If N 4 and N is a prime number, then what is the remainder when N

Question

If N > 4 and N is a prime number, then what is the remainder when N^2 is divided by 6?

(A) 0
 (B) 1
 (C) 2
 (D) 3
 (E) 4

Princ · Answer

OA: B

As  N  can be any prime number such that  N>4  , Taking  N =5  and squaring it, we get  N^2=25. 
 \frac{25}{6}  will leave  1  as remainder.

Chethan92 · Answer

All Prime numbers greater than 3 can be expressed in the form of 6k+1 or 6k-1 , where k is a not negative integer.

Let N = 6k+1
N^2 = (6k+1)^2 = 36K^2 + 12K + 1 = 12(3K^2 + K) +1

Since 12(3K^2+K) is exactly divisible by 12 , therefore N^2 when divided by 12 leaves a remainder as 1.

B is the answer

Posted from my mobile device

GMATinsight · Answer

Smart Question:

It can be looked ta in two ways

1) By Properties of Prime numbers Every prime number greater than 3 when divided by 6 leaves remainder either +1 or -1 
i.e. N^2 divided by 6 will eave remainder ( + 1)^2 i.e. +1 hence

Answer: option B

2) Take a value of a few prime numbers greater than 4 
i.e. N may be 5, 7, 11, 13, ... etc
i.e. N^2 may be 25, 49, 121, 169, ... etc

Dividing each of these values of N^2 by 6 leaves remainder 1 hence

Answer: option B

Abhishek009 · Answer

Possible Values of  N = { 5, 7 , 11 , 13..............}

Try with the possible values of  \frac{N^2}{6}  , in each case answer must be 1, Thus answer must be (B) 1

Izzyjolly · Answer

I think the easiest way to solve this qs is number plugging. Since we can't have 2 correct answers at the same time, we just need to pick a number and see which answer choice matches the result.
In this case let N=5 -->  N^2  = 25 --> remainder when 25 is divided by 6 is 1.
Answer B.

hasnain3047 · Answer

if N = 5
then N^2 = 25
25/6 remainder is 1

So Answer is B

KSBGC · Answer

we can plug numbers for N. It's given that N is prime greater than 4.

So, N can be : 5, 7 , 11.

\frac{(5)^2}{6}= 24 + 1

\frac{(7)^2}{6}= 48 + 1

So, in all case we will have a remainder 1.

The best answer is B.

JeffTargetTestPrep · Answer

We can let N = 5, so N^2 = 25, and we have:

25/6 = 4 remainder 1

Answer: B

If N > 4 and N is a prime number, then what is the remainder when N

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions