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OG2016 - If n is a prime number greater than 3

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by boomgoesthegmat » Sun May 01, 2016 9:37 am

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Answers

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B

C

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Difficulty—

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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by Brent@GMATPrepNow » 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

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by OptimusPrep » 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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by [email protected] » Sat Feb 24, 2018 1:19 pm
Hi All,

We're told that N is a PRIME number GREATER than 3. We're asked for the remainder when N^2 is divided by 12. Many questions in the GMAT Quant section can be solved by TESTing VALUES - and this question can be too. In general, you want to choose the 'easiest' value(s) that fit the given situation. You might notice that two of the explanations to this question us N=5 and N=7 - and they both lead to the SAME correct answer. These patterns hold true even when you use a value that isn't the 'easiest' one available. For example...

IF... N=11, then N^2 = (11)^2 = 121
121/12 = 10 r 1

Final Answer: B

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by Scott@TargetTestPrep » Tue Mar 27, 2018 10:42 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
We can let n = 5. Thus n^2 = 25 and 25/12 = 2 R 1.

(Note: Since the answer choices don't have a choice such as "Can't be determined." We can safely say the correct answer must be 1, though we only used one value for n. If we want to make sure further that the answer must be 1, we can use another value for n such as n = 7. We see that n^2 = 49 and 49/12 = 4 R 1. The remainder once again is 1.)

Answer: B

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