Data Sufficiency

BTGmoderatorDC wrote:If s and t are two different numbers on the number line, is s + t = 0 ?

(1) Distance between s and 0 is the same as distance between t and 0
(2) 0 is between s and t

OA A

Source: GMAT Prep

Given: s and t are two different numbers on the number line.

=> s ≠ t

Question: Is s + t = 0 ?

Let's take each statement one by one.

(1) Distance between s and 0 is the same as distance between t and 0.

There can be two possibilities:

1. s = t; however, this is not possible since we know that s ≠ t.
2. s = -t => s + t = 0. Sufficient.

(2) 0 is between s and t.

Case 1: Say 0 is at midway between s and t; thus, s = -t => s + t = 0. The answer is Yes.
Case 2: Say 0 is at not midway between s and t; thus, s ≠ -t => s + t ≠ 0. The answer is No.

No unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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Hi All,

We're told that S and T are two DIFFERENT numbers on the number line. We're asked if S + T = 0. This is a YES/NO question and can be solved by TESTing VALUES and a bit of Number Property logic.

1) The distance between S and 0 is the SAME as the distance between T and 0

Since S and T are DIFFERENT numbers, the only way for their respective distances from 0 to be the SAME is if S and T are 'opposites.'

IF....
S = +1, T = -1; the distances from 0 are the same and S+T = (1) + (-1) = 0, so the answer to the question is YES
S = -2, T = +2; the distances from 0 are the same and S+T = (-2) + (+2) = 0, so the answer to the question is YES.
Etc.
The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) 0 is between S and T

With the information in Fact 2, we know that 0 is some point between S and T, but that does NOT necessarily mean the "exact midpoint."

IF...
S = +1, T = -1; then S+T = (1) + (-1) = 0, so the answer to the question is YES
S = +1, T = -2; then S+T = (1) + (-2) = -1, so the answer to the question is NO
Fact 2 is INSUFFICIENT

Final Answer: A

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