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

## exponents

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clock60 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

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

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

=> (5^2)*(z) = (3)*(x^y)

This means z must contain at least one 3 in it and (x^y) must contain at least one 25 in it.

**Statement 1:**y is prime.

For x = any multiple of 5 we can take any prime value of x as z may contain the extra 5's. For example, say x = 5, y = 3 => One extra 5 on RHS which may come from z. For x = 25, y = 2 => Two extra 5's on RHS which may come from z.

Not sufficient.

**Statement 2:**x is prime.

Only possible value of x is 5. For x = any other prime, (x^y) cannot contain 5 in it.

Sufficient.

The correct answer is B.

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Quant Expert

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On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits

1-800-566-4043 (USA)

+91-99201 32411 (India)