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17! + 2 <= Z <= 17! + 17 means that z is like 17! + 2, 17! + 3 etc. So you can factor out a common integer from the expressions that will divide 17! + n (2 <= n <=17), e.g. 2 divides 17! + 2 because 17! also includes 2.

So z is not a prime.

(1) is not sufficient because there are primes and non-primes above 15!

Please ask if you have any more queries.
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17! + 2 is Divisible by 2 . Hence not prime 17! + 3 is Divisible by 3 . Hence not prime 17! + 4 is Divisible by 4 . Hence not prime 17! + 5 is Divisible by 5 . Hence not prime 17! + 6 is Divisible by 6 . Hence not prime 17! + 7 is Divisible by 7 . Hence not prime 17! + 8 is Divisible by 8 . Hence not prime 17! + 9 is Divisible by 9 . Hence not prime 17! + 10 is Divisible by 10 . Hence not prime 17! + 11 is Divisible by 11 . Hence not prime 17! + 12 is Divisible by 12 . Hence not prime 17! + 13 is Divisible by 13 . Hence not prime 17! + 14 is Divisible by 14 . Hence not prime 17! + 15 is Divisible by 15 . Hence not prime 17! + 16 is Divisible by 16 . Hence not prime 17! + 17 is Divisible by 17 . Hence not prime

In any case z cannot not be prime hence answer is B
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17! + 2 is Divisible by 2 . Hence not prime 17! + 3 is Divisible by 3 . Hence not prime 17! + 4 is Divisible by 4 . Hence not prime 17! + 5 is Divisible by 5 . Hence not prime 17! + 6 is Divisible by 6 . Hence not prime 17! + 7 is Divisible by 7 . Hence not prime 17! + 8 is Divisible by 8 . Hence not prime 17! + 9 is Divisible by 9 . Hence not prime 17! + 10 is Divisible by 10 . Hence not prime 17! + 11 is Divisible by 11 . Hence not prime 17! + 12 is Divisible by 12 . Hence not prime 17! + 13 is Divisible by 13 . Hence not prime 17! + 14 is Divisible by 14 . Hence not prime 17! + 15 is Divisible by 15 . Hence not prime 17! + 16 is Divisible by 16 . Hence not prime 17! + 17 is Divisible by 17 . Hence not prime

In any case z cannot not be prime hence answer is B

Oh yes! thats correct if it would have been 17! + 1 instead of 17!+2 it would be insufficient. But rest all values are not prime. Thank you for the explanation.

+1 Kudos
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Oh yes! thats correct if it would have been 17! + 1 instead of 17!+2 it would be insufficient. But rest all values are not prime. Thank you for the explanation.

+1 Kudos

How did u figured out that 17!+1 is a prime number ? I dont think thats safe to assume unless you really did calculated

Cause

17!+1 will be insufficient only if 17!+1 is a prime number. I believe It is not practice to figure that out manually hence it is not included in the range.

May be you can solve and let us know
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I don't understand the official explanation, can anyone help out here?

2 is sufficient because if z is an integer, then z can only be 17!+k, and 2<=k<=17 but 17! has all the factors from 2 to 17, so z=k(17!/k+1), and is not a prime

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