Number factors

[gmatrant]

If x,y,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.

The answer is C.

Choice b is further explained to state that y is a factor of z.
I quite don't agree because all of the prime factors of z are also factors of y.
So y can be 6 while z can be 12, prime factors of 12 is 2 & 3, which are factors of y i.e 6.

Please let me know how answer is C.

[Gurpinder]

question: x/yz = int?

(1) a) y is a factor of x more than once

but we dont know anything about z so insufficient.
for ex. 15=x,y=3 --> 15/3=5 but if z=2 then 15/6 = not int

(2) All of the prime factors of z are also factors of y.

doesn't say anything about x.
y=3,z=3 so their prime factors are the same. but then> x/9

so by itself, 2 is insufficient.

Together:

x/y=int
primes of y = z
if the primes of y = z, that means that x/z is also an int.
if x/y = int and x/z = int then x/yz must be an int.

for ex. x=18, x=3,z=3 then > 18/9=2
another ex. x=100 y=10,z=5 > 100/50=2

So (C)

[gmatrant]

Cant y can be 6 while z can be 12, prime factors of 12 is 2 & 3, which are factors of 6 i.e y.

Z= 12 {prime factors = 2,3}
Y = 6 { prime factors = 2,3}
prime factors of z = prime factors of Z.

Now x = 12

x/yz is not an integer.
Shouldn't the answer be E.

[Gurpinder]

Cant y can be 6 while z can be 12, prime factors of 12 is 2 & 3, which are factors of 6 i.e y.

Z= 12 {prime factors = 2,3}
Y = 6 { prime factors = 2,3}
prime factors of z = prime factors of Z.

Now x = 12

x/yz is not an integer.
Shouldn't the answer be E.

No. The trick is ALL of the prime factors of z are also factors of y.

So as you said, cant y can be 6 while z can be 12 - NO.

prime factors of 12 = 3,2,2
prime factors of 6 = 3, 2

they are not the same. 12 has 1 more 2.