they're not asking
us that.

00:01:47.340 --> 00:01:49.720
We need to figure out
what angle z is.

00:01:49.720 --> 00:01:52.520
And this statement alone would
not tell us what angle z is

00:01:52.520 --> 00:01:53.860
because we don't know
what angle y is.

00:01:53.860 --> 00:01:55.900
But statement one alone works.

00:01:55.900 --> 00:01:58.890
So the answer is A.

00:01:58.890 --> 00:02:01.280
Next problem.

00:02:01.280 --> 00:02:03.470
Turn the page.

00:02:03.470 --> 00:02:08.949
52.

00:02:08.949 --> 00:02:18.620
If x y and z are non-0-- they
could have written x times y

00:02:18.620 --> 00:02:22.220
times z does not equal 0 because
that's the same thing.

00:02:22.220 --> 00:02:24.690
Because if any of them were 0,
it would have been equal 0.

00:02:24.690 --> 00:02:28.240
So I could have written
xyz does not equal 0.

00:02:28.240 --> 00:02:30.880
Because if you multiply three
non-0 numbers it's not going

00:02:30.880 --> 00:02:32.410
to equal zero.

00:02:32.410 --> 00:02:37.110
But anyway, they're asking
is xz equal to 12?

00:02:37.110 --> 00:02:41.330
xz equal to 12 is
the question.

00:02:41.330 --> 00:02:43.580
Statement one tells us-- and
I'll do it in a different

00:02:43.580 --> 00:02:47.280
color-- e is the monotony.

00:02:47.280 --> 00:02:51.600
Statement one tells us
that x squared times

00:02:51.600 --> 00:03:00.310
yz is equal to 12xy.

00:03:00.310 --> 00:03:01.560
So let's see what we can do.

00:03:01.560 --> 00:03:06.380
What if we were to divide both
sides of this equation by xy?

00:03:06.380 --> 00:03:09.020
Well, let's divide both sides
by x first. So if you divide

00:03:09.020 --> 00:03:11.745
both sides by x, and we can do
that because we know that x

00:03:11.745 --> 00:03:12.762
does not equal 0.

00:03:12.762 --> 00:03:14.400
soon.

00:03:14.400 --> 00:03:17.710
Divide both sides by
x, you get xyz is

00:03:17.710 --> 00:03:20.430
equal to 12y, right?

00:03:20.430 --> 00:03:22.270
Divided by x on both sides.

00:03:22.270 --> 00:03:23.870
Now let's divide both
sides by y.

00:03:23.870 --> 00:03:27.030
You get xz is equal to 12.

00:03:27.030 --> 00:03:27.960
And we're done.

00:03:27.960 --> 00:03:29.860
Statement alone is enough.

00:03:29.860 --> 00:03:31.900
And remember, the only reason
why we we're able to divide

00:03:31.900 --> 00:03:35.510
both sides by y is because we
knew it didn't equal 0.

00:03:35.510 --> 00:03:38.580
Now what does statement
two tell us?

00:03:38.580 --> 00:03:45.830
Statement two tells us that
z/4 is equal to 3/x.

00:03:45.830 --> 00:03:48.900
And here we can cross multiply,
x times z is equal

00:03:48.900 --> 00:03:50.390
to 3 times 4.

00:03:50.390 --> 00:03:52.230
And if that didn't make sense
to you, you could do it one

00:03:52.230 --> 00:03:52.830
step at a time.

00:03:52.830 --> 00:03:58.710
Multiply both sides by 4, you
get z is equal to 12/x, just

00:03:58.710 --> 00:04:00.510
multiplied both sides by 4.

00:04:00.510 --> 00:04:05.260
Then multiply both sides by x
and you get xz is equal to 12.

00:04:05.260 --> 00:04:08.570
So each statement,
independently, is enough to

00:04:08.570 --> 00:04:09.530
solve the equation.

00:04:09.530 --> 00:04:12.050
So that's D.

00:04:12.050 --> 00:04:14.070
I always have to keep looking
back and looking at which

00:04:14.070 --> 00:04:15.470
letter I have to say.

00:04:15.470 --> 00:04:16.800
I should memorize that.

00:04:16.800 --> 00:04:19.130
You should at least, you
have to take the GMAT.

00:04:19.130 --> 00:04:25.890
Alright, 53.

00:04:25.890 --> 00:04:29.280
A certain company currently
has how many employees?

00:04:29.280 --> 00:04:32.070
So we want to know the
number of emps.

00:04:32.070 --> 00:04:34.560
How many employees.

00:04:34.560 --> 00:04:35.120
OK.

00:04:35.120 --> 00:04:40.790
So statement number one: if 3
additional employees are hired

00:04:40.790 --> 00:04:44.200
by the company and all of the
present employees remain,

00:04:44.200 --> 00:04:48.270
there will be at least 20
employees in the company.

00:04:48.270 --> 00:04:52.490
So let's say e is the number
of employees today.

00:04:52.490 --> 00:04:57.010
So e plus 3.

00:04:57.010 --> 00:04:59.440
So the current number of
employees and three additional

00:04:59.440 --> 00:05:01.490
are hired and all
of them remain.

00:05:01.490 --> 00:05:03.490
There will be at least 20
employees in the company.

00:05:03.490 --> 00:05:06.020
So it at least tells
us greater than

00:05:06.020 --> 00:05:08.760
or equal to 20 employees.

00:05:08.760 --> 00:05:10.210
That's what statement one is.

00:05:10.210 --> 00:05:12.625
And that by itself doesn't tell
me how many employees are

00:05:12.625 --> 00:05:13.450
at the company.

00:05:13.450 --> 00:05:17.150
It tells us that there at least
17 employees at the

00:05:17.150 --> 00:05:19.220
company but it doesn't tell
us anything else.

00:05:19.220 --> 00:05:21.880
I mean you can subtract 3 from
both sides and you say e is

00:05:21.880 --> 00:05:23.420
greater than or equal to 17.

00:05:23.420 --> 00:05:24.680
But e could be 100.

00:05:24.680 --> 00:05:25.760
I don't know.

00:05:25.760 --> 00:05:25.950
OK.

00:05:25.950 --> 00:05:31.570
Statement two: if no additional
employees are hired

00:05:31.570 --> 00:05:36.240
by the company and 3 at the
present employees resign-- so

00:05:36.240 --> 00:05:41.570
e minus 3-- there will
be fewer than 15

00:05:41.570 --> 00:05:43.730
employees at the company.

00:05:43.730 --> 00:05:48.150
So fewer than 15 employees.

00:05:48.150 --> 00:05:49.950
So not 15 or lower.

00:05:49.950 --> 00:05:56.460
They say fewer than 15,
so less than 15.

00:05:56.460 --> 00:05:59.300
Right here they said at least
20, so that's greater than 20,

00:05:59.300 --> 00:06:00.780
greater than or equal to.

00:06:00.780 --> 00:06:03.740
Here they said fewer than, they
didn't say 15 or fewer,

00:06:03.740 --> 00:06:04.970
they said fewer than 15.

00:06:04.970 --> 00:06:08.050
So if you simplify this you
get-- add 3 to both sides--

00:06:08.050 --> 00:06:13.060
you say e is less than 18.

00:06:13.060 --> 00:06:15.110
So, let me ask you a question.

00:06:15.110 --> 00:06:17.220
First of all this by itself
isn't helpful because this

00:06:17.220 --> 00:06:20.210
just tells us we could only 5
employees at the company or we

00:06:20.210 --> 00:06:20.810
could have 10.

00:06:20.810 --> 00:06:22.430
This doesn't tell
us by itself.

00:06:22.430 --> 00:06:25.770
But if we use both of these in
conjunction, you if we know

00:06:25.770 --> 00:06:31.320
that e is less than-- so
if we say 17 is less

00:06:31.320 --> 00:06:32.780
than or equal to e.

00:06:32.780 --> 00:06:34.870
I just wrote this in
a different order.

00:06:34.870 --> 00:06:38.720
Alright, 17 is less than or
equal to e, which is less 18--

00:06:38.720 --> 00:06:42.320
I'm using both statements--
what is e?

00:06:42.320 --> 00:06:43.905
It has to be greater than
or equal the 17,

00:06:43.905 --> 00:06:45.186
so it could be 17.

00:06:45.186 --> 00:06:46.470
Can it be 18?

00:06:46.470 --> 00:06:48.700
Well, no, because it has
to be less than 18.

00:06:48.700 --> 00:06:51.170
So e has to be 17.

00:06:51.170 --> 00:06:54.090
So both statements together
are needed

00:06:54.090 --> 00:06:55.850
to solve this problem.

00:06:55.850 --> 00:06:59.300
And that is C.

00:06:59.300 --> 00:07:02.860
Both statements, together,
are sufficient.

00:07:02.860 --> 00:07:04.110
Next problem.

00:07:06.130 --> 00:07:10.205
54.

00:07:10.205 --> 00:07:14.470
Let me erase this little
5 I drew here.

00:07:14.470 --> 00:07:18.130
54.

00:07:18.130 --> 00:07:26.290
Alright, what is the value of
n in the equation minus 25

00:07:26.290 --> 00:07:33.160
plus 19 plus n is equal to s?

00:07:33.160 --> 00:07:36.800
Well, just to simplify it, we
could add up minus 25 plus 19,

00:07:36.800 --> 00:07:42.285
you get minus 6?

00:07:42.285 --> 00:07:46.940
So you get n minus 6 is
equal to s, right?

00:07:46.940 --> 00:07:47.890
That's right.

00:07:47.890 --> 00:07:48.770
Actually, you don't
have to do this.

00:07:48.770 --> 00:07:51.220
Remember the whole point of this
is to figure out whether

00:07:51.220 --> 00:07:51.940
you can solve the problem.

00:07:51.940 --> 00:07:53.860
You don't always have to solve
it but I'm solving them here

00:07:53.860 --> 00:07:57.270
just to prove it to you.

00:07:57.270 --> 00:07:59.510
To give you the intuition of
when you can solve it.

00:07:59.510 --> 00:08:00.390
So if you add 6 to both sides.

00:08:00.390 --> 00:08:01.750
So anyway, this was just
a simplification.

00:08:01.750 --> 00:08:02.530
Let's read the statements.

00:08:02.530 --> 00:08:03.480
I haven't read them yet.

00:08:03.480 --> 00:08:05.890
Maybe I didn't have
to do any of that.

00:08:05.890 --> 00:08:08.160
Alright, what problem
was I-- 54.

00:08:08.160 --> 00:08:10.360
OK. s is equal to 2.

00:08:10.360 --> 00:08:12.950
Well, clearly, if we know that
s is equal to 2, we can solve

00:08:12.950 --> 00:08:14.510
for n. n would be equal to 8.

00:08:14.510 --> 00:08:16.820
This statement alone
is sufficient.

00:08:16.820 --> 00:08:24.530
Now statement number two tells
us n/s is equal to 4, and once

00:08:24.530 --> 00:08:27.770
again, as long as we have some
relation with n and s and we

00:08:27.770 --> 00:08:31.360
can solve for s and then
substitute back in, we can

00:08:31.360 --> 00:08:32.480
solve for n.

00:08:32.480 --> 00:08:34.070
And to prove it, let me do it.

00:08:34.070 --> 00:08:41.549
We have n is equal to 4s, and if
we know that n is equal to

00:08:41.549 --> 00:08:42.429
4-- what are we doing?

00:08:42.429 --> 00:08:45.430
We're trying to solve for n.

00:08:45.430 --> 00:08:49.230
We could write s is equal
to n divided by 4.

00:08:49.230 --> 00:08:51.830
And then you can substitute
back into that equation.

00:08:51.830 --> 00:08:55.440
So then you would get
n is equal to s,

00:08:55.440 --> 00:08:59.100
which is n/4 plus 6.

00:08:59.100 --> 00:09:00.600
And then you could
just solve for n.

00:09:00.600 --> 00:09:02.780
And if you want to do it, let's
see, multiply both sides

00:09:02.780 --> 00:09:08.740
by 4, you get 4n is equal
to n plus 24.

00:09:08.740 --> 00:09:11.690
That's an equal sign
not a not-equal.

00:09:11.690 --> 00:09:13.660
I just multiplied
both sides by 4.

00:09:13.660 --> 00:09:16.520
4n is equal to n plus 24.

00:09:16.520 --> 00:09:21.150
Subtract n from both sides, you
get 3n is equal to 24 and

00:09:21.150 --> 00:09:23.000
then you get n is equal
to 8 again.

00:09:23.000 --> 00:09:26.650
So each statement alone
is sufficient.

00:09:26.650 --> 00:09:29.430
And that is-- I should really
memorize this-- that's D.

00:09:29.430 --> 00:09:32.230
Each statement alone
is sufficient.

00:09:32.230 --> 00:09:32.610
OK.

00:09:32.610 --> 00:09:34.870
Let's see, do I have
time for 55?

00:09:34.870 --> 00:09:36.490
Let me wait for that
for the next video.

00:09:36.490 --> 00:09:37.740
See


GMAT: Data sufficiency 9

WEBVTT
Kind: captions
Language: en

00:00:00.570 --> 00:00:04.000
All right, problem 42.

00:00:04.000 --> 00:00:06.270
So say for the system of
equations given, and this is

00:00:06.270 --> 00:00:12.240
the system of equations they
give, they say x minus 4 is

00:00:12.240 --> 00:00:14.460
equal to z.

