GMATPrep: DS Problem

[kookoo4tofu]

This one was on my GMATPrep practice test. and i still dont know how to do it. please help. thanks.

If x and y are positive integers, what is the value of x + y?
(1) (2^x)(3^y) = 72
(2) (2^x)(2^y) = 32

[bww]

Hi,

Is the answer D? Unless I'm mistaken, this is how I got that answer:

1) plug in values. You know that (2^x)(3^y)=72. Off the top of your head you know that 8*9=72, and that works here: x=3 and y=2. 1) is sufficient.

2) (2^x) and (2^y) share the same root ("2") so you should be able to combine (add) the exponents to get 2^(x+y)=32. Let's rewrite 32 as 2^n, so you now have 2^(x+y)=2^n knowing that 2^n must equal 32. n must equal 5. You don't need to know the individual values of x and y, but you now now what their sum is: 5. 2) is sufficient.

Hope I'm right/this helps!

[kookoo4tofu]

yes! the OA is D. thanks

[Cybermusings]

If x and y are positive integers, what is the value of x + y?
(1) (2^x)(3^y) = 72
(2) (2^x)(2^y) = 32

Statement I : 72 when broken down into its primes = (2^3)*(3^2)
Since the bases are the same we can equate the powers...hence x = 3 and y =2 so x+y = 5
Sufficient

Statement II : 32 when broken down into its primes = 2^5
2^x * 2^y = 2^(x+y) [law of indices]
Hence x+y = 5
Sufficient

Hence D