If x and y are integers and (15^x + 15^x+1)/4^y = 15^y , wh

[mitzwillrockgmat]

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

So this is what i did:

15^x + 15^x+1=15^y*4^y
15^x(1+15^1)=15^y*4^y
15^x(16)=15^y*4^y
15^x(2^4)=15^y*4^y
(3*5)^x(2^4)=(3*5)^y(2^2y)
(3^x*5^x)(2^4)=(3^y*5^y)(2^2y)

so now all the bases are same so i can equate the exponents.

x+x+4 = y+y+2y
2x+4=4y

this is where i get stuck! how do i get a value with this? Pls help!

[liferocks]

(15^x + 15^x+1)/4^y = 15^y
or 15^x*(1+15)/4^y=15^y
or 15^x*4*(2-y)=15^y*4^0

so x=y and y-2=0 or y=2
so x=2

Ans option a

[selango]

ans is 2

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

3^x.5^y.4^2=3^y.5^y.4^2

Comparing the exponent with same base we get,

x=y

y=2

Hence x=2


what is the source?

[mitzwillrockgmat]

ans is 2

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

3^x.5^y.4^2=3^y.5^y.4^2 correction 4^y

Comparing the exponent with same base we get,

x=y

y=2

Hence x=2

what is the source?

thanks!! it's on manhattangmat cat exam.

[Jeff@TargetTestPrep]

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

We can simplify the given equation:

15^x + 15^x * 15 = 15^y * 4^y

15^x(1 + 15) = 15^y * 2^(2y)

15^x(2^4) = 15^y * 2^(2y)

Thus, we see that:

15^x = 15^y, so x = y

and

2^4 = 2^(2y), so 4 = 2y, or 2 = y.

Thus, x = 2.

Answer: A