GMAT Prep Question Pack 1 DS If a, b, and c are three numbe

[richachampion]

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

1) b<0
2) a-b > c

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Hi richachampion,

This question can be solved by TESTing VALUES. To start though, it's important to note that we don't know the 'relative scale' of this number line. A and B might be 'close together' or 'far apart.' We also don't know if the three variables (A, B and C) are integers or not. We DO know that B is GREATER than A though (since it's farther right on the number line).

We're asked if C is between A and B. This is a YES/NO question.

1) B < 0

This Fact tells us that B is NEGATIVE (so A must ALSO be negative - since it's farther to the left than B is). However, we don't know anything about C.
Fact 1 is INSUFFICIENT

2) (A - B) > C

IF....
A = -2 and B = -1, then (A-B) = -1.... and -1 > C....

IF....
C = -1.5, then the answer to the question is YES
C = -3, then the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, the two TESTs that I used in Fact 2 fit both Facts and provide different answers to the question (one YES and one NO).
Combined, INSUFFICIENT

Final Answer: E

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

[richachampion]

I have a new learning while solving this question.

Statement 1 alone is not sufficient.

Let us discuss the statement 2 and statement 1 + statement 2.

A finding →

a-b will always lie between a and b irrespective of the sign of a and b.

Precisely, this one →

a-b = - |a-b|

a-b > c doesn't tell anything. That means statement 2 is also discarded.

The combination of statement 1 and statement 2 only tells that we are now dealing with the negative axis, but still, the statement 2 is valid and hence we can't infer whether "C" lies between a and b or away from "a" on the negative axis.

[Brent@GMATPrepNow]

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

1) b < 0
2) a - b > c

Target question: is c between a and b?

Statement 1: b < 0
No information about c, so statement 1 is NOT SUFFICIENT

Statement 2: a - b > c
There are several sets of numbers that meet this condition. Here are two:
Case a: a = -3, b = -1 and c = -2.5 in which case c is between a and b
Case b: a = -3, b = -1 and c = -5 in which case c is not between a and b
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
There are still several sets of numbers that meet this condition. Here are two:
Case a: a = -3, b = -1 and c = -2.5 in which case c is between a and b
Case b: a = -3, b = -1 and c = -5 in which case c is not between a and b
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent