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

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Senior Manager
Joined: 30 Sep 2017
Posts: 253
Concentration: Technology, Entrepreneurship
GMAT 1: 720 Q49 V40
GPA: 3.8
WE: Engineering (Real Estate)
If a and b are integers, is a > b?  [#permalink]

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Updated on: 11 Aug 2019, 17:29
3
00:00

Difficulty:

65% (hard)

Question Stats:

48% (01:53) correct 52% (01:45) wrong based on 61 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, 10:05.
Last edited by chondro48 on 11 Aug 2019, 17:29, edited 4 times in total.
Senior Manager
Joined: 30 Sep 2017
Posts: 253
Concentration: Technology, Entrepreneurship
GMAT 1: 720 Q49 V40
GPA: 3.8
WE: Engineering (Real Estate)
If a and b are integers, is a > b?  [#permalink]

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11 Aug 2019, 10:14
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

VP
Joined: 03 Jun 2019
Posts: 1115
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Re: If a and b are integers, is a > b?  [#permalink]

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12 Aug 2019, 22:46
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
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Re: If a and b are integers, is a > b?   [#permalink] 12 Aug 2019, 22:46
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