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For a positive integer n, when 12n is divided by 15

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For a positive integer n, when 12n is divided by 15

by NandishSS » Thu Jul 27, 2017 5:11 am

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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

OA: C

Used brute force method, saw multiple of 12 and found that only ans is 5. Any other method?

Source:MathRevolution
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by Jay@ManhattanReview » Thu Jul 27, 2017 5:48 am
NandishSS 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

OA: C

Used brute force method, saw multiple of 12 and found that only ans is 5. Any other method?

Source:MathRevolution
Say the remainder upon diving 12n by 5 is m.

Thus,

12n - m = 15

= m = 12n - 15
= m = 3(4n - 5)

We see that m, the remainder, is a multiple of 3. All the options except option C, 5 is a multiple of 3.

The correct answer: C

Hope this helps!

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by GMATGuruNY » Thu Jul 27, 2017 7:22 am
NandishSS 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
In other words:
12n is equal to a MULTIPLE OF 15 plus a remainder.
Translated into math:
12n = 15a + R
12n - 15a = R
3(4n - 5a) = R.

The resulting equation indicates that R must be a multiple of 3.
Of the 5 answer choices, only C is not divisible by 3.

The correct answer is C.
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by Scott@TargetTestPrep » Mon Aug 14, 2017 1:08 pm
NandishSS 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

OA: C
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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by Matt@VeritasPrep » Fri Aug 18, 2017 2:16 pm
12n / 15 =>

4n/5 =>

(4/5) * n

Since n divides into 5 pieces, we can't have 5 left over. (If this doesn't make sense, imagine I have 10 cookies and 5 friends. Each friend gets 2 cookies and there are 0 left over.)
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