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Number Properties

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Number Properties

by sparkle6 » Tue Sep 27, 2011 6:21 am
If x and y are integers and

(15^x + 15^(x+1)) / 4^y = 15^y

What is the value of x?

a. 2
b. 3
c. 4
d. 5
e. Cannot be determined


[spoiler]Answer: A. Does anyone know how to solve?[/spoiler]
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by Brent@GMATPrepNow » Tue Sep 27, 2011 6:56 am
sparkle6 wrote:If x and y are integers and

(15^x + 15^(x+1)) / 4^y = 15^y

What is the value of x?

a. 2
b. 3
c. 4
d. 5
e. Cannot be determined


[spoiler]Answer: A. Does anyone know how to solve?[/spoiler]
Given: (15^x + 15^(x+1)) / 4^y = 15^y
To eliminate the fraction, first multiply both sides by 4^y:
15^x + 15^(x+1) = (15^y)(4^y)
Now factor 15^x from left-hand-side: 15^x(1 + 15^1) = (15^y)(4^y)
Simplify: (15^x)(16) = (15^y)(4^y)
Rewrite 16 as power of 4: (15^x)(4^2) = (15^y)(4^y)
At this point, we can see that the blue part of the equation works well if y=2
If y=2, then x must equal 2 (for the red part of the equation to work)

So, the answer is A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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