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OG2016 - If n is a prime number greater than 3

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boomgoesthegmat Senior | Next Rank: 100 Posts Default Avatar
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OG2016 - If n is a prime number greater than 3

Post Sun May 01, 2016 9:37 am
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12?

A) 0
B) 1
C) 2
D) 3
E) 5

OA: B

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OptimusPrep Master | Next Rank: 500 Posts
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Post Mon May 02, 2016 7:32 pm
boomgoesthegmat wrote:
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12?

A) 0
B) 1
C) 2
D) 3
E) 5

OA: B
We can solve this problem by testing values easily.
Assume n = 7, n^2 = 49
Remainder of (49/12) = 1

Another approach: Always remember that any prime number apart from 2 is of the form (6k +- 1)

Assume n = 6k + 1, n^2 = 36k^2 + 12k + 1
Remainder of (n^2/12) = 1

Assume n = 6k - 1, n^2 = 36k^2 - 12k + 1
Remainder of (n^2/12) = 1

Correct option: B

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Top Reply
Post Sun May 01, 2016 9:48 am
boomgoesthegmat wrote:
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12?

A) 0
B) 1
C) 2
D) 3
E) 5

OA: B
A nice fast approach is to TEST a possible value of n. Since n must be a prime number that’s greater than 3, let’s TEST n = 5

If n = 5, then n² = 5² = 25, and when we divide 25 by 12, we get 2 with REMAINDER 1

Answer: B

Cheers,
Brent

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