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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?

\(3^{27}*5^{10}*z = 5^8*9^{14}*x^y = 5^8*3^{28}*x^y\)
\(5^2*z = 5^8*9^{14}*x^y = 3*x^y\)
\(x^y = \frac{5^2*z}{3}\)

(1) y is prime.
Case 1: x = 5; y = 2; z = 3; Feasible
Case 2: x = 15; y = 2; z = 27; Feasible
NOT SUFFICIENT

(2) x is prime.
x = 5;
SUFFICIENT

IMO B
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If x=5, y=3, z=15, it still holds true for statement 2. Please clarify.
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If x=5, y=3, z=15, it still holds true for statement 2. Please clarify.
­Hi Param_91

Statement 2 says x is prime, in your case x=5, which is prime & obviously the answer.

But if your doubt is regarding statement 1, Statement 1 gives following answers
1. x = 5, y = 2, z = 3
2. x = 10, y=2, z=4
3. x = 5, y=3, z=15

So here you have 2 values of x, when y is prime (y=2 for x=5 & x = 10). So we cannot conclude the answer

But in statement 2, x is explicitly stated as prime. On sloving the equantion we know the form in 5^y. Therefore answer is 5 irrespective of y
1. x = 5, y = 2, z = 3
2. x = 5, y=3, z=15
3. x = 5, y=4, z=25
and so on
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