If the remainder is 27 when an integer is divided by 36, then the inte

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. 6
B. 7
C. 8
D. 9
E. 10

Abhineetegi · Answer

@bunuel..some issue with options?

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BrentGMATPrepNow · Answer

As with many Integer Properties questions, we can quickly solve this question by testing a value that satisfies the given information.

If the number leaves a remainder of 27 when divided by 36, the number COULD be 27 (since 27 divided by 36 equals 0 with remainder 27). 
Check the answer choices......
Only answer choice D (9) is a divisor of 27 (which also means 27 is a multiple of 27)

Answer: D

Kshitijvool · Answer

Let the number be N. So,

N = 36K + 27
N = 3 (12K + 9)
N = 9 (4K + 3)

Ans = 9
Among the options provided, the only possible answer is D.

Bunuel · Answer

________________
Fixed. Thank you.

Capakki · Answer

N=36k+27
Also, N= 9(4k+3)

Shows N is surely a multiple of 9. 
Hence D.

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Akp880 · Answer

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. 6
B. 7
C. 8
D. 9
E. 10

Explanation:

let the no. be  I=36Q+27

Clearly it is divisible by 9

Hence D is the correct answer.

Fdambro294 · Answer

Whatever the number is, call it N, when we Divide N by 36 this means:

we can break N into some Integer Q number of groups of 36 ——where 27 will be left over unable to complete another group of 36

Thinking of each 1 Digit as 1 Block:

N will be broken up into Q groups of 36 Blocks:

(Group of 36 blocks)

..... etc

And 27 blocks will be on the Side, unable to complete another (Group of 36) blocks

If you visualize all the blocks scattered on the floor:

We can Sub-Divide EACH (Group of 36) Blocks into:

4 groups of 9 blocks each

And the 27 blocks that were left over can be Divided into 3 groups of 9 blocks each

Therefore, no matter how many groups of 36 blocks we can make (which following the Analogy would be the Quotient) ——- when there is 27 blocks left over (the Remainder)

The original number N will ALWAYS be Divisible by 9

-D-

Formalizing this logic into a Rule:

For every Unique Integer N, we can create an Equation when we divide that N by some Divisor

(N/36) = Q-quotient + (9/36)

N = 36 * Q + 9

—where Q = some Integer——-

The only answer choice that evenly divide the Right Hand Side of the Equation, regardless of the Value of Q, is 9

Thus, N must be Divisible by 9

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chetan2u · Answer

It is too straightforward to not follow the basic formula for remainder, quotient etc. 
D=qx + r 
D=q*36+27=9(4q+3)

So D is a multiple of 9 for sure as q or quotient is always a non negative integer

D

If the remainder is 27 when an integer is divided by 36, then the inte

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If the remainder is 27 when an integer is divided by 36, then the inte

Prep Toolkit

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