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Tough DS, Please help

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by chrisgiles01 » Sat Jun 30, 2007 8:34 pm
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

I can simplify the equation down to: 5^2*z=3*x^y but I need an explanation on why when x or z are prime you can solve for x.
(answer is D)

Appreciate any assistance I can get.

Chris
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by givemeanid » Sat Jun 30, 2007 9:27 pm
After simplifying, you get 5^2 * z = 3 * x^y

(1) z is prime.
Now, 3 on the right side has to be balanced by z because 5^2 doesn't have 3 as a factor. Since z is prime, z = 3
That means x^y = 5^2 and x = 5

(2) x is prime
5^2 has to be factored by x^y since 3 is not a factor of 5^2. If x is prime, then the only possibility is x = 5

Answer is (D)
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by chrisgiles01 » Sun Jul 01, 2007 10:15 am
Thank you. Explanation is great! I Appreciate your help.

Chris
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