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## GMAT

### Course: GMAT > Unit 1

Lesson 2: Data sufficiency- GMAT: Data sufficiency 1
- GMAT: Data sufficiency 2
- GMAT: Data sufficiency 3
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- GMAT: Data sufficiency 5
- GMAT: Data sufficiency 6
- GMAT: Data sufficiency 7
- GMAT: Data sufficiency 8
- GMAT: Data sufficiency 9
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- GMAT: Data sufficiency 21
- GMAT: Data sufficiency 21 (correction)
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# GMAT: Data sufficiency 9

42-46, pg. 281. Created by Sal Khan.

## Want to join the conversation?

- Q46. If X is less than 1/3 (as represented by 0.3333) then the possible answers would be 0, 0.1, 0.2, 0.3. And if X is greater than 1/4 (as represented by 0.25) then the possible answers would be 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. But only one answer is in both sets. 0.3 - Right?(1 vote)
- Putting both statements in play gives us: .25 < x < .33; therefore, x could be .26, .27, .28, .29, .30, .31, .32. This alone shows us that the tenths digit could be either 2 or 3.(1 vote)

## Video transcript

All right, problem 42. So say for the system of
equations given, and this is the system of equations they
give, they say x minus 4 is equal to z. They say y minus x is equal
to 8, and that 8 minus z is equal to t. So they say for the system
equation, what is the value of z? So we're trying to figure
out z in this. Statement number one: they tell
us that x is equal to 7. Well, if we know x is equal to
7, we can solve for z right here because x is 7 and 7 minus
4 is z, so 7 minus 4 is 3, so z is equal to 3. That was pretty straightforward. So one alone is sufficient just
using this first equation in the system. So let's see if two
is of any use. t is equal to 5. Well, this is an
easy one, too. You put t is equal to 5 right
here and then you could easily solve for z, right? You get 8 minus z is equal to
5 and you can solve for it, but I'm not even
going to do it. You just have to know
that you can. So this alone is sufficient
as well. So the answer is D. Each statement alone
is sufficient. Problem 43. Is x equal to 5? In statement number one,
they say x is greater than or equal to 5. Well, that doesn't tell me
whether x is equal to 5. It just says it's
greater than 5. Statement number two tells us x
is less than or equal to 5. Once again, that does not tell
me whether x is 5, but if I told you that both of these are
true, x is greater than or equal 5, and-- not or-- and x
is less than or equal to 5, well, actually, that still--
well, the only x that satisfies that equation,
that satisfies both of these, is 5, right? I mean, you put 3 in, 3 will
not satisfy this one. If you put 7 in, 7 will
not satisfy this one. So the only thing that satisfies
this is 5, so you need both of these. So the answer is both statements
together are sufficient, C. That one's confusing because
it's so simple on some level. 44. The table above shows that
this-- let me see if I can draw this table. And they write R, S T, U,
and R, S, T, and U. They have a bunch of things. I don't even know what
these are yet. I haven't read the question, but
let's see, 0, y, x, 62, y, 0, 56, 75, x, 56, 0, 69. And then 62-- that's a 6--
62, 75, 69, and 0. And what are they
going to ask? They're saying the table above
shows the distance in kilometers by the most direct
route between any two of the four cities. For example, the distance
between city R and city U is 62. Or if you said between U and
R, it's going to be 62 as well, right? That's the same thing. Fair enough. What is the value of x? So the value of x is the
distance between T and R. Let me circle that. They want to know what
the value of x is. It's the distance between T
and R, so it's that one. And another way to look at
distance between T and R, that's this one so,
these are both x. Fair enough. OK. So statement number one tells
us, by the most direct route, the distance between S and T,
so we could say the distance between S and T, I'll just say
it's line segment ST, is equal to twice the distance
between S and R. It's equal to two times SR.
So let's see, do we know what SR is? SR is equal to y, right? And ST is equal to 56. So 56 is equal to 2 times SR.
The distance between S and R is y, so it equals 2y. And so we can solve for y. y is equal to 28. And we didn't have to solve
it, but let's see. I'm just trying to see
where this goes. But that still doesn't help
me figure out the distance between R and T. That just tells me solve
for y. y is 28. Statement number two, see
where this is going. By the most direct route the
distance between T and U is 1.5 times the distance
between R and T. So the distance between R and
T, this is the interesting thing, because R and
T is x, right? So they're saying the distance
between T and U is equal to 1.5 times x. And what's this between
T and U? The distance between T
and U is 69, right? You don't even have
to solve it. You just know that you can
usually solve for x if you know statement number two. So statement number two
alone helps you figure out what x is. Statement number one
is fairly useless. So the answer is B. Statement two alone
is sufficient. Let me draw a line here. I don't want to-- OK, problem number 45. What is the value of the
two-digit integer x? So 2-dig integer x equals,
who knows? All right. Statement number one: The sum
of the two digits is 3. So let's that x is equal to the
number AB where this is the tens digits and this
is the ones digit. So statement number one says the
sum of the two digits is 3, so A plus B is equal to 3. Well, that doesn't help us. There's a lot of-- well, you
know that these are going to be positive numbers, but we
don't know whether they're two different numbers. Two: x is divisible by 3. x is divisible at 3. Well, I don't know if you
learned that trick in school, but any number that is divisible
by 3, the sum of their digits are also
divisible by 3. So once again, that just means
that A plus B is equal to some multiple of 3. Well, if you keep adding them,
they eventually add up. So if you had a two
digit number, so this is-- let's see. Let's think. Just A plus B is equal to 3. This could be a couple
of different things. It could be a two-digit
number. It could be 30. It could be 1. It could be 12. It could be 21. I think those are all of the
possibilities that we can have just off of statement
number one. And x is divisible by three,
well, all of these are divisible by 3, so really, both
statements give you no information. So the answer is E, that both
statements combined still give me nothing. But all of these are
possibilities. And actually, this one leads
to many, many more possibilities that x is
divisible by 3 because then you could have things
like-- I don't know. This would have been a
valid number as well. This would actually
give a lot more. This is a little bit
more strict. But anyway, either way, we can't
figure out what x is. It could be 30. It could be 12. It could be 21. It could be anything. All right. Problem 46. What is the tenth digit in the
decimal representation of a certain number? So the tenth, that's the
number right behind the decimal point. So the number-- let's just
call it x-- so statement number one says x is
less than 1/3. And two says that x is
greater than 1/4. So this is enough to figure out
what the tenth digit is. So what's the number that's
less than 1/3? Let me to think of
a couple of them. Well, 1/3 is like 0.333
repeating, so if I just write 0.32 that satisfies one and
it satisfies 2, right? 0.32 is greater than 1/4. But what's another? And then in this case, a tenth
digit would be a 3, but let me try to find another one that
would satisfy these both. Well, let's see, greater than
1/4, what about 0.26? 0.26 is definitely greater than
1/4 and is definitely less than 1/3, but both of these
have different tens. One has a 2, one
has a 3 there. So even both statements combined
still do not allow me to solve the problem. There's not enough information
given. So once again, E, together I'm
still not getting enough information. Oh, I'm almost at 10 minutes. Anyway, I'll see you
in the next video.