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# if the remainder is 27 when an integer is divided by 36

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if the remainder is 27 when an integer is divided by 36 [#permalink]  30 Jul 2020, 15:23
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100% (00:17) correct 0% (00:00) wrong based on 5 sessions

if the remainder is 27 when an integer is divided by 36, then the integer must be a multiple of which of the following integer?

A. 8
B. 7
C. 8
D. 9
E. 10

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Re: if the remainder is 27 when an integer is divided by 36 [#permalink]  30 Jul 2020, 23:04
A number is divided by 36, and the remainder is 27. Thus, number should be 36+27= 63.
Now divide this number with the given options, 7 and 9 can divide this option.
Now, try another number which when divided by 36 can give 27 as remainder, 36*2 = 72 + 27 = 99.
Now, only 9 can divide 99 completely. Thus, answer is D
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Re: if the remainder is 27 when an integer is divided by 36 [#permalink]  03 Aug 2020, 04:12
Let y and m be integers

y/36=m+(27/36)
here m is the whole number part of the division and 27 is the remainder

therefore
y=36m+27
y=9(4m+3)

So y is divisible by 9, because 9 is a factor of y

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Re: if the remainder is 27 when an integer is divided by 36 [#permalink]  04 Aug 2020, 12:31
Saraforgre wrote:

if the remainder is 27 when an integer is divided by 36, then the integer must be a multiple of which of the following integer?

A. 8
B. 7
C. 8
D. 9
E. 10

Since the problem states that the solution MUST be divisible by one of the answer choices, we know that it doesn't matter what value of n we use as long as there is a remainder of 27 when it's divided by 36. In that case, why not use the easiest test value of all, n=27? The only choice 27 is divisible by is 9 so the answer is D.

Alternatively, choose any multiple of 36, add 27 and see what it's divisible by.
Re: if the remainder is 27 when an integer is divided by 36   [#permalink] 04 Aug 2020, 12:31
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