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# If x, y, and z are integers greater than 1, and

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If x, y, and z are integers greater than 1, and [#permalink]

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18 May 2008, 15:41
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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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Director
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18 May 2008, 16:05
chineseburned wrote:
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

If you simplify everything down, you have Z = (3(x^y)) / (5^2)

statement 1: if z is prime, then x^y has to be 5^2 or 25^1, BUT since y has to be > 1, x has to be 5
suff

statement 2: If you rearrange the equation, you have x^y = (5^2)(z)/3
z has to be divisible by 3
if z = 3, x = 5
if z = 12 = 3*2*2, then x = 10
Insuff

A

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18 May 2008, 16:57
chineseburned wrote:
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

(3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y)
(3^27) [(7^10) (5^10)] (z) = (5^8)(7^10)(3^28)(x^y)
(5^2) (z) = (3) (x^y)
(5x5) (z) = 3 (x^y)

1: if z is a prime, it can only be 3. in that case, x^y = 5^2. suffff.
2: if x is a prime, it should be 5 then only 3x^y has 5 in its unit digit. so suff.

got D.
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Re: DS: exponents   [#permalink] 18 May 2008, 16:57
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