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10 May 2023, 01:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
50% (02:06) correct
50%
(02:30)
wrong
based on 247
sessions
History
Date
Time
Result
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What is the remainder when \(11^{704}\) is divided by 17 ?
A. 1
B. 5
C. 6
D. 11
E. 13
A. 1
B. 5
C. 6
D. 11
E. 13
10 May 2023, 05:33
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Bunuel
Remainder (\(\frac{11^{704} }{ 17}\))
Remainder (\(\frac{(-6)^{704} }{ 17}\))
Remainder (\(\frac{(36)^{352} }{ 17}\))
Remainder (\(\frac{(2)^{352} }{ 17}\))
Remainder (\(\frac{(2)^{4*88} }{ 17}\))
Remainder (\(\frac{16^{88} }{ 17}\))
Remainder (\(\frac{(-1)^{88} }{ 17}\))
\(= 1\)
Option A
10 May 2023, 06:10
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This sum can be done in a couple of ways. There is actually a formula as well but that is out of the purview of GMAT.
We use the remainder of 11/17 to find the remainder for 11^2/17, then we use the remainder of 11^2/17 to find the remainder for 11^3/17, and so on. Until we get a remainder of 1/-1.
Remainder (11/17)=11,
Remainder (11^2/17)=2
.
.
.
Remainder (11^8)/17=-1
704= 8 * 88
Therefore, 11^704=88 (11^8)
Hence the remainder = -1 * -1 * -1... 88 times.
This will give us the remainder = 1
Option A
We use the remainder of 11/17 to find the remainder for 11^2/17, then we use the remainder of 11^2/17 to find the remainder for 11^3/17, and so on. Until we get a remainder of 1/-1.
Remainder (11/17)=11,
Remainder (11^2/17)=2
.
.
.
Remainder (11^8)/17=-1
704= 8 * 88
Therefore, 11^704=88 (11^8)
Hence the remainder = -1 * -1 * -1... 88 times.
This will give us the remainder = 1
Option A
