value of x

[orel]

If x, y, and z are integers greater than 1, and (3^27)(5^10)(z) = (5^8)(9^14)(x^y), then what is the value of x?

(1) y is prime

(2) x is prime

[Stuart@KaplanGMAT]

If x, y, and z are integers greater than 1, and (3^27)(5^10)(z) = (5^8)(9^14)(x^y), then what is the value of x?

(1) y is prime

(2) x is prime

Whenever you have a complicated question stem in DS, take some time to simplify it.

(3^27)(5^10)(z) = (5^8)(9^14)(x^y)

(3^27)(5^10)/(5^8)(9^14)= (x^y)/z

(3^27)(5^10)/(5^8)(3^28)= (x^y)/z

(5^2)/3 = (x^y)/z

In other words, the ratio of (x^y):z = 25:3

(1) y is prime

We could have x = 5, y = 2 and z = 3

We could have x = 15, y = 2 and z = 27

(we see that we can simply increase both x and z to maintain the ratio)

More than 1 possible value for x: insufficient.

(2) x is prime

The first part of our ratio is a multiple of 25.

If x^y is a multiple of 25 AND x is prime, then x must equal 5: sufficient.

(2) is sufficient alone, (1) isn't: choose (B)

Note that from (2) we may or may not be able to determine the values of y and z. I say "may or may not", because we don't care! The question is only asking about the value of x, so that's all that matters to us.

[orel]

Thanks a lot for explanation, Stuart.

Really appreciate your time.