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I actually just got this question in GMATprep#2 yesterday. Here's what I did.

Factor the four terms into primes:

(400)(6000)=(240)(100^x)

(2^4 5^2)(2^4 3^1 5^3)=(2^4 3^1 5^1)(2^2x 5^2x)

Combine to get, remember that (X^a)(X^b)=(X^a+b)

(2^8)(5^5)(3^1)=(2^4+2x)(5^1+2x)(3^1)

Cancel out the (3^1) to get:

(2^8)(5^5)=(2^4+2x)(5^1+2x)

Remember that there must be an equal number of exponents for each term on boths ides of the equation. Here there are eight 2's on the left side this means that there must be eight 2's on the right side, so 4+2x must equal 8.

4+2x=8 2x=4 x=2

D

You can use the same process for the exponents of 5 and you will arrive at the same answer.

Is there an easier/faster way to do this b/c this ate up alot of time during my test. especially b/c I had to factor out all the numbers.

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