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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] New post 30 Jul 2020, 15:23
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Please help me with this GRE math question.

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

I know the answer is D. 9. But I do not know why. Please help me!
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Re: if the remainder is 27 when an integer is divided by 36 [#permalink] New post 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] New post 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

Final Answer: D
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Re: if the remainder is 27 when an integer is divided by 36 [#permalink] New post 04 Aug 2020, 12:31
Saraforgre wrote:
Please help me with this GRE math question.

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

I know the answer is D. 9. But I do not know why. Please help me!


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

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