If a positive integer n divided by 5 has a remainder 2 which of the following must be true ........

Quantitative Aptitude ( CCS) Number System

If a positive integer n, divided by 5 has a remainder 2, which of the following must be true?

n is odd

n + 1 cannot be a prime number

(n + 2) divided by 7 has remainder 2

n + 3 is divisible by 5

You can find the integers which when divided by 5 have a remainder 2 by adding 2 to all multiples of 5.

So we have n = 7 , 12, 17, 22 etc.

From this series we can see that n does not have to be odd.

Also n + 1 can be a prime because, for example, 12 + 1 = 13

And (n + 2) / 7 has a remainder 2 in some cases but not all.

Remember the question asks us for what MUST be true, and we see that none of the statements are true in all cases.

However, adding 3 to any of the values of n will always give a multiple of 5.

Hence, option 4 is the correct answer.

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