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

Question

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

BrentGMATPrepNow · Accepted Answer

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

AnkithaSrinivas · Answer

If the question had asked - largest it would have been 11
2*4*6 + 7 = 55

Largest is 11

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem ↧↧↧

https://www.youtube.com/watch?v=AzsfNwK6aes

x# is defined for every positive even integer x as the product of all even integers from 2 to x

Lets take an example values of x
Lets say x = 4
4# = 2*4 = 8

What is the smallest possible prime factor of (x#+7)? 
 
Now, x# will always be an even number as it is product of even numbers
=> x# + 7 = Even + Odd = Odd
=> 2 cannot be the factor
=>   Eliminate A

Lets take values of x and test. Let x be 4 itself
=> 4# + 7 = 8 + 7 = 15
=> 3 is a factor

So,  Answer will be B 
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

https://www.youtube.com/watch?v=b7JoMX0gk8M

onlyPlanA · Answer

Is this question valid for all even numbers???!!!
What about when x = 8?

8# = 2 * 4 * 6 * 8 = 384
8# + 7 = 391
And 391's prime factorization is 17 * 23.

In that case, none of the options are suitable!!! And unfortunately this is the example I took.

Bunuel · Answer

Check the question again: “What is the   smallest possible   prime factor of (x# + 7)?”

It asks for the smallest prime factor that is   possible  , not one that must occur for every even x. When x = 2, x# + 7 = 2 + 7 = 9, whose smallest prime factor is 3.

onlyPlanA · Answer

Ah, I get it. This is the second question in my today's practice that has tripped me up using this kind of round-about words.... Phew...😓

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

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

Prep Toolkit

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