hutch27 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
OA is D
I simplified the original equation to [spoiler]25z=3x^y[/spoiler] but couldnt deduce anything based on the statements. how can i logically figure this out?
(3²�)(35¹�)(z) = (5�)(7¹�)(9¹�)(x^y)
(3²�)(7¹�5¹�)(z) = (5�)(7¹�)(3²)¹�(x^y)
(3²�)(7¹�5¹�)(z) = (5�)(7¹�)(3²�)(x^y)
(5²)(z) = (3)(x^y)
z = (3) * (x^y)/5².
The equation above implies that z is a multiple of 3 and that x^y is a multiple of 5².
Statement 1: z is prime
Since z is prime and a multiple of 3, z=3.
Thus, (x^y)/5² = 1, implying that x=5 and y=2.
SUFFICIENT.
Statement 2: x is prime
Since x^y is a multiple of 5² and x is prime, x=5 and y≥2.
SUFFICIENT.
The correct answer is
D.
Last edited by
GMATGuruNY on Tue Oct 08, 2013 5:01 am, edited 1 time in total.
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