Math Challenge: (2^4x)(4^3x) = 8^(x + 42) Quantitative Comparison

GRE Math Challenge Question

                                                    (2^4x)(4^3x) = 8^{x + 42}

Quantity A	QuantityB
x	17

1. Quantity A is greater.
2. Quantity B is greater.
3. The two quantities are equal.
4. The relationship cannot be determined from the information given.

Explanation:

Choice (A) is correct.

Remember, when you have variables in the exponents, you want to get everything in the same base, so you can drop the bases and focus on the exponents. Let's replace 4 with 2² and 8 with 2³. The equation can be rewritten:

2^4x(2²)^3x = (2³)^{x + 42}

2^4x(2^6x) = 2^{3x + 126}

2^{4x + 6x} = 2^{3x + 126}

2^10x = 2^{3x + 126}

Now that everything is in the same base, we know the exponents are equal to each other, so we can focus on solving for x:

10x = 3x + 126

7x = 126

x = 18

Quantity A, which is 18, is greater than Quantity B, which is 17. Choice (A) is correct.