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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For a positive integer n, when 12n is divided by 15
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Jay@ManhattanReview
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Say the remainder upon diving 12n by 5 is m.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
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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In other words: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
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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Scott@TargetTestPrep
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When n = 1, 12(1) = 12 and 12/15 has a remainder of 12.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 = 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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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.)
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.)
