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Director  V
Joined: 30 Sep 2017
Posts: 969
GMAT 1: 720 Q49 V40 GPA: 3.8
If a and b are integers, is a > b?  [#permalink]

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3 00:00

Difficulty:   75% (hard)

Question Stats: 45% (01:57) correct 55% (01:47) wrong based on 66 sessions

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If a and b are non-zero integers, is a > b?
(1) a - $$\frac{b}{2}$$ > 0
(2) $$b^a < 0$$

Source: modified from GMAT OG

Originally posted by chondro48 on 11 Aug 2019, 09:05.
Last edited by chondro48 on 11 Aug 2019, 16:29, edited 4 times in total.
Director  V
Joined: 30 Sep 2017
Posts: 969
GMAT 1: 720 Q49 V40 GPA: 3.8
If a and b are integers, is a > b?  [#permalink]

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Is a>b ?

(1) a - 0.5b > 0
--> a> 0.5b
ie. a=3, b=3, a> 0.5b but a=b
ie. a=3, b=-3, a> 0.5b and a>b
Not Sufficient

(2) $$b^a < 0$$
Given this statement, then b is negative. Let's analyze
ie. a=3, b=-3, $$(-3)^3 < 0$$ and a>b
ie. a=-3, b=-3, $$(-3)^{-3} < 0$$ but a = b
Not Sufficient

Combining (1) and (2),
We know b<0 and a>0.5b, then a must be less negative than b. In other words, it must be true that a>b

CEO  V
Joined: 03 Jun 2019
Posts: 3255
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
Re: If a and b are integers, is a > b?  [#permalink]

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chondro48 wrote:
If a and b are non-zero integers, is a > b?
(1) a - $$\frac{b}{2}$$ > 0
(2) $$b^a < 0$$

Source: modified from GMAT OG

Given: a and b are non-zero integers

(1) a - $$\frac{b}{2}$$ > 0
a>b/2
but it is not certain that b/2>b
NOT SUFFICIENT

(2) $$b^a < 0 b<0 But we don't know about whether a>b NOT SUFFICIENT Combining (1) & (2) (1) a - [m]\frac{b}{2}$$ > 0
a>b/2
(2) [m]b^a < 0
b<0
Since b<0 0>b/2>b
a>b/2>b
a>b
SUFFICIENT

IMO C
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com Re: If a and b are integers, is a > b?   [#permalink] 12 Aug 2019, 21:46

# If a and b are integers, is a > b?  