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If 108 is a factor of N2 then which of the following could be the rema
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12 Jul 2023, 00:55
12 Jul 2023, 00:55
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If 108 is a factor of \(N^2\) then which of the following could be the remainder when integer N is divided by 36?
Indicate all that apply
A. 0
B. 6
C. 18
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
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Indicate all that apply
A. 0
B. 6
C. 18
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE NUMBER PROPERTIES
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Re: If 108 is a factor of N2 then which of the following could be the rema
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15 Jul 2023, 03:26
15 Jul 2023, 03:26
1
Given that 108 is a factor of \(N^2\) and we need to find which of the following could be the remainder when integer N is divided by 36?
108 is a factor of \(N^2\)
=> \(N^2\) is a multiple of 108
108 = \(2^2 * 3^3\)
=> \(N^2\) is a multiple of \(2^2 * 3^3\)
Making \(2^2 * 3^3\) close to the next even power (\(2^2 * 3^4\))
=> \(N^2\) = \(2^2 * 3^4\) * \(k^2\) (where k is an integer)
=> N = \(2*3^2\)k = 18k
=> N can be
18*0 = 0
18*1 = 18
18*2 = 36
and so on
=> 0/36 remainder is 0
=> 18/36 remainder is 18
=> 36/36 remainder is 0
=> Possible values of remainders are 0 and 18
So, Answer will be A and C
Hope it helps!
Watch the following video to learn the Basics of Factors and Multiples
108 is a factor of \(N^2\)
=> \(N^2\) is a multiple of 108
108 = \(2^2 * 3^3\)
=> \(N^2\) is a multiple of \(2^2 * 3^3\)
Making \(2^2 * 3^3\) close to the next even power (\(2^2 * 3^4\))
=> \(N^2\) = \(2^2 * 3^4\) * \(k^2\) (where k is an integer)
=> N = \(2*3^2\)k = 18k
=> N can be
18*0 = 0
18*1 = 18
18*2 = 36
and so on
=> 0/36 remainder is 0
=> 18/36 remainder is 18
=> 36/36 remainder is 0
=> Possible values of remainders are 0 and 18
So, Answer will be A and C
Hope it helps!
Watch the following video to learn the Basics of Factors and Multiples
gmatclubot
Re: If 108 is a factor of N2 then which of the following could be the rema [#permalink]
15 Jul 2023, 03:26
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