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

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Manager
Joined: 21 Jul 2009
Posts: 242

Kudos [?]: 135 [1], given: 23

Location: New York, NY
If x, y, and z are integers greater than 1, and [#permalink]

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16 Oct 2009, 12:36
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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?

(1) y is prime

(2) x is prime

Kudos [?]: 135 [1], given: 23

Manager
Joined: 11 Sep 2009
Posts: 129

Kudos [?]: 425 [0], given: 6

Re: x, y and z [#permalink]

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16 Oct 2009, 12:54
I believe the correct answer is B.

$$(3^27)(5^10)(z) = (5^8)(9^14)(x^y)$$

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

$$(5^2)(z) = 3x^y$$

If x, y, and z are all integers, two conditions must be met:

a) x^y must be a multiple of 25, and
b) z must be a multiple of 3.

Statement 1: y is prime

x = 5, y = 2: x^y = 5^2 = 25
x = 25, y = 3: x^y = 25^3

Therefore, insufficient.

Statement 2: x is prime

For x^y to be a multiple of 25, x MUST BE a multiple of 5. Since x is given to be a prime number however, x must be 5, since all other multiples would consist of three or more factors. Therefore, sufficient.

Kudos [?]: 425 [0], given: 6

Manager
Joined: 12 Oct 2009
Posts: 114

Kudos [?]: 68 [0], given: 3

Re: x, y and z [#permalink]

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16 Oct 2009, 13:01
will go with B as y is prime in option1 will not give a definite answer and x is prime give 5 as the only answer

Kudos [?]: 68 [0], given: 3

Re: x, y and z   [#permalink] 16 Oct 2009, 13:01
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