Problem Solving

Of the four numbers represented on the number line, is r closest to zero?

(1) q = -s
(2) -t < q

Target question: Is r closest to zero?

Statement 1: q = -s
This tells us that q and s are on opposite sides of zero (i.e., one is positive and one is negative) AND it tells us that q and s are the same distance from zero.
So, we get something like this: q.....0.....s
Since r is between points q and s, r must be the closest point to zero
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: -t < q
There are several sets of values that satisfy this condition. Here are two:
Case a: q = -1, r = 0, s = 1 and t = 2, in which case r IS the closest to zero
Case b: q = 0, r = 1, s = 2 and t = 3, in which case r is NOT the closest to zero
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

Hi jmacym,

This question can be solved by TESTing VALUES. Here are some hints and perspective on this prompt (so that you can re-attempt it on your own):

When you choose to TEST VALUES on DS questions, you have to focus on the "thoroughness" of your examples. DS questions often come with "restrictions" that you have to account for and the specific question that is asked often focuses on a specific idea that should help you to further measure the thoroughness of your work.

As a general rule, you want to use small, simple values (-3, -2, -1, 0, 1, 2, 3, etc.)...unless something in the prompt clues you in to do otherwise.

Here, we're first restricted by the picture. Since we're dealing with a number line, we know that Q < R < S < T. 4 variables is A LOT, so you really should focus on simple values. Now, consider the possibilities:

all positive
all negative
0 could be in there
a mix of positives, 0 and negatives is possible

Next, we have the question: "Is R closest to zero?"

If Q, S or T is actually 0, then the answer is NO.
If Q, S or T is closer to 0 than R, then the answer is NO.
If R actually is closer than both Q and S, then we'll know that it's closer than T, so the answer would be YES.

Once you get down to the two Facts, additional restrictions show up. As a general rule, I choose values first for the variables that I know the most about.

In Fact 1, Q = -S

This means that Q and S are OPPOSITES (and neither can be 0). From the number line, we know that Q < S, so Q MUST be negative and S MUST be positive. After making these deductions, what values would YOU choose for Q and S? Now, since R is somewhere between Q and S, what COULD you choose for R?

With enough practice, all of these steps will become natural (and faster). This type of work requires lots of note-taking though, so you should NEVER do this work in your head.

GMAT assassins aren't born, they're made,
Rich