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What is the remainder when n2 + 7 is divided by 8, where n is an odd p

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What is the remainder when n2 + 7 is divided by 8, where n is an odd p  [#permalink]

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New post 19 Dec 2018, 10:21
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A
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C
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E

Difficulty:

  5% (low)

Question Stats:

88% (00:39) correct 12% (00:34) wrong based on 90 sessions

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What is the remainder when \(n^2 + 7\) is divided by 8, where n is an odd prime number?

    A. 0
    B. 2
    C. 3
    D. 4
    E. 6

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Re: What is the remainder when n2 + 7 is divided by 8, where n is an odd p  [#permalink]

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New post 19 Dec 2018, 11:26
EgmatQuantExpert wrote:
What is the remainder when \(n^2 + 7\) is divided by 8, where n is an odd prime number?

A. 0
B. 2
C. 3
D. 4
E. 6


let n=3
3^2+7=16
16/8 gives 0 remainder
A
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Re: What is the remainder when n2 + 7 is divided by 8, where n is an odd p  [#permalink]

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New post 20 Dec 2018, 00:30
upon checking relation for n^2+7 ; at n= 1,3,5,7,11.. we can say that the remainder would always be 0

IMO A ..


EgmatQuantExpert wrote:
What is the remainder when \(n^2 + 7\) is divided by 8, where n is an odd prime number?

    A. 0
    B. 2
    C. 3
    D. 4
    E. 6

To read all our articles:Must read articles to reach Q51

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Re: What is the remainder when n2 + 7 is divided by 8, where n is an odd p  [#permalink]

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New post 01 Jan 2019, 21:46

Solution


Given:
We are given that
    • “n” is an odd prime number

To find:
We need to find,
    • The remainder when \(n^2 + 7\) is divided by 8

Approach and Working:
    • If we observe, all the positive integers can be written in the form 4k or + 4k + 1 or 4k + 2 or 4k + 3, where k is a non-negative integer.
      o Out of these, 4k and 4k + 2 cannot be prime numbers, since they are divisible by 2, for any value of k.

    • Thus, all odd prime numbers must be of the form 4k + 1 or 4k + 3

So, \(n^2\) will be \((4k + 1)^2\) or \((4k + 3)^2\)
    • And, \(n^2 + 7\) = \((16k^2 + 8k + 8)\) or \((16k^2 + 24k + 16)\) = \(8(2k^2 + k + 1)\) or \(8(2k^2 + 3k + 2)\)
    • Thus, both these expressions are divisible by 8, for any value of k

Therefore, the remainder is 0

Hence the correct answer is Option A.

Answer: A

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Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
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Re: What is the remainder when n2 + 7 is divided by 8, where n is an odd p &nbs [#permalink] 01 Jan 2019, 21:46
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