00:00:14.460 --> 00:00:20.760
They say y minus x is equal
to 8, and that 8 minus

00:00:20.760 --> 00:00:22.340
z is equal to t.

00:00:28.560 --> 00:00:29.990
So they say for the system
equation, what is

00:00:29.990 --> 00:00:31.060
the value of z?

00:00:31.060 --> 00:00:32.070
So we're trying to figure
out z in this.

00:00:32.070 --> 00:00:36.170
Statement number one: they tell
us that x is equal to 7.

00:00:39.110 --> 00:00:41.580
Well, if we know x is equal to
7, we can solve for z right

00:00:41.580 --> 00:00:48.020
here because x is 7 and 7 minus
4 is z, so 7 minus 4 is

00:00:48.020 --> 00:00:50.130
3, so z is equal to 3.

00:00:50.130 --> 00:00:51.380
That was pretty straightforward.

00:00:51.380 --> 00:00:53.910
So one alone is sufficient just
using this first equation

00:00:53.910 --> 00:00:55.410
in the system.

00:00:55.410 --> 00:00:58.690
So let's see if two
is of any use.

00:00:58.690 --> 00:00:59.940
t is equal to 5.

00:01:02.450 --> 00:01:03.990
Well, this is an
easy one, too.

00:01:03.990 --> 00:01:08.180
You put t is equal to 5 right
here and then you could easily

00:01:08.180 --> 00:01:09.180
solve for z, right?

00:01:09.180 --> 00:01:13.050
You get 8 minus z is equal to
5 and you can solve for it,

00:01:13.050 --> 00:01:13.650
but I'm not even
going to do it.

00:01:13.650 --> 00:01:15.380
You just have to know
that you can.

00:01:15.380 --> 00:01:18.140
So this alone is sufficient
as well.

00:01:18.140 --> 00:01:20.050
So the answer is D.

00:01:20.050 --> 00:01:23.500
Each statement alone
is sufficient.

00:01:23.500 --> 00:01:28.040
Problem 43.

00:01:28.040 --> 00:01:29.570
Is x equal to 5?

00:01:34.040 --> 00:01:38.690
In statement number one,
they say x is greater

00:01:38.690 --> 00:01:40.760
than or equal to 5.

00:01:40.760 --> 00:01:42.710
Well, that doesn't tell me
whether x is equal to 5.

00:01:42.710 --> 00:01:45.080
It just says it's
greater than 5.

00:01:45.080 --> 00:01:48.900
Statement number two tells us x
is less than or equal to 5.

00:01:48.900 --> 00:01:54.600
Once again, that does not tell
me whether x is 5, but if I

00:01:54.600 --> 00:01:57.230
told you that both of these are
true, x is greater than or

00:01:57.230 --> 00:02:05.020
equal 5, and-- not or-- and x
is less than or equal to 5,

00:02:05.020 --> 00:02:11.340
well, actually, that still--
well, the only x that

00:02:11.340 --> 00:02:14.120
satisfies that equation,
that satisfies both of

00:02:14.120 --> 00:02:16.980
these, is 5, right?

00:02:16.980 --> 00:02:20.170
I mean, you put 3 in, 3 will
not satisfy this one.

00:02:20.170 --> 00:02:23.010
If you put 7 in, 7 will
not satisfy this one.

00:02:23.010 --> 00:02:29.120
So the only thing that satisfies
this is 5, so you

00:02:29.120 --> 00:02:30.260
need both of these.

00:02:30.260 --> 00:02:33.270
So the answer is both statements
together are

00:02:33.270 --> 00:02:36.490
sufficient, C.

00:02:36.490 --> 00:02:40.370
That one's confusing because
it's so simple on some level.

00:02:40.370 --> 00:02:43.950
44.

00:02:43.950 --> 00:02:46.230
The table above shows that
this-- let me see if I can

00:02:46.230 --> 00:02:47.480
draw this table.

00:02:54.130 --> 00:03:05.325
And they write R, S T, U,
and R, S, T, and U.

00:03:05.325 --> 00:03:06.930
They have a bunch of things.

00:03:06.930 --> 00:03:07.780
I don't even know what
these are yet.

00:03:07.780 --> 00:03:17.960
I haven't read the question, but
let's see, 0, y, x, 62, y,

00:03:17.960 --> 00:03:30.130
0, 56, 75, x, 56, 0, 69.

00:03:30.130 --> 00:03:39.910
And then 62-- that's a 6--
62, 75, 69, and 0.

00:03:39.910 --> 00:03:41.100
And what are they
going to ask?

00:03:41.100 --> 00:03:42.710
They're saying the table above
shows the distance in

00:03:42.710 --> 00:03:45.740
kilometers by the most direct
route between any two of the

00:03:45.740 --> 00:03:46.760
four cities.

00:03:46.760 --> 00:03:50.920
For example, the distance
between city R

00:03:50.920 --> 00:03:52.740
and city U is 62.

00:03:52.740 --> 00:03:55.030
Or if you said between U and
R, it's going to be 62 as

00:03:55.030 --> 00:03:55.430
well, right?

00:03:55.430 --> 00:03:56.530
That's the same thing.

00:03:56.530 --> 00:03:57.700
Fair enough.

00:03:57.700 --> 00:04:00.620
What is the value of x?

00:04:00.620 --> 00:04:04.490
So the value of x is the
distance between T and R.

00:04:04.490 --> 00:04:06.010
Let me circle that.

00:04:06.010 --> 00:04:07.600
They want to know what
the value of x is.

00:04:07.600 --> 00:04:12.195
It's the distance between T
and R, so it's that one.

00:04:12.195 --> 00:04:14.390
And another way to look at
distance between T and R,

00:04:14.390 --> 00:04:17.660
that's this one so,
these are both x.

00:04:17.660 --> 00:04:18.750
Fair enough.

00:04:18.750 --> 00:04:19.510
OK.

00:04:19.510 --> 00:04:24.100
So statement number one tells
us, by the most direct route,

00:04:24.100 --> 00:04:27.920
the distance between S and T,
so we could say the distance

00:04:27.920 --> 00:04:31.300
between S and T, I'll just say
it's line segment ST, is equal

00:04:31.300 --> 00:04:33.450
to twice the distance
between S and R.

00:04:33.450 --> 00:04:40.000
It's equal to two times SR.
So let's see, do we

00:04:40.000 --> 00:04:41.670
know what SR is?

00:04:41.670 --> 00:04:45.230
SR is equal to y, right?

00:04:45.230 --> 00:04:56.320
And ST is equal to 56.

00:04:56.320 --> 00:05:03.180
So 56 is equal to 2 times SR.
The distance between S and R

00:05:03.180 --> 00:05:05.810
is y, so it equals 2y.

00:05:05.810 --> 00:05:07.590
And so we can solve for y.

00:05:07.590 --> 00:05:11.050
y is equal to 28.

00:05:11.050 --> 00:05:13.290
And we didn't have to solve
it, but let's see.

00:05:13.290 --> 00:05:15.010
I'm just trying to see
where this goes.

00:05:15.010 --> 00:05:18.630
But that still doesn't help
me figure out the distance

00:05:18.630 --> 00:05:22.440
between R and T.

00:05:22.440 --> 00:05:27.880
That just tells me solve
for y. y is 28.

00:05:27.880 --> 00:05:32.210
Statement number two, see
where this is going.

00:05:32.210 --> 00:05:38.970
By the most direct route the
distance between T and U is

00:05:38.970 --> 00:05:45.510
1.5 times the distance
between R and T.

00:05:45.510 --> 00:05:47.670
So the distance between R and
T, this is the interesting

00:05:47.670 --> 00:05:52.450
thing, because R and
T is x, right?

00:05:52.450 --> 00:05:55.420
So they're saying the distance
between T and U is equal to

00:05:55.420 --> 00:05:57.760
1.5 times x.

00:05:57.760 --> 00:06:00.450
And what's this between
T and U?

00:06:00.450 --> 00:06:09.410
The distance between T
and U is 69, right?

00:06:09.410 --> 00:06:10.210
You don't even have
to solve it.

00:06:10.210 --> 00:06:12.790
You just know that you can
usually solve for x if you

00:06:12.790 --> 00:06:14.260
know statement number two.

00:06:14.260 --> 00:06:17.270
So statement number two
alone helps you

00:06:17.270 --> 00:06:19.000
figure out what x is.

00:06:19.000 --> 00:06:21.120
Statement number one
is fairly useless.

00:06:21.120 --> 00:06:23.020
So the answer is B.

00:06:23.020 --> 00:06:26.905
Statement two alone
is sufficient.

00:06:26.905 --> 00:06:28.040
Let me draw a line here.

00:06:28.040 --> 00:06:30.022
I don't want to--

00:06:30.022 --> 00:06:34.790
OK, problem number 45.

00:06:34.790 --> 00:06:38.180
What is the value of the
two-digit integer x?

00:06:38.180 --> 00:06:44.310
So 2-dig integer x equals,
who knows?

00:06:44.310 --> 00:06:45.560
All right.

00:06:45.560 --> 00:06:49.730
Statement number one: The sum
of the two digits is 3.

00:06:49.730 --> 00:06:53.600
So let's that x is equal to the
number AB where this is

00:06:53.600 --> 00:06:55.820
the tens digits and this
is the ones digit.

00:06:55.820 --> 00:06:58.540
So statement number one says the
sum of the two digits is

00:06:58.540 --> 00:07:04.400
3, so A plus B is equal to 3.

00:07:04.400 --> 00:07:05.430
Well, that doesn't help us.

00:07:05.430 --> 00:07:08.170
There's a lot of-- well, you
know that these are going to

00:07:08.170 --> 00:07:10.990
be positive numbers, but we
don't know whether they're two

00:07:10.990 --> 00:07:12.860
different numbers.

00:07:12.860 --> 00:07:18.360
Two: x is divisible by 3.

00:07:18.360 --> 00:07:19.440
x is divisible at 3.

00:07:19.440 --> 00:07:21.960
Well, I don't know if you
learned that trick in school,

00:07:21.960 --> 00:07:24.170
but any number that is divisible
by 3, the sum of

00:07:24.170 --> 00:07:29.320
their digits are also
divisible by 3.

00:07:29.320 --> 00:07:35.430
So once again, that just means
that A plus B is equal to some

00:07:35.430 --> 00:07:38.110
multiple of 3.

00:07:38.110 --> 00:07:40.520
Well, if you keep adding them,
they eventually add up.

00:07:40.520 --> 00:07:41.700
So if you had a two
digit number, so

00:07:41.700 --> 00:07:43.330
this is-- let's see.

00:07:43.330 --> 00:07:43.770
Let's think.

00:07:43.770 --> 00:07:46.650
Just A plus B is equal to 3.

00:07:46.650 --> 00:07:48.290
This could be a couple
of different things.

00:07:48.290 --> 00:07:51.170
It could be a two-digit
number.

00:07:51.170 --> 00:07:56.610
It could be 30.

00:07:56.610 --> 00:07:58.100
It could be 1.

00:07:58.100 --> 00:07:59.300
It could be 12.

00:07:59.300 --> 00:08:01.670
It could be 21.

00:08:01.670 --> 00:08:04.850
I think those are all of the
possibilities that we can have

00:08:04.850 --> 00:08:07.760
just off of statement
number one.

00:08:07.760 --> 00:08:09.380
And x is divisible by three,
well, all of these are

00:08:09.380 --> 00:08:12.170
divisible by 3, so really, both
statements give you no

00:08:12.170 --> 00:08:12.860
information.

00:08:12.860 --> 00:08:16.060
So the answer is E, that both
statements combined still give

00:08:16.060 --> 00:08:17.970
me nothing.

00:08:17.970 --> 00:08:21.540
But all of these are
possibilities.

00:08:21.540 --> 00:08:24.220
And actually, this one leads
to many, many more

00:08:24.220 --> 00:08:27.200
possibilities that x is
divisible by 3 because then

00:08:27.200 --> 00:08:30.100
you could have things
like-- I don't know.

00:08:30.100 --> 00:08:33.230
This would have been a
valid number as well.

00:08:33.230 --> 00:08:34.400
This would actually
give a lot more.

00:08:34.400 --> 00:08:35.460
This is a little bit
more strict.

00:08:35.460 --> 00:08:38.559
But anyway, either way, we can't
figure out what x is.

00:08:38.559 --> 00:08:39.090
It could be 30.

00:08:39.090 --> 00:08:39.669
It could be 12.

00:08:39.669 --> 00:08:40.090
It could be 21.

00:08:40.090 --> 00:08:41.559
It could be anything.

00:08:41.559 --> 00:08:42.429
All right.

00:08:42.429 --> 00:08:45.650
Problem 46.

00:08:45.650 --> 00:08:49.540
What is the tenth digit in the
decimal representation of a

00:08:49.540 --> 00:08:50.120
certain number?

00:08:50.120 --> 00:08:52.760
So the tenth, that's the
number right behind the

00:08:52.760 --> 00:08:54.170
decimal point.

00:08:54.170 --> 00:08:56.490
So the number-- let's just
call it x-- so statement

00:08:56.490 --> 00:09:01.620
number one says x is
less than 1/3.

00:09:01.620 --> 00:09:06.790
And two says that x is
greater than 1/4.

