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Math Expert V
Joined: 02 Sep 2009
Posts: 56261
If N > 4 and N is a prime number, then what is the remainder when N  [#permalink]

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Difficulty:   5% (low)

Question Stats: 98% (00:43) correct 2% (01:01) wrong based on 62 sessions

### HideShow timer Statistics 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

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Senior Manager  V
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Posts: 426
If N > 4 and N is a prime number, then what is the remainder when N  [#permalink]

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Bunuel wrote:
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

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.
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If N > 4 and N is a prime number, then what is the remainder when N  [#permalink]

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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.

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If N > 4 and N is a prime number, then what is the remainder when N  [#permalink]

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Bunuel wrote:
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

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

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

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Re: If N > 4 and N is a prime number, then what is the remainder when N  [#permalink]

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Bunuel wrote:
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

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
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Re: If N > 4 and N is a prime number, then what is the remainder when N  [#permalink]

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Bunuel wrote:
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

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.
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Re: If N > 4 and N is a prime number, then what is the remainder when N  [#permalink]

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

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Re: If N > 4 and N is a prime number, then what is the remainder when N  [#permalink]

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Bunuel wrote:
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

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.

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Re: If N > 4 and N is a prime number, then what is the remainder when N  [#permalink]

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Bunuel wrote:
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

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

25/6 = 4 remainder 1

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If N > 4 and N is a prime number, then what is the remainder when N   [#permalink] 20 Aug 2018, 11:20
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