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prime

by GmatKiss » Mon Aug 15, 2011 3:47 am
If x, y, and z are integers greater than 1, and (3^27)(35^10)(z) = (5^8 )(7^10)(9^14)(x^y), then what is the value of x?

(1) z is prime

(2) x is prime
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by gmatboost » Mon Aug 15, 2011 10:15 am
(3^27)(35^10)(z) = (5^8 )(7^10)(9^14)(x^y)

(3^27)(5^10)(7^10)(z) = (5^8)(7^10)((3^2)^14)(x^y)
(3^27)(5^10)(7^10)(z) = (5^8)(7^10)(3^28)(x^y)
(5^10)(7^10)(z) = (5^8)(7^10)(3^1)(x^y)
(5^10)(z) = (5^8)(3^1)(x^y)
(5^2)(z) = (3^1)(x^y)
(5^2)(z) = 3(x^y)

So z must contain a 3, and x^y must contain 25

St 1. [spoiler]z = 3, but x^y could be 5^2 or 25^1[/spoiler]
St 2. [spoiler]x = 5[/spoiler]
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