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13 Mar 2018, 01:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
87% (01:11) correct
13%
(01:07)
wrong
based on 177
sessions
History
Date
Time
Result
Not Attempted Yet
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
A. 99
B. 84
C. 72
D. 65
E. 57
13 Mar 2018, 04:05
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Bunuel
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
A. 99
B. 84
C. 72
D. 65
E. 57
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
14 Mar 2018, 16:10
Kudos
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Bunuel
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
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