00:09:09.700 --> 00:09:13.080
So this is enough to figure out
what the tenth digit is.

00:09:13.080 --> 00:09:14.950
So what's the number that's
less than 1/3?

00:09:14.950 --> 00:09:16.060
Let me to think of
a couple of them.

00:09:16.060 --> 00:09:19.440
Well, 1/3 is like 0.333
repeating, so if I just write

00:09:19.440 --> 00:09:26.870
0.32 that satisfies one and
it satisfies 2, right?

00:09:26.870 --> 00:09:28.800
0.32 is greater than 1/4.

00:09:28.800 --> 00:09:29.790
But what's another?

00:09:29.790 --> 00:09:32.920
And then in this case, a tenth
digit would be a 3, but let me

00:09:32.920 --> 00:09:35.720
try to find another one that
would satisfy these both.

00:09:35.720 --> 00:09:39.660
Well, let's see, greater than
1/4, what about 0.26?

00:09:39.660 --> 00:09:42.920
0.26 is definitely greater than
1/4 and is definitely

00:09:42.920 --> 00:09:46.050
less than 1/3, but both of these
have different tens.

00:09:46.050 --> 00:09:47.970
One has a 2, one
has a 3 there.

00:09:47.970 --> 00:09:51.150
So even both statements combined
still do not allow me

00:09:51.150 --> 00:09:52.030
to solve the problem.

00:09:52.030 --> 00:09:53.230
There's not enough information
given.

00:09:53.230 --> 00:09:56.410
So once again, E, together I'm
still not getting enough

00:09:56.410 --> 00:09:58.620
information.

00:09:58.620 --> 00:09:59.840
Oh, I'm almost at 10 minutes.

00:09:59.840 --> 00:10:02.280
Anyway, I'll see you
in the next video.


GMAT: Data sufficiency 8

WEBVTT
Kind: captions
Language: en

00:00:00.890 --> 00:00:05.350
Now on problem 37.

00:00:05.350 --> 00:00:08.160
And they say what is the
value of xy minus yz.

00:00:14.250 --> 00:00:19.330
Statement one says,
y is equal to 2.

00:00:19.330 --> 00:00:20.640
Well, that by itself
doesn't help us.

00:00:20.640 --> 00:00:22.690
That just tells us
2x minus 2z.

00:00:22.690 --> 00:00:25.500
So if you don't know what x and
z are you can't figure out

00:00:25.500 --> 00:00:27.520
what this whole thing is if you
just know y is equal to 2.

00:00:27.520 --> 00:00:29.180
So that alone doesn't help.

00:00:29.180 --> 00:00:33.633
Statement two is x minus
z is equal to 5.

00:00:37.230 --> 00:00:39.740
Now this is interesting because
this expression, we

00:00:39.740 --> 00:00:40.710
can factor out the y.

00:00:40.710 --> 00:00:44.680
What happens if we factor
y out of both of these

00:00:44.680 --> 00:00:46.180
expressions?

00:00:46.180 --> 00:00:47.320
I'm going to just rewrite it.

00:00:47.320 --> 00:00:52.920
xy minus zy-- I just switched
the y and z-- that equals x

00:00:52.920 --> 00:00:56.700
minus z times y.

00:00:56.700 --> 00:00:58.490
Well, we can figure
out x minus z from

00:00:58.490 --> 00:00:59.920
statement number two.

00:00:59.920 --> 00:01:02.760
x minus z, this is equal 5.

00:01:02.760 --> 00:01:06.340
And we know what y is equal
to from statement one.

00:01:06.340 --> 00:01:08.690
So y is equal to 2.

00:01:08.690 --> 00:01:11.070
So we can definitely figure it
out as long as we have both

00:01:11.070 --> 00:01:13.450
statements and we can show
that the answer is

00:01:13.450 --> 00:01:14.570
y is equal to 2.

00:01:14.570 --> 00:01:17.330
So the answer is,
2 times 5 is 10.

00:01:17.330 --> 00:01:18.190
But we didn't have
to figure it out.

00:01:18.190 --> 00:01:20.960
We just have to know that we
could figure it out if we had

00:01:20.960 --> 00:01:22.170
both of these data points.

00:01:22.170 --> 00:01:24.720
One by themselves, you wouldn't
be able to solve it.

00:01:24.720 --> 00:01:26.720
So the answer is C.

00:01:26.720 --> 00:01:28.610
Both statements together
are sufficient but

00:01:28.610 --> 00:01:30.480
neither alone is.

00:01:30.480 --> 00:01:35.060
Problem 38.

00:01:35.060 --> 00:01:36.950
OK, they drew us a picture.

00:01:36.950 --> 00:01:40.470
Let me see if I can draw that
same picture, looks like some

00:01:40.470 --> 00:01:42.970
type of device.

00:01:42.970 --> 00:01:48.065
So it looks like that and then
they have the other end, and

00:01:48.065 --> 00:01:50.530
the other end looks like that.

00:01:50.530 --> 00:01:52.390
There are these handles,
or something

00:01:52.390 --> 00:01:53.130
that looks like handles.

00:01:53.130 --> 00:01:55.211
I haven't read the
problem yet.

00:01:55.211 --> 00:02:01.490
So they say will the first
10 volumes of a 20 volume

00:02:01.490 --> 00:02:06.420
encyclopedia fit upright in
the book rack shown above?

00:02:06.420 --> 00:02:07.210
So this is a book rack.

00:02:07.210 --> 00:02:08.630
So I guess the books get
stacked that way.

00:02:08.630 --> 00:02:11.960
And they labeled this right
here, this dimension is x.

00:02:11.960 --> 00:02:15.510
And they're saying, will the
first 10 volumes of a 20

00:02:15.510 --> 00:02:17.730
volume encyclopedia
fit upright in the

00:02:17.730 --> 00:02:19.790
book rack shown above?

00:02:19.790 --> 00:02:22.900
So essentially I'm going to
put the first 10 in there.

00:02:22.900 --> 00:02:26.230
So the first statement they say,
is that x is equal to 50

00:02:26.230 --> 00:02:27.800
centimeters.

00:02:27.800 --> 00:02:31.460
Well, that doesn't help me
because I don't know how big

00:02:31.460 --> 00:02:34.060
the first 10 volumes of
the encyclopedia are.

00:02:34.060 --> 00:02:37.640
If each of them are, at least
the first 10 are, less than 5

00:02:37.640 --> 00:02:40.860
centimeters each or on average
less than 5 centimeters, then

00:02:40.860 --> 00:02:41.690
maybe I could fit them.

00:02:41.690 --> 00:02:44.780
But one by itself
doesn't help me.

00:02:44.780 --> 00:02:51.700
Two: 12 of the volumes have
an average thickness of 5

00:02:51.700 --> 00:02:52.950
centimeters.

00:02:58.780 --> 00:03:00.910
Well, that doesn't help me
either because remember,

00:03:00.910 --> 00:03:03.950
they're saying will the first
10 volumes of a 20 volume

00:03:03.950 --> 00:03:05.080
encyclopedia?

00:03:05.080 --> 00:03:08.370
Maybe the 12 that have an
average thickness of 5

00:03:08.370 --> 00:03:13.040
centimeters, maybe those are the
volumes 8 through 20 and

00:03:13.040 --> 00:03:16.410
maybe volumes 1 through 7 have
an average thickness of 50

00:03:16.410 --> 00:03:18.990
centimeters each or 5 million
centimeters each.

00:03:18.990 --> 00:03:22.550
So even both of these conditions
combined don't help

00:03:22.550 --> 00:03:26.950
me know if I can definitely fit
the first 10 volumes of

00:03:26.950 --> 00:03:29.080
the 20 volume encyclopedia.

00:03:29.080 --> 00:03:31.500
So that is E.

00:03:31.500 --> 00:03:35.940
Both statements together are
still not sufficient.

00:03:35.940 --> 00:03:41.370
Problem 39.

00:03:41.370 --> 00:03:43.430
A circular tub-- OK, so
they've drawn this

00:03:43.430 --> 00:03:45.090
circular-looking tub.

00:03:45.090 --> 00:03:47.670
So the top looks like that.

00:03:47.670 --> 00:03:49.780
And then there's two sides.

00:03:49.780 --> 00:03:52.950
Let's me see how well I can
construct what they've drawn.

00:03:55.690 --> 00:03:59.820
And the bottom looks something
like that.

00:03:59.820 --> 00:04:04.170
And then they shade in a
little area, a strip

00:04:04.170 --> 00:04:09.050
of this, like that.

00:04:09.050 --> 00:04:13.920
And they say a circular tub has
a painted band around its

00:04:13.920 --> 00:04:14.870
circumference as show above.

00:04:14.870 --> 00:04:18.920
So this is the painted band
around its circumference.

00:04:18.920 --> 00:04:21.125
What is the surface area
of the painted band?

00:04:21.125 --> 00:04:23.230
And they tell us that
the height of the

00:04:23.230 --> 00:04:24.910
painted band is x.

00:04:24.910 --> 00:04:26.780
So in order to essentially know
the surface area, you'd

00:04:26.780 --> 00:04:31.370
have to know the height, which
is x, times the circumference

00:04:31.370 --> 00:04:33.750
of the circle, which would
be the length.

00:04:33.750 --> 00:04:35.680
So if you knew the height times
circumference of the

00:04:35.680 --> 00:04:37.170
circle, you'd be able to
know the surface area.

00:04:37.170 --> 00:04:44.860
So they tell us, the first
statement, x is equal to 0.5,

00:04:44.860 --> 00:04:45.640
whatever, meters.

00:04:45.640 --> 00:04:47.380
So this is in meters.

00:04:47.380 --> 00:04:51.080
0.5 meters, so that alone
doesn't help us.

00:04:51.080 --> 00:04:53.570
We have to be able to figure out
the circumference of this

00:04:53.570 --> 00:04:56.000
tub in order to really be able
to figure out the surface area

00:04:56.000 --> 00:04:57.670
because the circumference times
this height will be the

00:04:57.670 --> 00:04:59.480
service area.

00:04:59.480 --> 00:05:02.180
Point two: they say the height
of the tub is one meter.

00:05:02.180 --> 00:05:05.440
So they're telling us that
this is one meter.

00:05:05.440 --> 00:05:06.250
Well that doesn't help us.

00:05:06.250 --> 00:05:08.910
That still doesn't tell us how
far around the tub goes.

00:05:08.910 --> 00:05:11.780
If they had given us the
diameter or the radius or the

00:05:11.780 --> 00:05:14.830
circumference then we could've
used our basic geometry to

00:05:14.830 --> 00:05:16.980
figure out the circumference.

00:05:16.980 --> 00:05:17.540
But they didn't.

00:05:17.540 --> 00:05:21.360
So either way-- it's a one meter
height-- both of these

00:05:21.360 --> 00:05:24.600
combined still do not allow us
to figure out the surface area

00:05:24.600 --> 00:05:27.060
of this green band.

00:05:27.060 --> 00:05:28.800
E again.

00:05:28.800 --> 00:05:33.000
Problem 40.

00:05:33.000 --> 00:05:36.470
What is the value
of integer n?

00:05:36.470 --> 00:05:37.950
And n as an integer.

00:05:37.950 --> 00:05:45.310
So statement number one: they
tell us that n times n plus 1

00:05:45.310 --> 00:05:48.770
is equal to 6.

00:05:48.770 --> 00:05:52.250
Now we should already be able
to figure this out because n

00:05:52.250 --> 00:05:55.210
is an integer, n plus
1 is an integer.

00:05:55.210 --> 00:05:58.970
So what are the factorizations
of 6?

00:05:58.970 --> 00:06:02.010
You could have 1 times 6.

00:06:02.010 --> 00:06:03.810
But that doesn't fit n
and n plus 1, right?

00:06:03.810 --> 00:06:05.730
This is n and n plus 5.

00:06:05.730 --> 00:06:09.550
You have 2 times 3,
which work, right.

00:06:09.550 --> 00:06:13.280
If 2 is n, n plus 1 is
3 and they equal 6.

00:06:13.280 --> 00:06:14.880
So let me circle that.

00:06:14.880 --> 00:06:16.050
And then what other
factorizations?

00:06:16.050 --> 00:06:18.550
You don't have any other--
these are all

00:06:18.550 --> 00:06:19.950
of the factors 6.

00:06:19.950 --> 00:06:23.280
So just looking at the first
statement, you know that n has

00:06:23.280 --> 00:06:25.140
to be equal to 2.

00:06:25.140 --> 00:06:27.470
This is the only integer
where this is true.

00:06:27.470 --> 00:06:30.810
Actually, let me take
a step back.

00:06:30.810 --> 00:06:33.330
No, what if n is negative?

00:06:33.330 --> 00:06:35.370
Because I was assuming it's a
positive integer but they

00:06:35.370 --> 00:06:36.915
didn't say it's a positive
integer, so let

00:06:36.915 --> 00:06:38.980
me think about that.

00:06:38.980 --> 00:06:46.100
If I did minus 3 times minus
2, that also equals 6 and

00:06:46.100 --> 00:06:48.660
these are both integers.

00:06:48.660 --> 00:06:50.600
OK, so this isn't enough.

00:06:50.600 --> 00:06:53.190
Because in this case, n could
be-- this would be n and this

00:06:53.190 --> 00:06:57.740
is would be n plus 1-- so n is
either equal to 2 or n is

00:06:57.740 --> 00:06:59.240
equal to minus 3.

