Factors

[Guest]

13. If xy is divisible by 10, yz is divisible by 15 and z^2 is divisible by 14, xyz must be divisible by which of the following?
a. 30
b. 100
c. 60
d. 28

I do not understand how I must attack the question after the prime factorization.

[Guest]

SOurce: Gmat Guru

[michael_shaunn]

Well,here's how i tried to solve it.Let me know if you are not satisfied with my explanation.

xy seems to be a two digit number which is divisible by 10.Now one point to observe is that for a number to be divisible by 10,the last digit must be 0.Hence y is equal to 0.For the time being lets forget about x as we can't perdict anything about x at this moment.

Now yz is divisible by 15. But as per our findings y=0.So yz is basically a single digit number which is divisible by 15.None of the single digit numbers are divisible by 15.Hence z has to be zero for yz to be divisible by 15.

Now we can make out that whatever the value of xyz................it will always have 2 zeros at the last thus making it divisible by 100.

I think 100 is the right answer.

[JonathanSchneider]

I don't think the problem means for us to read "xy" as digits, but rather as a product, though I might be mistaken. Regardless, we would need to be told that x, y, and z are integers (or, at the very least, that z is an integer, from which the rest would follow). Even if I assume x,y, and z to be integers, however, I still arrive at an answer of 210, which is not listed here. So I'm not quite sure what to make of this problem...