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

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

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New post Updated on: 14 Jan 2018, 07:30
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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, 07:27.
Last edited by Bunuel on 14 Jan 2018, 07:30, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If a < 0, is b < 0 ? (1) b/a > 0 (2) a - b > 0  [#permalink]

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New post 14 Jan 2018, 07:33
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.

Answer: 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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New post 14 Jan 2018, 07:46
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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New post 14 Jan 2018, 08:12
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.
Answer 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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New post 27 Feb 2018, 09:04
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.

Looking forward to your comments.

Best,
Jakub
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Joined: 02 Sep 2009
Posts: 51188
Re: If a < 0, is b < 0 ? (1) b/a > 0 (2) a - b > 0  [#permalink]

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New post 27 Feb 2018, 09:22
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.

Looking forward to your comments.

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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: If a < 0, is b < 0 ? (1) b/a > 0 (2) a - b > 0 &nbs [#permalink] 27 Feb 2018, 09:22
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