00:06:59.240 --> 00:07:00.200
That's a little tricky.

00:07:00.200 --> 00:07:02.390
The intuition is to just assume
that n is positive but

00:07:02.390 --> 00:07:04.000
it doesn't have to
be positive.

00:07:04.000 --> 00:07:07.720
So n could be 2 or
minus 3 here.

00:07:07.720 --> 00:07:08.820
That's a tricky one.

00:07:08.820 --> 00:07:12.490
So that one by itself does not
help us solve the problem.

00:07:12.490 --> 00:07:18.580
The second part of it, point
two it says, 2 to the 2n is

00:07:18.580 --> 00:07:20.195
equal to 16.

00:07:20.195 --> 00:07:23.900
And whenever you have these
in the SAT or the GMAT or

00:07:23.900 --> 00:07:26.910
anything, whenever you have a
variable in the exponent, your

00:07:26.910 --> 00:07:30.250
goal really is to just get
everything in the same base.

00:07:30.250 --> 00:07:32.950
So we could write the left-hand
side the same.

00:07:32.950 --> 00:07:35.740
So that's 2 to the 2n.

00:07:35.740 --> 00:07:40.920
And how do we write 16
with the base 2?

00:07:40.920 --> 00:07:42.560
Well, 16 is just 2 to
the fourth, right?

00:07:45.740 --> 00:07:50.700
And so we get 2n
is equal to 4.

00:07:50.700 --> 00:07:53.860
n is equal to 2.

00:07:53.860 --> 00:08:00.100
So this statement alone is
enough to figure it out.

00:08:00.100 --> 00:08:01.460
This statement alone is not.

00:08:01.460 --> 00:08:06.250
So the answer is B.

00:08:06.250 --> 00:08:08.960
Statement two alone
is sufficient.

00:08:08.960 --> 00:08:12.040
40 is B.

00:08:12.040 --> 00:08:14.760
And this was tricky because one,
you think that 1n alone

00:08:14.760 --> 00:08:16.910
is sufficient but it is
ambiguous because and n could

00:08:16.910 --> 00:08:19.720
be minus 3.

00:08:19.720 --> 00:08:23.800
41.

00:08:23.800 --> 00:08:25.060
OK.

00:08:25.060 --> 00:08:28.530
They've drawn a bunch of,
if I see this right, a

00:08:28.530 --> 00:08:30.972
bunch of-- two lines.

00:08:30.972 --> 00:08:33.530
Let's see if I can draw this.

00:08:33.530 --> 00:08:35.490
So a line and then there's
a bunch of circles.

00:08:41.880 --> 00:08:49.965
One circle, two circles
they have, and

00:08:49.965 --> 00:08:51.215
then they keep going.

00:08:54.400 --> 00:08:58.858
Three circles, and
then one more.

00:08:58.858 --> 00:09:00.920
It's going to be right there.

00:09:00.920 --> 00:09:01.830
Four circles.

00:09:01.830 --> 00:09:03.590
I think that's about right.

00:09:03.590 --> 00:09:06.120
And they say essentially that
the circles just keep

00:09:06.120 --> 00:09:08.580
going on and on.

00:09:08.580 --> 00:09:11.000
That's what I think the
drawing implies.

00:09:11.000 --> 00:09:14.810
They say the inside of a
rectangular carton is 48

00:09:14.810 --> 00:09:31.210
centimeters long, 32 centimeters
wide and 15

00:09:31.210 --> 00:09:32.460
centimeters high.

00:09:36.796 --> 00:09:37.210
OK.

00:09:37.210 --> 00:09:39.320
So that's the inside.

00:09:39.320 --> 00:09:41.460
Kind of from the other wall.

00:09:41.460 --> 00:09:44.390
This is the floor of the inside
of the container and

00:09:44.390 --> 00:09:45.980
then there would be
another up here.

00:09:45.980 --> 00:09:48.460
But I think you get the idea.

00:09:48.460 --> 00:09:51.360
The carton is filled to capacity
with k identical

00:09:51.360 --> 00:09:55.290
cylindrical cans of fruit that
stand upright in rows and

00:09:55.290 --> 00:09:57.270
columns as indicated in
the figure above.

00:09:57.270 --> 00:09:57.450
OK.

00:09:57.450 --> 00:09:59.350
So this is like a
top view of it.

00:09:59.350 --> 00:10:04.440
So we could say that this side
up here, this is 48 and then

00:10:04.440 --> 00:10:06.130
this is 32.

00:10:06.130 --> 00:10:09.810
So we don't care so much about
the height, I think.

00:10:09.810 --> 00:10:12.980
So, let's see, the carton is
filled to capacity with k

00:10:12.980 --> 00:10:15.040
identical cylindrical cans of
fruit that stand upright in

00:10:15.040 --> 00:10:16.380
rows and columns as indicated
in figure above.

00:10:16.380 --> 00:10:19.170
If the cans are 15 centimeters
high-- OK, so each of the cans

00:10:19.170 --> 00:10:20.910
are exactly 15 centimeters
high.

00:10:20.910 --> 00:10:23.990
So they literally are exactly
as high as the carton.

00:10:23.990 --> 00:10:28.050
If the cans are 15 centimeters
high, what is the value of k?

00:10:28.050 --> 00:10:32.040
So we have to figure out how
many of these cans will fit in

00:10:32.040 --> 00:10:35.440
this area essentially?

00:10:35.440 --> 00:10:39.520
And then they tell us point
number one: each of the cans

00:10:39.520 --> 00:10:41.850
have a radius of
4 centimeters.

00:10:41.850 --> 00:10:44.350
Radius is 4 centimeters.

00:10:44.350 --> 00:10:46.370
Well, if we know that each of
them have a radius of 4

00:10:46.370 --> 00:10:51.220
centimeters then we know exactly
how much square area

00:10:51.220 --> 00:10:53.240
each of these circles will take
up, assuming that they're

00:10:53.240 --> 00:10:55.680
packed exactly like
this, right?

00:10:55.680 --> 00:10:59.300
Because if you think about it,
what is this area right here?

00:10:59.300 --> 00:11:02.040
Well, there's a bunch of
were different ways you

00:11:02.040 --> 00:11:02.930
could think about it.

00:11:02.930 --> 00:11:06.650
The easiest is that if the
radius is 4 centimeters, that

00:11:06.650 --> 00:11:08.870
the diameter right here
is 8 centimeters.

00:11:08.870 --> 00:11:12.500
So if this is 8 and you have a
48 length, you can only do 6

00:11:12.500 --> 00:11:14.320
of these, right?

00:11:14.320 --> 00:11:16.190
6 times 8 is 48.

00:11:16.190 --> 00:11:18.120
So you can only do 6 that way.

00:11:18.120 --> 00:11:20.970
And then if the diameter is 8
this way and this length is

00:11:20.970 --> 00:11:23.720
32, you can only
do 4 this way.

00:11:23.720 --> 00:11:28.010
So statement number one, alone,
is enough to figure out

00:11:28.010 --> 00:11:28.590
how many you can put.

00:11:28.590 --> 00:11:29.720
It would actually
be 4 times 6.

00:11:29.720 --> 00:11:33.600
You could put 24, k would be 24
cans that you could fit in.

00:11:33.600 --> 00:11:35.210
So statement one, alone,
is enough.

00:11:35.210 --> 00:11:37.280
Now what does statement
two tell us?

00:11:37.280 --> 00:11:40.830
6 of the cans sit exactly
along the

00:11:40.830 --> 00:11:43.565
length of the carton.

00:11:47.930 --> 00:11:52.020
So they're telling us that these
cans, there's 6 cans

00:11:52.020 --> 00:11:53.940
that fit right along the length,
which we figured out

00:11:53.940 --> 00:11:55.230
from statement number one.

00:11:55.230 --> 00:11:58.140
But that also gives you the same
information as statement

00:11:58.140 --> 00:11:58.580
number one.

00:11:58.580 --> 00:12:03.420
Because you know that these
are cylindrical cans.

00:12:03.420 --> 00:12:07.295
I think it's a safe assumption
to say that these are circles.

00:12:09.940 --> 00:12:10.260
Yeah.

00:12:10.260 --> 00:12:12.860
A cylinder, you're assuming
that the tops are circles.

00:12:12.860 --> 00:12:15.700
So if you say that 6 can fit
that way, then you know that

00:12:15.700 --> 00:12:18.090
the diameter of each of them is
8 centimeters and then you

00:12:18.090 --> 00:12:20.620
can make the same argument
that the diameter's 8

00:12:20.620 --> 00:12:23.650
centimeters to say that 4 can
fit the other way down.

00:12:23.650 --> 00:12:30.080
So two, alone, is also
sufficient by itself.

00:12:30.080 --> 00:12:32.360
So the answer is,
what is that, C?

00:12:32.360 --> 00:12:36.030
Both statements-- no D, each
statement, alone, is

00:12:36.030 --> 00:12:37.420
sufficient.

00:12:37.420 --> 00:12:39.270
See you in the next video.


GMAT: Data sufficiency 5

WEBVTT
Kind: captions
Language: en

00:00:00.860 --> 00:00:04.520
We are on problem number 22.

00:00:04.520 --> 00:00:06.900
And their question is
straightforward enough.

00:00:06.900 --> 00:00:08.920
What is the value of
the integer x?

00:00:08.920 --> 00:00:10.800
And they tells us
it's an integer.

00:00:10.800 --> 00:00:12.490
x is equal to what?

00:00:12.490 --> 00:00:16.270
So the first statement,
x is prime.

00:00:16.270 --> 00:00:17.360
Well, there are a lot
of prime integers.

00:00:17.360 --> 00:00:19.740
There's actually an infinite
number of them.

00:00:19.740 --> 00:00:23.300
So that alone doesn't
tell us what x is.

00:00:23.300 --> 00:00:25.570
Two.

00:00:25.570 --> 00:00:30.400
Let's see, 31 is less than or
equal to x, which is less than

00:00:30.400 --> 00:00:33.040
or equal to 37.

00:00:33.040 --> 00:00:37.330
Well, immediately, this is
useless information because 31

00:00:37.330 --> 00:00:41.330
and 37 are both prime numbers
as far as I can tell, right?

00:00:41.330 --> 00:00:42.750
They're both prime numbers.

00:00:42.750 --> 00:00:45.120
So this means that
x could be 31.

00:00:45.120 --> 00:00:46.430
It could be 37.

00:00:46.430 --> 00:00:48.360
Or let's see, are there any
prime numbers in between?

00:00:48.360 --> 00:00:50.780
32, 33, 34, 35.

00:00:50.780 --> 00:00:52.000
Well, there are no prime numbers
in between, but it

00:00:52.000 --> 00:00:56.190
could be either 31 or 37, so it
doesn't help us much even

00:00:56.190 --> 00:00:57.620
used in combination.

00:00:57.620 --> 00:00:59.740
I mean, this alone is definitely
useless, because

00:00:59.740 --> 00:01:01.550
this is a range of
six numbers.

00:01:01.550 --> 00:01:04.030
And even if we know x is prime,
if we use this and

00:01:04.030 --> 00:01:07.920
this, all we know is that
x is either 31 or 37, so

00:01:07.920 --> 00:01:11.060
the answer is E.

00:01:11.060 --> 00:01:15.860
Together, they're not
sufficient, E

00:01:15.860 --> 00:01:20.910
Now, if this was a little bit
different, if this was x is

00:01:20.910 --> 00:01:24.470
greater than 31 and less than or
equal to 37, then we would

00:01:24.470 --> 00:01:26.090
know, oh, x has to be 37.

00:01:26.090 --> 00:01:29.590
Or if this wasn't here and this
was there, then we would

00:01:29.590 --> 00:01:30.880
know that x is 31.

00:01:30.880 --> 00:01:32.140
But anyway, they
didn't do that.

00:01:32.140 --> 00:01:34.790
They gave us the option,
so and the answer is E.

00:01:34.790 --> 00:01:39.990
Problem 23.

00:01:39.990 --> 00:01:44.710
If P, Q and R are three distinct
points, do line

00:01:44.710 --> 00:01:50.660
segments PQ and PR have
the same length?

00:01:50.660 --> 00:01:57.380
So P, Q and R.

00:01:57.380 --> 00:02:00.240
They want to know if these two
lines are the same length.

00:02:00.240 --> 00:02:04.810
This is line PQ and this
is the line PR.

00:02:04.810 --> 00:02:06.680
So are those the same length?

00:02:06.680 --> 00:02:09.180
Let's see if we can
figure this out.

00:02:09.180 --> 00:02:14.320
Statement one tells us
P is the midpoint of

00:02:14.320 --> 00:02:16.200
line segment QR.

00:02:16.200 --> 00:02:20.240
OK, P, midpoint, so I've
already drawn it wrong.

00:02:20.240 --> 00:02:25.970
Midpoint of QR.

00:02:25.970 --> 00:02:30.830
So let me redraw it, so all
three points actually end up

00:02:30.830 --> 00:02:32.240
being on the same line,
because P is

00:02:32.240 --> 00:02:33.400
the midpoint of QR.

00:02:33.400 --> 00:02:34.650
So this is the line.

00:02:38.640 --> 00:02:40.860
This is point Q.

