Problem Solving

LUANDATO wrote:The product of first twelve positive integers is divisible by all of the following EXCEPT?

(A) 210
(B) 88
(C) 75
(D) 60
(E) 34

The OA is E.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. We see that option E: 34 is a factor of 2 and 17. Since the product of first twelve positive integers does not include 17, option E: 34 is the correct answer.

The correct answer: E

Hope this helps!

-Jay
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BTGmoderatorLU wrote:The product of first twelve positive integers is divisible by all of the following EXCEPT?

(A) 210
(B) 88
(C) 75
(D) 60
(E) 34

The OA is E.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

The product of the first twelve positive integers is 12!. Since it does not contain the prime factor of 17, it is not divisible by 34, which contains 17 as a factor.

Answer: E