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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shashank.ism
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If P represents the product of the first 15 integers, P would consist of the primeshashank.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
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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99 - 11*3^2shashank.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
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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Scott@TargetTestPrep
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Let's look at the answer choices.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
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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