00:02:40.860 --> 00:02:43.480
This is point R.

00:02:43.480 --> 00:02:47.720
So if P is the midpoint, P is
right there, and that tells us

00:02:47.720 --> 00:02:50.820
that this distance is the same
as this distance, which also

00:02:50.820 --> 00:02:59.290
tells us that QP, line segment
QP is equal to PR.

00:02:59.290 --> 00:03:01.630
And that's what I think what
they wanted us-- yeah, right.

00:03:01.630 --> 00:03:04.020
They want to say does PQ and
PR have same length?

00:03:04.020 --> 00:03:07.410
This is PQ So PQ and
PR definitely

00:03:07.410 --> 00:03:08.540
have the same length.

00:03:08.540 --> 00:03:10.900
So statement one is
definitely true,

00:03:10.900 --> 00:03:11.770
because P is the midpoint.

00:03:11.770 --> 00:03:13.980
Let's see about statement two.

00:03:13.980 --> 00:03:16.140
I mean, statement one implies
that they have to be on the

00:03:16.140 --> 00:03:19.040
same line; otherwise,
P couldn't

00:03:19.040 --> 00:03:19.770
have been the midpoint.

00:03:19.770 --> 00:03:23.590
Let's see if statement
two is interesting.

00:03:23.590 --> 00:03:30.440
Statement two: Q and R lie in
the same circle with center P.

00:03:30.440 --> 00:03:32.520
Interesting.

00:03:32.520 --> 00:03:49.020
So this is saying a circle with
center P, and Q and R

00:03:49.020 --> 00:03:50.650
both lie on this circle.

00:03:50.650 --> 00:03:52.400
So Q could be here.

00:03:52.400 --> 00:03:54.320
I'm just picking two
random points.

00:03:54.320 --> 00:03:57.550
R could be here.

00:03:57.550 --> 00:04:03.280
So we want to know whether
PQ is equal to PR, right?

00:04:03.280 --> 00:04:04.530
That was the question.

00:04:04.530 --> 00:04:07.790
Well, the definition of a circle
is all points that are

00:04:07.790 --> 00:04:09.760
equal distant from P.

00:04:09.760 --> 00:04:12.180
So R has to be the same
distance from P.

00:04:12.180 --> 00:04:16.209
It's going to be one radius of
the circle away from P as Q is

00:04:16.209 --> 00:04:18.529
because they're both on the
circle, and they're all equal

00:04:18.529 --> 00:04:19.820
distance from p.

00:04:19.820 --> 00:04:22.990
So PR is going to
be equal to PQ.

00:04:22.990 --> 00:04:24.510
They're going to be equal
to each other.

00:04:24.510 --> 00:04:27.430
So once again, two alone
is sufficient.

00:04:27.430 --> 00:04:33.440
So the answer is D, each
statement alone is sufficient.

00:04:33.440 --> 00:04:34.310
Problem 24.

00:04:34.310 --> 00:04:35.595
The problems are getting a
little bit more interesting.

00:04:39.190 --> 00:04:42.430
Is the number x between
0.2 and 0.7?

00:04:46.710 --> 00:04:51.320
So if I just write it 0.2 is
less than x, which less than

00:04:51.320 --> 00:04:53.760
0.7, that's what they
want to know.

00:04:53.760 --> 00:05:03.350
Statement one tells us that
560x is less than 280.

00:05:03.350 --> 00:05:06.500
You know you don't even
have to solve this.

00:05:06.500 --> 00:05:07.920
This is a fairly simple
equation.

00:05:07.920 --> 00:05:11.290
You can easily solve for x, and
if you can solve for x,

00:05:11.290 --> 00:05:12.330
you can answer this question.

00:05:12.330 --> 00:05:14.050
So you actually don't have
to go to the trouble.

00:05:14.050 --> 00:05:19.090
If you want to, you can then
just divide both sides by 560,

00:05:19.090 --> 00:05:20.730
but that takes time,
valuable time.

00:05:20.730 --> 00:05:23.356
You're taking the GMAT.

00:05:23.356 --> 00:05:25.410
And that is equal
to 1/2, right?

00:05:25.410 --> 00:05:28.820
28/56 is 1/2.

00:05:28.820 --> 00:05:33.050
And then you'd say, sure, x is
between the two numbers.

00:05:33.050 --> 00:05:34.180
But you didn't have
to do this.

00:05:34.180 --> 00:05:36.430
That's a waste of time.

00:05:36.430 --> 00:05:38.690
All you have to do say, oh, I
can solve for x, so I can test

00:05:38.690 --> 00:05:42.170
that, whether that's
true or not.

00:05:42.170 --> 00:05:47.120
Statement two says 700x
is equal to 280.

00:05:47.120 --> 00:05:47.710
Same thing.

00:05:47.710 --> 00:05:48.230
You just look at it.

00:05:48.230 --> 00:05:49.550
You're like, oh, I could
solve for x.

00:05:49.550 --> 00:05:51.830
If I can solve for x, I can tell
you whether x is between

00:05:51.830 --> 00:05:53.710
those two numbers, and
that's the end of it.

00:05:53.710 --> 00:05:56.310
And you say, oh, each of these
independently are sufficient

00:05:56.310 --> 00:05:57.800
to answer this question.

00:05:57.800 --> 00:06:00.210
But if you wanted to prove it
to yourself and see if this

00:06:00.210 --> 00:06:03.400
question is true or false, you
can just say, well, x is equal

00:06:03.400 --> 00:06:08.790
to 228/700.

00:06:08.790 --> 00:06:16.820
That is equal to 2.28/7.

00:06:16.820 --> 00:06:18.870
That is equal to 0.4.

00:06:18.870 --> 00:06:22.710
I just divide the top and the
bottom by 7, and you get 0.4.

00:06:22.710 --> 00:06:25.270
So once again, it
is between it.

00:06:25.270 --> 00:06:26.300
You answered the question.

00:06:26.300 --> 00:06:27.570
But you remember, the question
doesn't have to be

00:06:27.570 --> 00:06:27.800
affirmative.

00:06:27.800 --> 00:06:30.360
You just have to figure out if
the data is enough to answer

00:06:30.360 --> 00:06:31.940
the question, and we
didn't have to go

00:06:31.940 --> 00:06:33.370
through this and this.

00:06:33.370 --> 00:06:34.690
You could have just looked at
it and said, oh, I can solve

00:06:34.690 --> 00:06:37.440
for x in either way and
then just test it.

00:06:37.440 --> 00:06:44.850
Next, problem 25.

00:06:44.850 --> 00:06:51.390
If i and j are integers,
is i plus j even?

00:06:56.220 --> 00:07:00.680
So statement number one is
that i is less than 10.

00:07:00.680 --> 00:07:02.490
That tells me nothing.

00:07:02.490 --> 00:07:05.720
That to me seems kind
of useless.

00:07:05.720 --> 00:07:11.750
Statement number two
is i is equal to j.

00:07:11.750 --> 00:07:13.040
Well, that's interesting.

00:07:13.040 --> 00:07:15.840
So what's i plus j then
going to be equal to?

00:07:15.840 --> 00:07:18.570
Well, that's the same thing as--
since i is equal to j,

00:07:18.570 --> 00:07:23.010
that's the same thing as j
plus j, which equals 2j.

00:07:23.010 --> 00:07:25.990
Or you could say, if you
substitute j for i, or if you

00:07:25.990 --> 00:07:29.700
substitute i for j, that's the
same thing as i plus i, which

00:07:29.700 --> 00:07:30.535
is equal to 2i.

00:07:30.535 --> 00:07:33.330
In either case, you immediately
see that either of

00:07:33.330 --> 00:07:36.040
these numbers are a multiple of
two and therefore have to

00:07:36.040 --> 00:07:38.300
be even, because i and
j are integers.

00:07:38.300 --> 00:07:42.290
So statement two alone is
sufficient, and statement one

00:07:42.290 --> 00:07:44.230
is useless.

00:07:44.230 --> 00:07:53.880
Problem 26.

00:07:53.880 --> 00:07:59.780
n plus k is equal to m.

00:07:59.780 --> 00:08:01.110
What is the value of k?

00:08:03.950 --> 00:08:08.890
So we could solve for it, if we
could answer this, because

00:08:08.890 --> 00:08:11.350
k is equal to m minus n, and
that would solve our answer.

00:08:11.350 --> 00:08:15.390
Let's see if the statements
give us any help.

00:08:15.390 --> 00:08:18.750
n is equal to 10.

00:08:18.750 --> 00:08:21.470
Well, that'll just tells us that
k is equal to m minus 10.

00:08:21.470 --> 00:08:23.080
It still doesn't tell us
what k is, because we

00:08:23.080 --> 00:08:24.800
don't know what m is.

00:08:24.800 --> 00:08:27.040
Statement number two.

00:08:27.040 --> 00:08:29.750
m plus 10 is equal to n.

00:08:29.750 --> 00:08:31.000
This is interesting.

00:08:36.909 --> 00:08:40.059
So what does this tell us?

00:08:40.059 --> 00:08:43.270
So let's see, if we can figure
out from this statement what m

00:08:43.270 --> 00:08:46.610
minus n is, then we're
in business.

00:08:46.610 --> 00:08:48.310
Let's see, let's subtract
n from both sides.

00:08:48.310 --> 00:08:53.370
You get m minus n plus
10 is equal to 0.

00:08:53.370 --> 00:08:56.850
Subtract 10 from both sides,
you get m minus n is

00:08:56.850 --> 00:08:59.490
equal to minus 10.

00:08:59.490 --> 00:09:02.780
Well, we know that k is
equal to m minus n.

00:09:02.780 --> 00:09:07.840
m minus n is equal to minus
10, so this is equal to k.

00:09:07.840 --> 00:09:12.120
So we solved for k, using just
statement two alone.

00:09:12.120 --> 00:09:14.690
Just statement two alone
is sufficient.

00:09:14.690 --> 00:09:17.460
And statement one is-- I mean,
it kind of gets us halfway,

00:09:17.460 --> 00:09:18.530
but you really don't need it.

00:09:18.530 --> 00:09:22.871
Statement two is all you
need, so that is b.

00:09:22.871 --> 00:09:25.840
Let's see if we have
time for one more.

00:09:25.840 --> 00:09:27.090
Yeah, sure, why not.

00:09:31.180 --> 00:09:33.880
They have drawn a
triangle for us.

00:09:33.880 --> 00:09:35.260
I'll draw it quick and dirty.

00:09:39.290 --> 00:09:40.660
This is angle x.

00:09:40.660 --> 00:09:43.990
This is angle z, and
this is angle y.

00:09:43.990 --> 00:09:47.120
And they want to know is this
triangle equilateral, which

00:09:47.120 --> 00:09:49.620
means are all the sides
equal to each other?

00:09:49.620 --> 00:09:53.560
So statement one tells us
that x is equal to y.

00:09:53.560 --> 00:09:55.720
So we break out a little bit of
our eighth or ninth grade

00:09:55.720 --> 00:09:57.280
geometry here.

00:09:57.280 --> 00:10:00.940
So if x is equal to y, if these
angles are equal to each

00:10:00.940 --> 00:10:05.020
other, what that tells us is
that these sides are equal to

00:10:05.020 --> 00:10:07.260
each other, the corresponding
sides are the same.

00:10:07.260 --> 00:10:09.280
I could actually redraw this
triangle like this.

00:10:09.280 --> 00:10:13.970
Maybe it'll jog those neurons
from ninth grade.

00:10:13.970 --> 00:10:16.230
This is x.

00:10:16.230 --> 00:10:19.240
This is y, and this is z.

00:10:19.240 --> 00:10:20.690
And you could test it out,
if you don't believe me.

00:10:20.690 --> 00:10:22.940
And we've gone over this
in the geometry module.

00:10:22.940 --> 00:10:26.890
If x and y are equal to each
other, then these sides have

00:10:26.890 --> 00:10:27.980
to be equal to each other.

00:10:27.980 --> 00:10:30.120
And you could just try to
imagine drawing a triangle

00:10:30.120 --> 00:10:32.810
that has two base angles equal
to each other and the sides

00:10:32.810 --> 00:10:34.070
are different.

00:10:34.070 --> 00:10:35.170
It would be impossible.

00:10:35.170 --> 00:10:36.300
The sides would have
to be the same.

00:10:36.300 --> 00:10:40.030
This triangle would have to be
at least isosceles and maybe

00:10:40.030 --> 00:10:40.750
equilateral.

00:10:40.750 --> 00:10:43.320
Isosceles is two sides
being the same.

00:10:43.320 --> 00:10:46.540
But that by itself doesn't
tell us that this is an

00:10:46.540 --> 00:10:47.550
equilateral triangle.

00:10:47.550 --> 00:10:49.990
In order for this to be
equilateral, z has to be the

00:10:49.990 --> 00:10:51.590
same as x and y.

00:10:51.590 --> 00:10:52.560
They all have to be.

00:10:52.560 --> 00:10:54.190
And if they're all going to be
the same, they all add up to

00:10:54.190 --> 00:10:56.210
180, they all have
to be 60 degrees.

00:10:56.210 --> 00:10:58.740
So you could have a situation
where x and

00:10:58.740 --> 00:11:01.030
y are both 20 degrees.

00:11:01.030 --> 00:11:05.500
This is 20, this is 20, then
they add up to 40.

