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

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Intern
Joined: 20 Oct 2017
Posts: 27
If a < 0, is b < 0 ? (1) b/a > 0 (2) a - b > 0  [#permalink]

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Updated on: 14 Jan 2018, 08:30
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25% (medium)

Question Stats:

70% (01:01) correct 30% (01:09) wrong based on 98 sessions

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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.

Originally posted by kritikalal on 14 Jan 2018, 08:27.
Last edited by Bunuel on 14 Jan 2018, 08:30, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 56257
Re: If a < 0, is b < 0 ? (1) b/a > 0 (2) a - b > 0  [#permalink]

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14 Jan 2018, 08:33
1
kritikalal wrote:
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.

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.

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Re: If a < 0, is b < 0 ? (1) b/a > 0 (2) a - b > 0  [#permalink]

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14 Jan 2018, 08:46
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
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Re: If a < 0, is b < 0 ? (1) b/a > 0 (2) a - b > 0  [#permalink]

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14 Jan 2018, 09:12
kritikalal wrote:
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.

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.
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Joined: 26 Aug 2017
Posts: 3
Re: If a < 0, is b < 0 ? (1) b/a > 0 (2) a - b > 0  [#permalink]

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27 Feb 2018, 10:04
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.

Best,
Jakub
Math Expert
Joined: 02 Sep 2009
Posts: 56257
Re: If a < 0, is b < 0 ? (1) b/a > 0 (2) a - b > 0  [#permalink]

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27 Feb 2018, 10:22
Phlaryu wrote:
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.

Best,
Jakub

(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.
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Re: If a < 0, is b < 0 ? (1) b/a > 0 (2) a - b > 0   [#permalink] 27 Feb 2018, 10:22
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# If a < 0, is b < 0 ? (1) b/a > 0 (2) a - b > 0

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