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For a positive integer n, when 12n is divided by 15, which of the foll

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Math Revolution GMAT Instructor
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For a positive integer n, when 12n is divided by 15, which of the foll  [#permalink]

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New post 11 May 2017, 00:27
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A
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C
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For a positive integer n, when 12n is divided by 15, which of the following cannot be the remainder?

A. 0
B. 3
C. 5
D. 6
E. 9

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Re: For a positive integer n, when 12n is divided by 15, which of the foll  [#permalink]

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New post 11 May 2017, 00:35
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MathRevolution wrote:
For a positive integer n, when 12n is divided by 15, which of the following cannot be the remainder?

A. 0
B. 3
C. 5
D. 6
E. 9


\(\frac{12n}{15}=\frac{15n-3n}{15}=\frac{-3n}{15}\)

Hence, the remainder must be divisible by 3. Hence, 5 cannot be the remainder. The answer is C
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Re: For a positive integer n, when 12n is divided by 15, which of the foll  [#permalink]

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New post 14 May 2017, 17:33
==>From 12n=15Q+r, 12 and 15 are the multiples of 3, so remainder=r must also be the multiple of 3. Therefore, 5 cannot be the remainder.

The answer is C.
Answer: C
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Re: For a positive integer n, when 12n is divided by 15, which of the foll  [#permalink]

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New post 20 Dec 2017, 11:30
1
MathRevolution wrote:
For a positive integer n, when 12n is divided by 15, which of the following cannot be the remainder?

A. 0
B. 3
C. 5
D. 6
E. 9


When n = 1, 12(1) = 12 and 12/15 has a remainder of 12.

When n = 2, 12(2) = 24 and 24/15 has a remainder of 9.

When n = 3, 12(3) = 36 and 36/15 has a remainder of 6.

When n = 4, 12(4) = 48 and 48/15 has a remainder of 3.

When n = 5, 12(5) = 60 and 60/15 has a remainder of 0.

If we look at the given answer choices, we see that possible remainders of 12n/15 include 0, 3, 6, and 9, but don’t include 5, so 5 cannot be the remainder when 12n is divided by 15.

Answer: C
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Re: For a positive integer n, when 12n is divided by 15, which of the foll &nbs [#permalink] 20 Dec 2017, 11:30
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For a positive integer n, when 12n is divided by 15, which of the foll

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