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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
Joined: 16 Aug 2015
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For a positive integer n, when 12n is divided by 15, which of the foll  [#permalink]

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11 May 2017, 01:27
1
9
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Difficulty:

15% (low)

Question Stats:

81% (01:21) correct 19% (01:20) wrong based on 98 sessions

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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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Retired Moderator Status: Long way to go! Joined: 10 Oct 2016 Posts: 1346 Location: Viet Nam Re: For a positive integer n, when 12n is divided by 15, which of the foll [#permalink] ### Show Tags 11 May 2017, 01:35 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 $$\frac{12n}{15}=\frac{15n-3n}{15}=\frac{-3n}{15}$$ Hence, the remainder must be divisible by 3. Hence, 5 cannot be the remainder. The answer is C _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7468 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: For a positive integer n, when 12n is divided by 15, which of the foll [#permalink] ### Show Tags 14 May 2017, 18:33 ==>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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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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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20 Dec 2017, 12:30
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.

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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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05 Feb 2019, 21:23
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

for a divisor 15 to leave a remainder of 5,
the dividend must have a units digit of 5 or 0
multiples of 12 do not have units digits of 5,
and any multiple of 12 ending in 0 is also
a multiple of 15, leaving a remainder of 0
C
Re: For a positive integer n, when 12n is divided by 15, which of the foll   [#permalink] 05 Feb 2019, 21:23
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