If a 0

Question

If a < 0, is b < 0 ?

(1) b/a > 0
(2) a - b > 0

Can someone please explain this?

I understand why Statement 1 is sufficient, but do not understand how Statement 2 is sufficient.

I chose A which is wrong. The correct answer is below.

Bunuel · Answer

If a < 0, is b < 0 ? (1) b/a > 0. This implies that a and b have the same sign. Since it's given that a is negative, then b must be negative too. Sufficient. (2) a - b > 0. Re-arrange: a > b. Given that 0 > a, so 0 > a > b. Sufficient. Answer: D.

nahid78 · Answer

1) B/A> 0. Either both A and B are negative or both are positive. A is Negative then so is B . Sufficient.

2) a - b > 0 = a> b, a is negative so, b is also negative as b is smaller than a. Sufficient

Ans: D

souvonik2k · Answer

a<0 i.e. a is negative. S1 = b/a > 0 therefore, b also must be negative for b/a to be positive. b<0 . Sufficient. S2 = a - b > 0 i.e. a>b (Adding b to both sides, because adding or subtracting variables in both sides of inequalities is allowed, but multiplication or division is not allowed, if we don't know the sign of the variables - Refer to Inequalities theory for more details) Since a<0, b must be <0, because a>b. Sufficient. Answer D.

Phlaryu · Answer

Is it possible on gmat test to divide "0" by any given number (except 0 itself)?

If it is possible, then statement 1 would imply that B can also be "0" and it would not be possible to determine if b<0.

Looking forward to your comments.

Best,
Jakub

Bunuel · Answer

(1) says that b/a > 0, which implies that a and b have the same sign. Since it's given that a is negative, then b must be negative too. Sufficient.

Here b cannot be 0 because if it were then b/a would equal to 0 and not greater than 0.

antoj · Answer

Also ,in the statement 1 you could multiply both side with a and the equation becomes b>0 ,since a is -ve as per the question flip the sign so it becomes b<0.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If a < 0, is b < 0 ? (1) b/a > 0 (2) a - b > 0

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions