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(7^21+7^-21)^2
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12 Jan 2023, 07:56
12 Jan 2023, 07:56
Expert Reply
00:00
Question Stats:
58% (00:57) correct
41% (01:48) wrong based on 12 sessions
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Quantity A |
Quantity B |
\([7^{21}+7^{-21}]^2\) |
\([7^{42}+7^{-42}]\) |
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
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Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
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Re: (7^21+7^-21)^2
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14 Jan 2023, 22:39
14 Jan 2023, 22:39
1
Quantity A: \([7^{21}+7^{-21}]^2\)
Using \((a + b)^2 = a^2 + 2ab + b^2\) we get
\([7^{21}+7^{-21}]^2\) = \((7^{21})^2 + 2 * 7^{21} * 7^{-21} + (7^{-21})^2\)
= \(7^{21 *2} + 2 + 7^{-21 *2}\) = \(7^{42}+7^{-42} + 2\)
Clearly, Quantity A = Quantity B + 2
=> Quantity A > Quantity B
So, Answer will be A
Hope it helps!
Watch the following video to learn the Basics of Exponents
Using \((a + b)^2 = a^2 + 2ab + b^2\) we get
\([7^{21}+7^{-21}]^2\) = \((7^{21})^2 + 2 * 7^{21} * 7^{-21} + (7^{-21})^2\)
= \(7^{21 *2} + 2 + 7^{-21 *2}\) = \(7^{42}+7^{-42} + 2\)
Clearly, Quantity A = Quantity B + 2
=> Quantity A > Quantity B
So, Answer will be A
Hope it helps!
Watch the following video to learn the Basics of Exponents
gmatclubot
Re: (7^21+7^-21)^2 [#permalink]
14 Jan 2023, 22:39
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