If P represents the product of the first 13 positive integers, which

Question

Tough and Tricky questions: Number Properties.

If P represents the product of the first 13 positive integers, which of the following must be true?

I. P is an odd number
II. P is a multiple of 17
III. P is a multiple of 24

A) I only
B) II only
C) III only
D) None of the above
E) All of the above

Kudos for a correct  solution .

Source: Chili Hot GMAT

intheend14 · Answer

The question says that P = 13! (13 factorial)

So, this cannot be odd as it has at least one even factor.
This cannot be a multiple of 17 as there is no factor of 17 or any of its multiples.
But, this is a multiple of 24 as we have at least one factor of 24 (4*6 or 4*3*2) in P.

Choice C

PareshGmat · Answer

Answer = C) III only

P = 13!

I It is a multiple of 2, so cannot be ODD

II. 17 is a prime number; cannot be multiple

III. 24 = 8 * 3; Yes it is a multiple

Bunuel · Answer

The correct answer is C.

MathRevolution · Answer

P = 1 * 2 * 3 * .... * 11 * 12 * 13 = 13!

As it is a product of even * odd, P cannot be odd. Also, it is not a multiple of 17 as '17' is a prime number and not involved in the calculation.

P is multiple of 24 = 8 * 3 = 6 * 4 = 12 * 2

Answer C

If P represents the product of the first 13 positive integers, which

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