Solutions

Get detailed explanations to advanced GMAT questions.



Question

If a, b, c are three numbers on the number line shown above, is c between a and b.

I. b < 0

II. a – b > c


 

Option A:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Option B:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Option C:

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Option D:

EACH statement ALONE is sufficient to answer the question asked.

Option E:

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Difficulty Level

Hard

Solution

Option E is the correct answer.


Option Analysis

Probably the best way to solve this problem is to pick some smart numbers. Notice that from the diagram we have that a<b

Statement I is insufficient: b<0. Clearly insufficient since we know nothing about c.

Statement II is insufficient: a-b>c. If a=−10 and b=−1, then −10−(−1)=−9>c. Now, is c=−9.5, then the answer is YES but if c=−100, then the answer is NO. Not sufficient.

Together I and II, Example from (2) is still valid, so even when we consider the two statements together we cannot answer the question. Not sufficient.