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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pm; Location: Gandhinagar; Thanked: 41 times; Followed by:2 members

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by shashank.ism » Wed Feb 10, 2010 11:10 pm

If P represents the product of the first 15 positive integers, then P is not a multiple of:

A) 99
B) 84
C) 72
D) 65
E) 57

Ans E

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 am; Location: India; Thanked: 64 times; Followed by:6 members; GMAT Score:760

by harsh.champ » Wed Feb 10, 2010 11:13 pm

shashank.ism wrote:If P represents the product of the first 15 positive integers, then P is not a multiple of:

A) 99
B) 84
C) 72
D) 65
E) 57

Ans E

If P represents the product of the first 15 integers, P would consist of the prime
numbers that are below 15.
2,3,5,7,11,13
Any value that has a prime higher than 13 would not be a value of P.
57 = 3, 19
19 is a prime greater than 13, so the answer is E.

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pm; Location: Arabian Sea; Thanked: 125 times; Followed by:2 members

by ajith » Thu Feb 11, 2010 8:26 am

shashank.ism wrote:If P represents the product of the first 15 positive integers, then P is not a multiple of:

A) 99
B) 84
C) 72
D) 65
E) 57

Ans E

99 - 11*3^2
84 = 2^2*3*7
72 = 2^3*3^2
65= 13*5
57 = 19*3

15! = 2^11*3^6*5^3*7*11*13

Clearly 57 is not a factor

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by Scott@TargetTestPrep » Wed Mar 14, 2018 3:26 pm

shashank.ism wrote:If P represents the product of the first 15 positive integers, then P is not a multiple of:

A) 99
B) 84
C) 72
D) 65
E) 57

Let's look at the answer choices.

Since 99 = 9 x 11, both of which are included in the product of the first 15 integers, we see that P is a multiple of 99.

Similarly, since 84 = 42 x 2 = 21 x 4 = 7 x 3 x 4, we see that P is a multiple of 84.

Since 72 = 36 x 2 = 6 x 3 x 2 x 2 = 6 x 3 x 4, we see that P is a multiple of 72.

Since 65 = 5 x 13, we see that P is a multiple of 65.

Since 57 = 19 x 3, and since the product of the first 15 integers does not have a prime factor of 19, P cannot be a multiple of 57.

Answer: E

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