00:11:05.500 --> 00:11:09.450
And then z would have to be 140
in which case, we would

00:11:09.450 --> 00:11:12.420
not have an equilateral
triangle, so one alone is not

00:11:12.420 --> 00:11:13.126
sufficient.

00:11:13.126 --> 00:11:15.180
Let's see was statement
two tells us.

00:11:15.180 --> 00:11:22.110
Statement two tells us z
is equal to 60 degrees.

00:11:22.110 --> 00:11:25.900
So that by itself-- so first
of all, we know if we know

00:11:25.900 --> 00:11:28.820
both of these pieces of
information, we are definitely

00:11:28.820 --> 00:11:30.690
dealing with an equilateral
triangle.

00:11:30.690 --> 00:11:31.790
Because think about it.

00:11:31.790 --> 00:11:39.330
If z is 60, and then we use this
information that these

00:11:39.330 --> 00:11:41.530
two are equal to each other,
what do we know?

00:11:41.530 --> 00:11:45.350
If z is 60, then these two added
together have to-- so x

00:11:45.350 --> 00:11:50.060
plus y plus z are going
to be equal to 180.

00:11:50.060 --> 00:11:54.560
If z is 60, then x plus y have
to be equal to-- subtract z

00:11:54.560 --> 00:11:57.820
from both sides, or subtract 60
from both sides-- has to be

00:11:57.820 --> 00:11:59.110
equal to 120.

00:11:59.110 --> 00:12:02.490
And since these are equal to
each other, x and y both would

00:12:02.490 --> 00:12:04.890
have to be equal to
60 degrees, right?

00:12:04.890 --> 00:12:07.840
So if you use both of this
information, all of the angles

00:12:07.840 --> 00:12:10.880
are going to be 60 degrees
and it's eqilateral.

00:12:10.880 --> 00:12:14.340
So we know that definitely
in combination, we

00:12:14.340 --> 00:12:15.810
can figure it out.

00:12:15.810 --> 00:12:17.870
But what about just if
z is equal to 60?

00:12:17.870 --> 00:12:21.655
Well, I can easily draw a
triangle that disproves that.

00:12:21.655 --> 00:12:24.950
So if I have a 0-degree angle
here-- in fact, it might be a

00:12:24.950 --> 00:12:27.960
30-60-90 triangle like you
learned in school, so it could

00:12:27.960 --> 00:12:34.200
be 60 degrees, 30 degrees,
and 90 degrees.

00:12:34.200 --> 00:12:36.760
This could be z.

00:12:36.760 --> 00:12:39.980
And this definitely is not
an equilateral triangle.

00:12:39.980 --> 00:12:43.860
And so if just by z being 60
degrees, in no way are you

00:12:43.860 --> 00:12:45.720
saying that this is definitely
an equilateral triangle.

00:12:45.720 --> 00:12:47.760
You have to have the other
condition that

00:12:47.760 --> 00:12:49.700
x is equal to y.

00:12:49.700 --> 00:12:55.440
And so the answer is, let's
see, C, both statements

00:12:55.440 --> 00:12:58.840
together are sufficient, but
neither statement alone is

00:12:58.840 --> 00:12:59.105
sufficient.

00:12:59.105 --> 00:13:01.370
The answer is C.

00:13:01.370 --> 00:13:03.200
See you in the next video.


GMAT: Data sufficiency 7

WEBVTT
Kind: captions
Language: en

00:00:00.850 --> 00:00:06.095
Problem 33 asks: What distance
did Jane travel?

00:00:11.390 --> 00:00:13.440
What distance did she travel?

00:00:13.440 --> 00:00:14.790
So, one.

00:00:14.790 --> 00:00:26.250
Bill traveled 40 miles in 40
minutes, or essentially a mile

00:00:26.250 --> 00:00:29.980
a minute, which is 60 miles an
hour, whatever, 1 mile a

00:00:29.980 --> 00:00:31.380
minute, right?

00:00:31.380 --> 00:00:32.180
That's what we can figure out.

00:00:32.180 --> 00:00:35.680
1 mile per minute.

00:00:35.680 --> 00:00:38.420
That has no information about
how far did Jane travel.

00:00:38.420 --> 00:00:40.200
It's useless.

00:00:40.200 --> 00:00:41.500
Two.

00:00:41.500 --> 00:00:45.070
Jane traveled at the same
average rate as Bill.

00:00:45.070 --> 00:00:48.590
So that tells that Jane, if she
went at the same average

00:00:48.590 --> 00:00:49.900
rate as Bill, that means
that she also

00:00:49.900 --> 00:00:54.180
went 1 mile per minute.

00:00:54.180 --> 00:00:57.030
But we're not asking for how
fast did Jane travel or what

00:00:57.030 --> 00:00:58.220
was her average rate.

00:00:58.220 --> 00:01:00.700
We're asking for how
far did she travel?

00:01:00.700 --> 00:01:04.110
So with statements one and two
combined, all we know is

00:01:04.110 --> 00:01:06.850
Jane's rate, but we don't know
how long she traveled for.

00:01:06.850 --> 00:01:08.870
So we don't know the distance.

00:01:08.870 --> 00:01:12.310
So the answer is e, that both
statements together are not

00:01:12.310 --> 00:01:12.790
sufficient.

00:01:12.790 --> 00:01:16.800
If statement two told us that
Jane traveled at the same rate

00:01:16.800 --> 00:01:21.440
as Bill and she traveled at that
rate for 10 minutes, then

00:01:21.440 --> 00:01:23.470
we would be able to solve
this problem.

00:01:23.470 --> 00:01:25.910
But it didn't, so even with both
pieces of information, we

00:01:25.910 --> 00:01:28.705
still don't know how far
Jane traveled, only

00:01:28.705 --> 00:01:30.330
how fast she traveled.

00:01:30.330 --> 00:01:31.420
34.

00:01:31.420 --> 00:01:36.760
What number is 15% of x?

00:01:36.760 --> 00:01:42.100
So what we want to
know is 0.15x.

00:01:42.100 --> 00:01:43.910
That's what we're trying
to solve for.

00:01:43.910 --> 00:01:55.530
Statement one tells
us, 18 is 6% of x.

00:01:55.530 --> 00:01:57.580
So you normally wouldn't even
have to solve for it.

00:01:57.580 --> 00:02:00.370
All you know is, by looking
at this statement, you

00:02:00.370 --> 00:02:01.690
can solve for x.

00:02:01.690 --> 00:02:04.390
And if you can solve for x,
then you can just multiply

00:02:04.390 --> 00:02:06.910
that times 0.15, and you'll
have the answer to the

00:02:06.910 --> 00:02:07.920
original statement.

00:02:07.920 --> 00:02:11.750
So you immediately know that
statement one is sufficient.

00:02:11.750 --> 00:02:13.370
If you don't believe
me, you can just

00:02:13.370 --> 00:02:14.510
write this as a equation.

00:02:14.510 --> 00:02:18.940
18 is equal to 6% of x.

00:02:18.940 --> 00:02:20.535
And then you just solve for x.

00:02:20.535 --> 00:02:24.120
So 18 divided by 0.06, and then
multiply it times 0.15,

00:02:24.120 --> 00:02:25.370
and you've got your answer.

00:02:27.690 --> 00:02:30.340
Statement number two.

00:02:30.340 --> 00:02:35.650
2/3 of x is 200.

00:02:35.650 --> 00:02:38.200
Once again, you look at
this, and you say,

00:02:38.200 --> 00:02:39.630
this is a simple equation.

00:02:39.630 --> 00:02:41.120
I could solve for x.

00:02:41.120 --> 00:02:44.010
If I solve for x here, then I
just substitute it back here,

00:02:44.010 --> 00:02:48.450
and I will know what 15% of
x is, and I would be done.

00:02:48.450 --> 00:02:52.100
So each of these statements
individually are sufficient to

00:02:52.100 --> 00:02:59.560
answer our question
what is 15% of x.

00:02:59.560 --> 00:03:00.930
I don't think I've got to go
through the exercise of

00:03:00.930 --> 00:03:02.710
actually solving for that,
because I think you understand

00:03:02.710 --> 00:03:04.460
what I'm talking about.

00:03:04.460 --> 00:03:05.750
35.

00:03:05.750 --> 00:03:06.760
Oh, I like these.

00:03:06.760 --> 00:03:17.550
So they say 3.2 rectangle
triangle, or delta, 6.

00:03:17.550 --> 00:03:20.940
And they say, if rectangle and
delta, or triangle, soon. each

00:03:20.940 --> 00:03:24.560
represent single digits
in the decimal above.

00:03:24.560 --> 00:03:24.820
OK.

00:03:24.820 --> 00:03:25.550
So this is a decimal.

00:03:25.550 --> 00:03:26.860
I thought they might
be operations.

00:03:26.860 --> 00:03:27.630
So this is a decimal.

00:03:27.630 --> 00:03:31.410
So it's four digits behind
the decimal spot.

00:03:31.410 --> 00:03:34.115
What does rectangle represent?

00:03:34.115 --> 00:03:36.910
So we want to know what does
this decimal-- what's the

00:03:36.910 --> 00:03:39.440
digit right here?

00:03:39.440 --> 00:03:43.410
Statement number one tells us,
when the decimal is rounded to

00:03:43.410 --> 00:03:47.480
the nearest tenth, 3.2
is the result.

00:03:47.480 --> 00:03:49.140
The nearest tenth.

00:03:49.140 --> 00:03:51.250
So when you round, what you do
is you look at-- if we're

00:03:51.250 --> 00:03:55.020
rounding to the nearest tenth,
we look at this number, right?

00:03:55.020 --> 00:03:56.360
We look at the rectangle.

00:03:56.360 --> 00:04:01.036
And if the rectangle is 5 or
greater, we would round up, so

00:04:01.036 --> 00:04:02.520
we would get to 3.3.

00:04:02.520 --> 00:04:06.750
If the rectangle is less
than 5, then we would

00:04:06.750 --> 00:04:09.070
round down to 2.

00:04:09.070 --> 00:04:14.880
So statement number one tells
us that rectangle

00:04:14.880 --> 00:04:16.769
is less than 5.

00:04:16.769 --> 00:04:19.220
And we know it's greater
than or equal to 0,

00:04:19.220 --> 00:04:20.040
because it's a digit.

00:04:20.040 --> 00:04:22.650
It's 0, 1, 2, 3, or 4, right?

00:04:22.650 --> 00:04:26.410
So we can say it's
0, 1, 2, 3, or 4.

00:04:26.410 --> 00:04:27.010
That's rectangle.

00:04:27.010 --> 00:04:29.420
But that by itself does not
allow to figure out what

00:04:29.420 --> 00:04:31.040
rectangle is.

00:04:31.040 --> 00:04:37.420
Now statement number two tells
us, when the decimal is

00:04:37.420 --> 00:04:43.940
rounded to the nearest
hundredth, 3.24 is the result.

00:04:43.940 --> 00:04:46.910
3.24 is the result
when you round

00:04:46.910 --> 00:04:50.010
to the nearest hundredth.

00:04:50.010 --> 00:04:50.340
OK.

00:04:50.340 --> 00:04:53.340
So this is interesting.

00:04:53.340 --> 00:04:59.090
So this number here is either
going to be-- so when you're

00:04:59.090 --> 00:05:01.180
rounding to something, it's
either going to be either

00:05:01.180 --> 00:05:02.830
rounding down or rounding up.

00:05:02.830 --> 00:05:07.470
So this tells us-- so this
number right here can either

00:05:07.470 --> 00:05:14.130
be 3-- so we already know, it
can be 0, 1, 2, 3, or 4.

00:05:14.130 --> 00:05:18.060
But which of these numbers when
you round them could be

00:05:18.060 --> 00:05:21.520
rounded up or down to 4?

00:05:21.520 --> 00:05:28.830
Well, this could be
2, 3, 5, right?

00:05:28.830 --> 00:05:30.780
Let me give you one scenario.

00:05:30.780 --> 00:05:40.430
We could have 3.2356, where this
is the rectangle and this

00:05:40.430 --> 00:05:41.660
is triangle.

00:05:41.660 --> 00:05:44.690
So this would round to 3.24.

00:05:44.690 --> 00:05:52.630
You could also have 3.2416.

00:05:52.630 --> 00:05:57.040
where this is the rectangle
and this is the triangle.

00:05:57.040 --> 00:06:00.510
And either of these would
round to 3.24.

00:06:00.510 --> 00:06:04.450
So this tells us essentially
that the rectangle has to be

00:06:04.450 --> 00:06:05.710
either 3 or 4.

00:06:13.010 --> 00:06:16.400
And this tells us that it's
either 0, 1, 2, 3, or 4.

00:06:16.400 --> 00:06:18.670
But even when you use them
individually, they don't tell

00:06:18.670 --> 00:06:20.490
you exactly what the
rectangle is.

00:06:20.490 --> 00:06:22.340
And when you use them together,
you can just narrow

00:06:22.340 --> 00:06:25.380
down to 3 or 4, which just
statement two alone tells you.

00:06:25.380 --> 00:06:27.460
So this actually turns out
that when you use both

00:06:27.460 --> 00:06:30.670
statements together, you still
can't get the answer.

00:06:30.670 --> 00:06:32.810
You'd either need a third term
there, or we would have to

00:06:32.810 --> 00:06:34.490
have a little bit more
information about what the

00:06:34.490 --> 00:06:35.520
triangle is.

