Data Sufficiency

Hi,

Please explain the logic to solve this question!

Im not clear how it is A?

This is a number line, magnitude problem.

Remember: On a yes/no DS question, you don't need a yes answer. You only need a definitive yes or no.

It looks like the diagram doesn't provide any information. But it provides a lot of information:

q>r>s>t and all the numbers are real numbers. If they weren't real numbers, a number line couldn't represent them.

Anticipate the info needed to answer the question:

The location of 0 and the magnitudes (absolute values) of r, s and q.
Some relationship between numbers that could relate their values.


Evaluate 1. q=-s.

That means |q| = |s| - they are both the same distance from 0.

s is positive and q is negative because q<s and they have the same magnitude.

r might be positive, in which case it's closer to 0 than s ...|r| < |s| and therefore |r|<|q|. r is closer to 0 than q or s, and it's closer to 0 than t - t is even further from 0 than s. Yes.

r might be 0, in which case its distance from 0 is 0, so r has to be closest to 0. Yes.

r might be negative, in which case it's closer to 0 than q....|r|<|q| and |r| < |s|. r is closer to 0 than q or s. Yes.

1 is sufficient. Eliminate B, C, E. A and D remain.


Evaluate 2.

-t < q

Case 1. q = -1, r=2, s=3, t=4 .

-t = -4<-1. This fits statement 2.

r is not closest to 0. No.


Case 2. q=-1, r=0, s=1, t=2

-2 < -1. This fits statement 2.

r is closest to 0. Yes.

Statement 2 leads to multiple answers - it's either yes or no. It's wishy washy. Statement 2 isn't sufficient. Eliminate D.

The answer is A.

q, r, s and t must be in the order shown.

Statement 1: q = -s
Case 1: s=1, q=-1
q=-1.....0.....s=1.....t
Here, r must be in the RED PORTION between q and s.
Since the red portion includes 0, r will be closest to 0.

Case 2: s=10, q=-10
q=-10...............0...............s=10.....t
Once again, r must be in the RED PORTION between q and s.
Since the red portion includes 0, r will be closest to 0.

In every case, r will be in the red portion between q and s -- the portion that includes 0.
Thus, r will always be closest to 0.
SUFFICIENT.

Statement 2: -t < q
If t=10, then q>-10.
Thus, the number line could look like this:
q=-9...........r..........s............t=10.
No way to determine whether r or s is closest to 0.
INSUFFICIENT.

The correct answer is A.