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GRE Math Challenge #94-a = -219 [#permalink]
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Expert's post 00:00

Question Stats: 85% (00:21) correct 14% (00:40) wrong based on 130 sessions
$$a = -219$$

 Quantity A Quantity B $$a^7 + a^{15}$$ $$a^8 + a^{14}$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation
[Reveal] Spoiler: OA

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Sandy
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Last edited by Carcass on 19 Feb 2020, 15:56, edited 2 times in total.
Updated
GRE Instructor Joined: 10 Apr 2015
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Re: GRE Math Challenge #94 [#permalink]
Expert's post
sandy wrote:
a = -219

Quantity A: a^7 + a^15
Quantity B: a^8 + a^14

Two important rules:

ODD exponents preserve the sign of the base.
So, (NEGATIVE)^(ODD integer) = NEGATIVE
and (POSITIVE)^(ODD integer) = POSITIVE

An EVEN exponent always yields a positive result (unless the base = 0)
So, (NEGATIVE)^(EVEN integer) = POSITIVE
and (POSITIVE)^(EVEN integer) = POSITIVE

----------------------------

We're told that the base, a, is NEGATIVE value (it equals -219)
So, applying the above rules, we get:

Quantity A: (negative)^7 + (negative)^15 = NEGATIVE + NEGATIVE = NEGATIVE
Quantity B: (negative)^8 + (negative)^14 = POSITIVE + POSITIVE = POSITIVE

Since a positive number is always greater than a negative number, the correct answer is
[Reveal] Spoiler:
B

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com Intern Joined: 06 Dec 2018
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Re: GRE Math Challenge #94-a = -219 [#permalink]
$$(Negative number)^{odd power}$$ = negative
$$(Negative number)^{even power}$$ = positive

a=-219 means a is negative.

Quantity A will be a sum of two negative terms, hence will be negative
Quantity B will be a sum of two positive terms, hence will be positive

Positive>Negative, Quantity B is always greater. Re: GRE Math Challenge #94-a = -219   [#permalink] 28 Sep 2020, 09:18
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