00:06:35.520 --> 00:06:41.230
If they told us that the
triangle rounds you up or is

00:06:41.230 --> 00:06:43.590
greater than 5 or less than 5
or something like that, then

00:06:43.590 --> 00:06:46.400
we could figure out what
the rectangle is.

00:06:46.400 --> 00:06:49.220
So they answer here is E, if
I haven't missed something.

00:06:49.220 --> 00:06:52.340
That together, both statements
are not sufficient to answer

00:06:52.340 --> 00:06:53.590
the question.

00:06:55.320 --> 00:06:57.480
36.

00:06:57.480 --> 00:07:01.790
A profit from the sale of a
certain appliance increases,

00:07:01.790 --> 00:07:04.600
though not proportionally with
the number of units sold.

00:07:09.980 --> 00:07:13.950
So it's not-- you know, the
profits do not equal just some

00:07:13.950 --> 00:07:16.150
constant times units.

00:07:16.150 --> 00:07:19.060
It equals maybe some constant
times units squared or

00:07:19.060 --> 00:07:20.910
something like that.

00:07:20.910 --> 00:07:23.290
Did the profit exceed
4 million on

00:07:23.290 --> 00:07:26.360
sales of 380,000 units?

00:07:26.360 --> 00:07:31.440
So is profit greater than
4 million-- this one is

00:07:31.440 --> 00:07:41.080
interesting-- when units
is equal to 380,000?

00:07:41.080 --> 00:07:44.150
Let's see if we can
figure this out.

00:07:44.150 --> 00:07:47.110
So they say that the
profit exceeds 2

00:07:47.110 --> 00:07:50.890
million on sales of 200,000.

00:07:50.890 --> 00:07:56.460
So statement one says profit is
greater than 2 million when

00:07:56.460 --> 00:08:00.890
units is equal to 200,000.

00:08:00.890 --> 00:08:04.760
Now, if they told us that profit
was proportional to

00:08:04.760 --> 00:08:10.150
units, then we could say, oh,
well, if we increase the units

00:08:10.150 --> 00:08:13.790
from 200,000 to 380,000, then
we're not doubling the units.

00:08:13.790 --> 00:08:17.640
So then we can't be-- well, it
still would be ambiguous

00:08:17.640 --> 00:08:19.260
because they're not saying
profit equals 2.

00:08:19.260 --> 00:08:21.560
They're saying that profit is
greater than 2, so this

00:08:21.560 --> 00:08:24.110
actually still doesn't give
me a lot of information.

00:08:24.110 --> 00:08:25.770
Statement number two.

00:08:25.770 --> 00:08:28.170
I'll do it in a different
color.

00:08:28.170 --> 00:08:32.190
Statement number two says the
profit exceeds 5 million on

00:08:32.190 --> 00:08:45.220
sales of 350,000 units.

00:08:45.220 --> 00:08:45.660
OK.

00:08:45.660 --> 00:08:47.390
So this is interesting.

00:08:47.390 --> 00:08:51.550
So this tells us that when units
are 350,000, our profit

00:08:51.550 --> 00:08:54.970
is already greater than 5
million, so they're definitely

00:08:54.970 --> 00:08:56.340
greater than 4 million.

00:08:56.340 --> 00:09:00.580
And notice, they told us that
the profit from the sale of an

00:09:00.580 --> 00:09:03.220
appliance increases, but not
proportionally, with the

00:09:03.220 --> 00:09:04.240
number of units sold.

00:09:04.240 --> 00:09:08.980
So if we made more than 5
million when there are 350,000

00:09:08.980 --> 00:09:13.130
units, we know that when you go
from 350,000 to 380,000, we

00:09:13.130 --> 00:09:15.570
know from the statement of
the problem that the

00:09:15.570 --> 00:09:16.800
profit has to increase.

00:09:16.800 --> 00:09:19.540
We don't know by how much, but
it's going to increase.

00:09:19.540 --> 00:09:21.955
So the profit was already
greater than 5 million.

00:09:21.955 --> 00:09:24.630
It's going to increase
above 5 million.

00:09:24.630 --> 00:09:27.130
So statement two tells us that
the profit is definitely going

00:09:27.130 --> 00:09:28.700
to be above 5 million, so
it's definitely going

00:09:28.700 --> 00:09:30.290
to be above 4 million.

00:09:30.290 --> 00:09:34.350
So statement two alone
is enough.

00:09:34.350 --> 00:09:36.550
And statement one actually
tells us very little

00:09:36.550 --> 00:09:39.420
information because we don't
know how does the profit

00:09:39.420 --> 00:09:42.100
change as you incrementally
add units.

00:09:42.100 --> 00:09:46.040
Maybe every other unit-- maybe
every unit above 200,000 that

00:09:46.040 --> 00:09:48.400
you add, you get, a millionth
of a penny.

00:09:48.400 --> 00:09:49.700
And then it doesn't
tell you anything.

00:09:49.700 --> 00:09:51.340
Or maybe you get a
million pennies.

00:09:51.340 --> 00:09:53.470
So it's very hard to tell.

00:09:53.470 --> 00:09:58.290
Problem number-- actually, I'm
already at 10 minutes.

00:09:58.290 --> 00:09:59.590
Let me do that in
the next video.

00:09:59.590 --> 00:10:00.840
See


GMAT: Data sufficiency 3

WEBVTT
Kind: captions
Language: en

00:00:00.740 --> 00:00:03.680
We're on problem number 10.

00:00:03.680 --> 00:00:06.330
And it says, in a certain class,
one student is to be

00:00:06.330 --> 00:00:08.600
selected at random to read.

00:00:08.600 --> 00:00:12.040
What is the probability
that a boy will read?

00:00:12.040 --> 00:00:12.550
OK.

00:00:12.550 --> 00:00:15.940
So I guess we can assume that
everyone in the class can

00:00:15.940 --> 00:00:18.700
read, because they don't really
talk much about that.

00:00:18.700 --> 00:00:21.580
And I think we can assume that
everyone in the class is

00:00:21.580 --> 00:00:26.030
either a boy or a girl, that
we don't have any third

00:00:26.030 --> 00:00:29.040
genders in this reality.

00:00:29.040 --> 00:00:29.370
OK.

00:00:29.370 --> 00:00:30.130
So what are the statements?

00:00:30.130 --> 00:00:31.690
So we essentially just want to
know, what's the probability

00:00:31.690 --> 00:00:33.710
we pick a boy in the
class, right?

00:00:33.710 --> 00:00:35.850
Whether or not they read is
kind of -- so what's the

00:00:35.850 --> 00:00:37.490
probably that we pick a boy?

00:00:37.490 --> 00:00:39.170
So to figure out whether we're
going to pick a boy, we have

00:00:39.170 --> 00:00:40.790
to know, essentially,
what percentage of

00:00:40.790 --> 00:00:42.080
the class are boys.

00:00:42.080 --> 00:00:45.120
So what are the statements
they give us?

00:00:45.120 --> 00:00:48.200
Statement number one is,
2/3 of the students in

00:00:48.200 --> 00:00:48.950
the class are boys.

00:00:48.950 --> 00:00:50.070
Well, that's just what
I asked for.

00:00:50.070 --> 00:00:52.410
2/3 boys.

00:00:52.410 --> 00:00:54.230
Well, that exactly tells
me the probability

00:00:54.230 --> 00:00:55.050
that I pick a boy.

00:00:55.050 --> 00:00:59.080
It's 2 out of 3, or 66.66
repeating percentage.

00:00:59.080 --> 00:01:00.780
So this alone is enough.

00:01:00.780 --> 00:01:03.740
So let's see if statement
two is at all useful.

00:01:03.740 --> 00:01:04.239
Statement two.

00:01:04.239 --> 00:01:07.090
10 of the students in
the class are girls.

00:01:07.090 --> 00:01:09.800
10 girls.

00:01:09.800 --> 00:01:12.200
Well, this, especially
by itself, is a

00:01:12.200 --> 00:01:13.680
fairly useless statement.

00:01:13.680 --> 00:01:17.400
Because maybe there are 10
girls, maybe there's 0 boys,

00:01:17.400 --> 00:01:19.540
in which case this probability
would be 0.

00:01:19.540 --> 00:01:22.770
Maybe there are 10 girls and
10 boys, in which case this

00:01:22.770 --> 00:01:24.080
would be 50%.

00:01:24.080 --> 00:01:27.700
So 10 girls, by itself, really
doesn't tell us much.

00:01:27.700 --> 00:01:29.660
So in this case, all we
need is statement one.

00:01:29.660 --> 00:01:31.940
And statement two alone
is not sufficient.

00:01:31.940 --> 00:01:33.870
So that is what?

00:01:33.870 --> 00:01:35.540
I always forget these.

00:01:35.540 --> 00:01:37.670
a, statement one alone is
sufficient, but statement two

00:01:37.670 --> 00:01:38.450
is not sufficient.

00:01:38.450 --> 00:01:40.470
That's a.

00:01:40.470 --> 00:01:41.850
Problem 11.

00:01:41.850 --> 00:01:44.930
Let me switch colors to green.

00:01:44.930 --> 00:01:46.880
Problem 11.

00:01:46.880 --> 00:01:56.540
If 5x plus 3y is equal to 17.

00:01:56.540 --> 00:02:00.940
They want to know what x is
equal to. x is equal to what?

00:02:00.940 --> 00:02:02.010
OK.

00:02:02.010 --> 00:02:06.170
The first statement
they give us is, x

00:02:06.170 --> 00:02:07.420
is a positive integer.

00:02:09.889 --> 00:02:12.070
Well, that doesn't
help us solve x.

00:02:12.070 --> 00:02:13.460
I mean, x could be any
positive integer.

00:02:13.460 --> 00:02:15.180
They gave us no constraints
on y.

00:02:15.180 --> 00:02:17.590
So we really could pick x
as any positive integer.

00:02:17.590 --> 00:02:20.030
So that doesn't help
us with that.

00:02:20.030 --> 00:02:23.670
Statement number two is,
y is equal to 4x.

00:02:23.670 --> 00:02:25.410
Well, this is a little
bit more interesting.

00:02:25.410 --> 00:02:27.030
y is equal to 4x.

00:02:27.030 --> 00:02:29.880
Well, here we could substitute
this in for y, and

00:02:29.880 --> 00:02:31.480
then solve for x.

00:02:31.480 --> 00:02:33.040
And remember, in these problems,
you really don't

00:02:33.040 --> 00:02:33.830
have to solve for x.

00:02:33.830 --> 00:02:35.230
You just have to know
that you could.

00:02:35.230 --> 00:02:37.300
So I, immediately just
recognizing it, I could say,

00:02:37.300 --> 00:02:39.200
well, this is all I need
to do to solve for x.

00:02:39.200 --> 00:02:41.340
And just to prove it to
you, let's do it.

00:02:41.340 --> 00:02:43.220
Although you shouldn't have
to do this on the GMAT.

00:02:43.220 --> 00:02:46.820
So 5x plus 3 times y,
where y is equal to

00:02:46.820 --> 00:02:50.130
4x, is equal to 17.

00:02:50.130 --> 00:02:55.590
So you get 5x plus 12x
is equal to 17, or

00:02:55.590 --> 00:02:59.020
17x is equal to 17.

00:02:59.020 --> 00:03:00.630
x is equal to 1.

00:03:00.630 --> 00:03:02.400
So all you needed was
statement two.

00:03:02.400 --> 00:03:04.640
And statement one was
fairly useless.

00:03:04.640 --> 00:03:07.260
So that is b, statement two
alone is sufficient, but

00:03:07.260 --> 00:03:09.570
statement one alone
is not sufficient.

00:03:09.570 --> 00:03:19.160
Problem 12.

00:03:19.160 --> 00:03:27.900
So they're asking whether the
product jkmn equal 1?

00:03:27.900 --> 00:03:29.650
Does that equal 1?

00:03:29.650 --> 00:03:32.250
So the first statement they give
us-- let me scroll down a

00:03:32.250 --> 00:03:39.910
little bit-- the first statement
they give us is, jk

00:03:39.910 --> 00:03:43.836
over mn is equal to 1.

00:03:43.836 --> 00:03:46.020
Let's see, we could do a little
algebraic manipulation.

00:03:46.020 --> 00:03:51.590
Multiply both sides by mn, you
get jk is equal to mn, right?

00:03:51.590 --> 00:03:53.500
I just multiplied both
sides by mn.

00:03:53.500 --> 00:03:55.770
But that really doesn't
help me.

00:03:55.770 --> 00:03:57.180
I mean, that just tells
me that this part is

00:03:57.180 --> 00:03:59.520
equal to this part.

00:03:59.520 --> 00:04:01.710
But it doesn't really tell me
that when you multiply them

00:04:01.710 --> 00:04:02.880
all together, you equal 1.

00:04:02.880 --> 00:04:05.700
Let's see if statement two
is it all helpful.

00:04:05.700 --> 00:04:16.910
Statement two tells us that j is
equal to 1 over k, and m is

00:04:16.910 --> 00:04:19.399
equal to 1 over n.

00:04:19.399 --> 00:04:21.370
So let's see if we could do
some interesting algebraic

00:04:21.370 --> 00:04:21.920
manipulations.

