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x# is defined for every positive even integer x as the product of all

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Carcass
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x# is defined for every positive even integer x as the product of all [#permalink] New post   12 Jan 2022, 07:33
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x# is defined for every positive even integer x as the product of all even integers from 2 to x. What is the smallest possible prime factor of (x#+7)?

A. 2
B. 3
C. 5
D. 7
E. 11
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B
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GreenlightTestPrep
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Re: x# is defined for every positive even integer x as the product of all [#permalink] New post   12 Jan 2022, 07:52
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Carcass wrote:
x# is defined for every positive even integer x as the product of all even integers from 2 to x. What is the smallest possible prime factor of (x#+7)?

A. 2
B. 3
C. 5
D. 7
E. 11

Let's check each answer choice, starting from the smallest....

A) 2
First recognize that x# will be even for all even integers x, which means x# + 7 will always be odd.
If x# + 7 is odd, then 2 cannot not be a divisor.

B) 3
If x = 2, then x# + 7 = 2# + 7
= 2 + 7
= 9

Since 3 is a factor of 9, the correct answer is B
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gmatclubot
Re: x# is defined for every positive even integer x as the product of all [#permalink]
12 Jan 2022, 07:52
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