Exponents Question (CAT) Manhattan

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EMAN: Master | Next Rank: 500 Posts; Posts: 162; Joined: Sun Aug 09, 2009 4:17 pm; Location: Minnesota; Thanked: 1 times

by EMAN » Sun Oct 11, 2009 2:10 pm

If x and y are integers and:

15^X + 15^X+1 / 4Y = 15^Y

what is the value of x?

(A) 2
(B) 3
(C) 4
(D) 5
(E) cannot be determined

I should have tried numbers but I immediately dismissed ths answer b/c there are two unknowns. Dumb. I got this one incorrect. If anybody knows how to solve this algebraically in an easy way please share.

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Source: Beat The GMAT — Problem Solving | Sun Oct 11, 2009 2:10 pm

ashis979: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Tue Jul 28, 2009 8:12 pm; Thanked: 4 times

by ashis979 » Sun Oct 11, 2009 2:27 pm

Denominator is supposed to be 4^y, not 4y
[(15^x)+(15^(x+1))]/4^y = 15^y
[(15^x)+(15^x*15)] = (15^y)(4^y)
(15^x)(1+15) = (15^y)(4^y)
(15^x)(16) = (15^y)(4^y)
(15^x)(4^2) = (15^y)(4^y)
Therefore, x=y; y=2 => x=y=2...A

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