Number Properties DS Question

[sonalibhangay]

If x, y , and z are integers, is x/ yz an integer?

A) y is a factor of x more than once.

B) All of the prime factors of z are also factors of y


I believe the answer should be [spoiler]E but OA is C Source: Princeton[/spoiler]

[Anju@Gurome]

If x, y , and z are integers, is x/ yz an integer?

A) y is a factor of x more than once.
B) All of the prime factors of z are also factors of y

Consider the following two cases,

• x = 4, y = 2, and z = 2 ---> x/yz is an integer
  x = 4, y = 2, and z = 4 ---> x/yz is not an integer

Both of the above cases satisfy both the statements but the answers are different in each case.

The correct answer is E.

Note : The 2nd statement is ambiguous. If it was supposed to mean that if y has n number of 2s or 3s in it, then z also have same number of 2s or 3s in it... The correct answer will be C. However, if someone simply asks, how many prime factors does 8 have? We say one, not three.

[sonalibhangay]

Thanks, that clears my doubt.

Regards, Sonali.