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

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If a and b are integers, is a > b?  [#permalink]

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New post Updated on: 11 Aug 2019, 17:29
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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
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If a and b are integers, is a > b?  [#permalink]

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New post 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

Answer is (C)
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Re: If a and b are integers, is a > b?  [#permalink]

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New post 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

Asked: Is a > b?

(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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