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# If a and b are nonzero integers, which of the following must be

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Joined: 26 Jun 2012
Posts: 24
Location: Germany
GMAT 1: 570 Q31 V39
GMAT 2: 710 Q43 V44
If a and b are nonzero integers, which of the following must be [#permalink]

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20 Jul 2013, 09:12
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If a and b are nonzero integers, which of the following must be negative?

A. $$(-a)^{-2b}$$

B. $$(-a)^{-3b}$$

C. $$-(a^{-2b})$$

D. $$-(a^{-3b})$$

E. None of these
[Reveal] Spoiler: OA

Last edited by kingflo on 20 Jul 2013, 09:37, edited 2 times in total.
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Posts: 43898
Re: If a and b are nonzero integers, which of the following must be [#permalink]

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20 Jul 2013, 09:34
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If a and b are nonzero integers, which of the following must be negative?

A. $$(-a)^{-2b}=\frac{1}{(-a)^{2b}}=positive$$.

B. $$(-a)^{-3b}$$ --> may be positive (consider a=1 and b=2) as well as negative (consider a=1 and b=1).

C. $$-(a^{-2b})=-\frac{1}{a^{2b}}=-\frac{1}{positive}=negative$$

D. $$-(a^{-3b})$$ --> may be positive (consider a=-1 and b=1) as well as negative (consider a=1 and b=1).

E. None of these

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Re: If a and b are nonzero integers, which of the following must be [#permalink]

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17 Jan 2018, 15:33
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kingflo wrote:
If a and b are nonzero integers, which of the following must be negative?

A. $$(-a)^{-2b}$$
B. $$(-a)^{-3b}$$
C. $$-(a^{-2b})$$
D. $$-(a^{-3b})$$
E. None of these

IMPORTANT CONCEPT
Rule #1: EVEN powers are always greater than or equal to zero.
So, (POSITIVE value)^(EVEN integer) > 0, and (NEGATIVE value)^(EVEN integer) > 0

So, the correct answer here is C. Here's why:

C) –[a^(-2b)]
Since b is an integer, we know that -2b is an EVEN integer.
So, we get: –[a^(EVEN integer)]
By our rule, a^(EVEN integer) is greater than or equal to zero
Since a is a NON-zero integer, we can conclude that a^(EVEN integer) is GREATER THAN zero
In other words, a^(EVEN integer) is POSITIVE
This means that -[a^(EVEN integer)] is NEGATIVE

[Reveal] Spoiler:
C

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Re: If a and b are nonzero integers, which of the following must be   [#permalink] 17 Jan 2018, 15:33
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# If a and b are nonzero integers, which of the following must be

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