If P represents the product of the first 15 positive integers, then P

Question

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

GMATinsight · Answer

P = 15! as per definition of question

A. 99 = 9*11 Yes 15! has both factors
B. 84 = 3*4*7 Yes 15! has both factors 
C. 72 = 9*8 Yes 15! has both factors
D. 65 = 9*13 Yes 15! has both factors
E. 57 = 3*19 NO 15! DOES NOT HAVE A FACTOR 19 hence CORRECT ANSWER

Answer: option E

ScottTargetTestPrep · Answer

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

EgmatQuantExpert · Answer

SOLUTION

P= 1*2*3*4*5*6*7*8*9*10*11*12*13*14*15 
For P to be a multiple of some number, P should be completely divisible by the same number.

Now let us find the option which does not divide P.

• 99= 9*11
  o Since P contains 9*11, hence P is divisible by 99.

• 84=7*12
 o Since P contains 7*12, hence P is divisible by 84.

• 72=8*9
 o Since P contains 8*9, hence P is divisible by 72.

• 65=5*13
 o Since P contains 5*13, hence P is divisible by 65. 
 
• 57=3*19
 o Since P does not contain 19, hence P is not divisible by 57.

Hence,  57 is not a multiple of P .

Answer: E

Digvijay101 · Answer

Lets have a look at the answer choices-
A. 99 - 9X11- both are in P
B. 84 - 7X12- both are in P
C. 72 - 7X8- both are in P
D. 65 - 5X13- both are in P
E. 57 - 3X19

19 is a prime number and not there in the product- P.
The correct answer is E

bumpbot · Answer

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If P represents the product of the first 15 positive integers, then P

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