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
(1) y is prime
(2) x is prime
Whenever you have a complicated question stem in DS, take some time to simplify it.Feruza Matyakubova wrote: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
(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.
