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GRE Math Challenge #94-a = -219
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Updated on: 19 Feb 2020, 15:56
Updated on: 19 Feb 2020, 15:56
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Question Stats:
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\(a = -219\)
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
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: GRE Math Challenge #94
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17 May 2015, 16:56
17 May 2015, 16:56
sandy wrote:
a = -219
Quantity A: a^7 + a^15
Quantity B: a^8 + a^14
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
Show: ::
B
Cheers,
Brent
Re: GRE Math Challenge #94-a = -219
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28 Sep 2020, 09:18
28 Sep 2020, 09:18
\((Negative number)^{odd power}\) = 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.
Correct answer is option B.
\((Negative number)^{even power}\) = 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.
Correct answer is option B.
