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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
75% (01:55) correct
25%
(02:15)
wrong
based on 449
sessions
History
Date
Time
Result
Not Attempted Yet
\((3^2+1)(81^2+1)(9^2+1)(3^2−1)=\)
A. \(81^4+1\)
B. \(9^9−1\)
C. \(3^{16}−1\)
D. \(3^{32}−1\)
E. \(3^{96}+1\)
A. \(81^4+1\)
B. \(9^9−1\)
C. \(3^{16}−1\)
D. \(3^{32}−1\)
E. \(3^{96}+1\)
Updated on: 08 Feb 2021, 15:42
Originally posted by BrentGMATPrepNow on 29 Aug 2016, 12:17.
Last edited by BrentGMATPrepNow on 08 Feb 2021, 15:42, edited 2 times in total.
Last edited by BrentGMATPrepNow on 08 Feb 2021, 15:42, edited 2 times in total.
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Bunuel
\((3^2+1)(81^2+1)(9^2+1)(3^2−1)=\)
A. \(81^4+1\)
B. \(9^9−1\)
C. \(3^{16}−1\)
D. \(3^{32}−1\)
E. \(3^{96}+1\)
A. \(81^4+1\)
B. \(9^9−1\)
C. \(3^{16}−1\)
D. \(3^{32}−1\)
E. \(3^{96}+1\)
This question tests our ability to recognize a potential difference of squares.
That is: (a + b)(a - b) = a² - b²
(3² + 1)(81² + 1)(9² + 1)(3² − 1) = (3² + 1)(3² − 1)(9² + 1)(81² + 1)
= (9 + 1)(9 − 1)(9² + 1)(81² + 1)
= (9² − 1)(9² + 1)(81² + 1)
= (81 - 1)(81 + 1)(81² + 1)
= (81² - 1)(81² + 1)
= 81⁴ - 1
Check the answer choices......81⁴ - 1 is not among the answer choices. We'll have to REWRITE our answer...
81⁴ - 1 = (3⁴)⁴ - 1
= 3¹⁶ - 1
Answer: C
General Discussion
Senthil1981
Joined: 23 Apr 2015
Last visit: 14 Oct 2021
Posts: 230
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Given Kudos: 36
Location: United States
Concentration: General Management, International Business
Schools: Booth PT '19 Ross Weekend"19
WE:Engineering (Consulting)
29 Aug 2016, 04:11
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Bunuel
(3^2+1)(81^2+1)(9^2+1)(3^2−1)=
A. 81^4+1
B. 9^9−1
C. 3^16−1
D. 3^32−1
E. 3^96+1
A. 81^4+1
B. 9^9−1
C. 3^16−1
D. 3^32−1
E. 3^96+1
(3^2+1)(81^2+1)(9^2+1)(3^2−1)=(81^2+1)(9^2+1)(9^2−1)=(81^2+1)(9^4-1)=(81^2+1)(81^2-1) = (81^4-1)
Answer is A