00:04:21.920 --> 00:04:22.230
Let's see.

00:04:22.230 --> 00:04:23.950
Multiply both sides
of this by k.

00:04:23.950 --> 00:04:29.350
You get jk is equal to 1.

00:04:29.350 --> 00:04:30.450
And do the same thing here.

00:04:30.450 --> 00:04:32.180
Multiply both sides times n.

00:04:32.180 --> 00:04:36.080
You get mn is equal to 1.

00:04:36.080 --> 00:04:39.230
Well, this is useful, because
if j times k is equal to 1,

00:04:39.230 --> 00:04:47.560
and m times n is equal to 1-- so
the whole product is going

00:04:47.560 --> 00:04:48.660
to be 1 times 1.

00:04:48.660 --> 00:04:50.640
Well, that's definitely going
to be equal to 1.

00:04:50.640 --> 00:04:53.270
So using just the information in
statement two, we were able

00:04:53.270 --> 00:04:56.510
to verify that j times
k, times m, times

00:04:56.510 --> 00:04:57.750
n is equal to 1.

00:04:57.750 --> 00:04:59.060
So this is all we needed.

00:04:59.060 --> 00:05:00.660
Statement one was
fairly useless.

00:05:00.660 --> 00:05:01.480
So that is what?

00:05:01.480 --> 00:05:04.680
That is b, statement two is
sufficient, and statement one

00:05:04.680 --> 00:05:06.543
alone is not sufficient.

00:05:06.543 --> 00:05:13.670
Let's do problem number 13.

00:05:13.670 --> 00:05:18.060
A certain expressway has exits
J, K, L, and M, in that order.

00:05:18.060 --> 00:05:19.940
All right.

00:05:19.940 --> 00:05:22.310
My guess is that it's going
to be some type of

00:05:22.310 --> 00:05:23.560
a number line problem.

00:05:26.730 --> 00:05:27.097
So let's see.

00:05:27.097 --> 00:05:34.980
The exits J, K, L, and M.

00:05:39.230 --> 00:05:41.140
That's the highway
in that order.

00:05:41.140 --> 00:05:43.220
And then they say, what is
the road distance from

00:05:43.220 --> 00:05:44.990
exit K to exit L.

00:05:44.990 --> 00:05:48.870
So they want to know this
distance right here.

00:05:48.870 --> 00:05:51.130
That's what we have to see, if
we have sufficient data to

00:05:51.130 --> 00:05:52.290
figure out.

00:05:52.290 --> 00:05:54.920
So statement one.

00:05:54.920 --> 00:05:58.870
They tell us the road distance
from exit J to L is 21.

00:05:58.870 --> 00:06:00.540
So we can just write that in.

00:06:00.540 --> 00:06:03.870
So line segment to JL
is equal to 21.

00:06:03.870 --> 00:06:09.320
So that tells us that this
distance right here is 21.

00:06:09.320 --> 00:06:11.730
Well, that by itself-- because
we don't know where K is

00:06:11.730 --> 00:06:14.080
within that 21 miles-- so that
alone doesn't help us.

00:06:14.080 --> 00:06:16.850
Let's see if statement two
helps figure out things.

00:06:16.850 --> 00:06:21.160
The road distance from
K to M is 26.

00:06:21.160 --> 00:06:25.400
K to M is equal to 26.

00:06:25.400 --> 00:06:29.870
So this distance
is equal to 26.

00:06:29.870 --> 00:06:32.270
This doesn't really help us at
all, because if you think

00:06:32.270 --> 00:06:36.800
about it, the distance between
K and M is fixed, right?

00:06:36.800 --> 00:06:40.605
But K could be here, which
would put M here.

00:06:43.910 --> 00:06:46.370
And then, of course, that would
change the KL distance.

00:06:46.370 --> 00:06:49.860
Or K could be really close to
L, which would put M here.

00:06:52.740 --> 00:06:57.140
M is definitely 26 miles, or
whatever it is, 26 kilometers

00:06:57.140 --> 00:06:58.270
further from K.

00:06:58.270 --> 00:06:59.870
So we don't know where K is.

00:06:59.870 --> 00:07:03.400
This second constraint still
doesn't tell us where K is,

00:07:03.400 --> 00:07:05.610
relative to-- is it closer
to J, is it closer

00:07:05.610 --> 00:07:06.970
to L, we don't know.

00:07:06.970 --> 00:07:10.580
So both of them combined
are useless.

00:07:10.580 --> 00:07:12.310
So that is e.

00:07:12.310 --> 00:07:14.350
Problem number 14.

00:07:14.350 --> 00:07:17.270
Unless I missed something.

00:07:17.270 --> 00:07:20.890
Problem number 14.

00:07:20.890 --> 00:07:23.350
Is the integer k
a prime number?

00:07:23.350 --> 00:07:24.600
So k prime.

00:07:29.890 --> 00:07:32.660
So the first statement
they give us, is that

00:07:32.660 --> 00:07:34.890
2k is equal to 6.

00:07:34.890 --> 00:07:36.950
Well, we could just do a
little algebra here.

00:07:36.950 --> 00:07:40.780
Divide both sides by 2, and
we get k is equal to 3.

00:07:40.780 --> 00:07:42.440
And 3 is prime.

00:07:42.440 --> 00:07:43.990
So this is good, that's
all we needed.

00:07:43.990 --> 00:07:44.560
We're done.

00:07:44.560 --> 00:07:45.710
Well, let's see what
two gives us.

00:07:45.710 --> 00:07:47.320
Maybe two also gives us that.

00:07:47.320 --> 00:07:51.650
Let's see, two says that
1 is less than k, which

00:07:51.650 --> 00:07:52.950
is less than 6.

00:07:52.950 --> 00:07:55.220
Well, this is kind of useless,
because this is just telling

00:07:55.220 --> 00:07:59.080
us that k-- we know it's an
integer, because they say, is

00:07:59.080 --> 00:08:01.730
the integer k a prime number?--
but k could be 2, in

00:08:01.730 --> 00:08:04.490
which case it wouldn't be--
well, 2 is prime-- but k could

00:08:04.490 --> 00:08:06.780
be 4, in which case
it's not prime.

00:08:06.780 --> 00:08:08.250
Or it could still be 3,
so we don't know.

00:08:08.250 --> 00:08:10.010
So this is kind of useless.

00:08:10.010 --> 00:08:12.690
So all we need is statement one,
and statement two is not

00:08:12.690 --> 00:08:13.160
sufficient.

00:08:13.160 --> 00:08:16.630
So that's a.

00:08:16.630 --> 00:08:18.375
Problem number 15.

00:08:18.375 --> 00:08:19.625
Let me switch colors.

00:08:23.900 --> 00:08:29.350
OK, so they've drawn some
type of x, y axes.

00:08:29.350 --> 00:08:32.280
That's the y-axis.

00:08:32.280 --> 00:08:33.809
That's is the x-axis.

00:08:36.789 --> 00:08:38.039
All right.

00:08:40.486 --> 00:08:46.250
x, y, and then they have
this, they drew 1, 1.

00:08:46.250 --> 00:08:49.460
And then they labeled the
quadrants, quadrant I,

00:08:49.460 --> 00:08:53.080
quadrant II, quadrant III.

00:08:53.080 --> 00:08:54.970
We're doing roman numerals.

00:08:54.970 --> 00:08:58.740
And they say quadrant IV.

00:08:58.740 --> 00:09:02.620
And they say if ab
does not equal 0.

00:09:02.620 --> 00:09:06.870
So a times b does not equal 0,
which essentially tells us

00:09:06.870 --> 00:09:11.700
that neither a or b-- neither
a nor b-- is 0.

00:09:11.700 --> 00:09:12.090
OK.

00:09:12.090 --> 00:09:14.360
ab does not equal 0.

00:09:14.360 --> 00:09:16.310
In what quadrant of the
coordinate system

00:09:16.310 --> 00:09:19.190
does point a, b lie?

00:09:19.190 --> 00:09:20.890
So they want to know
where a, b is.

00:09:20.890 --> 00:09:23.520
So quadrant of a, b.

00:09:23.520 --> 00:09:23.830
OK.

00:09:23.830 --> 00:09:25.990
Let's look at the data.

00:09:25.990 --> 00:09:26.390
All right.

00:09:26.390 --> 00:09:29.560
So we know a, b-- well, we know
it's not along the axes,

00:09:29.560 --> 00:09:31.610
because if one of these were
0, then we'd be along the

00:09:31.610 --> 00:09:35.370
axes, if either a or b were 0.

00:09:35.370 --> 00:09:44.480
It says, this is interesting,
it says b, a

00:09:44.480 --> 00:09:47.400
is in quadrant IV.

00:09:47.400 --> 00:09:48.470
b, a.

00:09:48.470 --> 00:09:49.370
So this is interesting.

00:09:49.370 --> 00:09:54.230
So quadrant IV tells us what?

00:09:54.230 --> 00:09:55.760
If something is in quadrant
IV-- let me do that in a

00:09:55.760 --> 00:09:56.210
different color.

00:09:56.210 --> 00:09:58.290
This is, I think, the first
interesting problem we've

00:09:58.290 --> 00:09:59.230
encountered.

00:09:59.230 --> 00:10:04.290
Quadrant IV tells us that x is
greater than 0, right, because

00:10:04.290 --> 00:10:05.920
we're in the positive x-axis.

00:10:05.920 --> 00:10:09.720
And tells is that y is less than
0, right, because we're

00:10:09.720 --> 00:10:11.630
in the negative y-axis, right?

00:10:11.630 --> 00:10:12.770
We're here.

00:10:12.770 --> 00:10:16.570
So if b, a is in quadrant IV, in
this case b is playing the

00:10:16.570 --> 00:10:18.590
role of x, right?

00:10:18.590 --> 00:10:20.980
This is the point b, a.

00:10:20.980 --> 00:10:25.140
So that tells us that b has
to be greater than 0.

00:10:25.140 --> 00:10:27.680
b is greater than 0.

00:10:27.680 --> 00:10:29.970
And this is telling us that a,
because it's playing the

00:10:29.970 --> 00:10:33.300
function of the y coordinate
here, a has to be less than 0.

00:10:36.100 --> 00:10:42.290
So if we talk about the point a
comma b, well, now we're in

00:10:42.290 --> 00:10:45.630
a situation where we know
that a is less than 0.

00:10:45.630 --> 00:10:48.680
So we know that x
is less than 0.

00:10:48.680 --> 00:10:51.120
And we know that b is
greater than 0.

00:10:51.120 --> 00:10:52.670
And now b is playing
the y coordinate.

00:10:52.670 --> 00:10:54.410
So we know that y is
greater than 0.

00:10:54.410 --> 00:10:57.160
So if x is less than 0, we're
in the [? plot ?]

00:10:57.160 --> 00:10:59.770
negative x, and y is greater
than 0 over here.

00:10:59.770 --> 00:11:03.930
So a comma b is going to have
to be there some place.

00:11:03.930 --> 00:11:07.090
So statement number one was
all we needed to know that

00:11:07.090 --> 00:11:09.790
it's going to be
in quadrant II.

00:11:09.790 --> 00:11:11.220
So statement number
one is good.

00:11:11.220 --> 00:11:14.990
Now let's take a look at
statement number two.

00:11:14.990 --> 00:11:16.650
Well, statement number two is
kind of the same thing.

00:11:16.650 --> 00:11:18.210
So we actually don't even
have to work it out.

00:11:18.210 --> 00:11:20.770
That statement two alone is
also sufficient, just

00:11:20.770 --> 00:11:23.385
eyeballing it, but let
me work it out.

00:11:23.385 --> 00:11:26.320
But we can apply the
exact same logic.

00:11:26.320 --> 00:11:35.160
Statement two says a comma
minus b in quadrant III.

00:11:35.160 --> 00:11:41.040
Well, if we're in quadrant III,
that means that x is less

00:11:41.040 --> 00:11:42.280
than 0, right?

00:11:42.280 --> 00:11:44.370
And a plays the x role.

00:11:44.370 --> 00:11:48.350
So this tells us that
a is less than 0.

00:11:48.350 --> 00:11:52.530
And quadrant III tells us that
y is also less than 0.

00:11:52.530 --> 00:11:54.610
And the y coordinate
here is minus b.

00:11:54.610 --> 00:11:58.240
So it tells us that minus
b is less than 0.

00:11:58.240 --> 00:12:02.410
This point is minus b, so minus
b has to be less than 0,

00:12:02.410 --> 00:12:04.240
which tells us-- you can
multiply both sides by

00:12:04.240 --> 00:12:06.270
negative 1, or divide-- and
that tells us that b is

00:12:06.270 --> 00:12:07.640
greater than 0.

00:12:07.640 --> 00:12:10.300
So you get the same information
from statement two

00:12:10.300 --> 00:12:13.000
as you get from statement one,
that a is less than 0, and b

00:12:13.000 --> 00:12:13.890
as greater than 0.

00:12:13.890 --> 00:12:17.250
And then you can use that to
figure out that a, b has to be

00:12:17.250 --> 00:12:18.220
in quadrant II.

00:12:18.220 --> 00:12:21.230
So each of them independently
are sufficient

00:12:21.230 --> 00:12:22.290
to answer the question.

00:12:22.290 --> 00:12:24.270
So the answer is d.

00:12:24.270 --> 00:12:26.250
See you in the next video.