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exponents

by clock60 » Sat Nov 27, 2010 11:06 am
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

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by [email protected] » Sat Nov 27, 2010 11:20 am
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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by clock60 » Sat Nov 27, 2010 11:48 am
really helpfull Rahul!!!
i love you solution
thanks