Suppose x is the product of all the primes less than or equal to 59. How many primes appear in the set {x + 2, x + 3, x + 4, …, x + 59}?

A. 0
B. 17
C. 18
D. 23
E. 24
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manpreetsingh86 ..... [x+9] doesn't have a common factor ....[9 is not prime] ....i doubt if any product these two primes gives you a multiple of 9.

So that's glitch in the logic here. Anyways i too chose 0 as the answer..but had they given 1, 2, etc...i would have got confused.

Bunuel / VeritasPrepKarishma please help.

Since 2 * 3* 5 *... *59 is even, x is even.
As x is even, so will be x+2, x+4, x+6...... x+58, so these numbers cannot be prime.
Now x+3 is nothing but (2*3*... 59) + 3. Rewriting this as {3 * (2 * 5*.... 59)} +3.
One can observe here that the term in the curly brace is a multiple of 3 and that term plus 3 will definitely be a multiple of 3 .
(Multiple of 3 + 3 is a multiple of 3, Multiple of 59 + 59 is a multiple of 59)
As x+3 is a multiple of 3 it cannot be a prime.
Similarly x+5 can be written as {5 * (2 * 3* 7*.... 59)} +5 which is a multiple of 5.

Like wise we can see that all the terms in the set are multiples of prime numbers.


Ambarish
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