GRE Quantitative Comparison Problem: Exponents


GRE Math isn’t so scary. Just try this GRE example problem.

Consider the following quantitative comparison problem:

Column A

Column B



Remember, with quantitative comparison questions, you are to grid (A) if the quantity in Column A is greater; (B) if the quantity in Column B is greater; (C) if the two quantities are equal; or (D) if the relationship cannot be determined from the information given. Many students find quantitative comparison problems tricky because unlike traditional math problems, you are not being asked to solve for a single numerical answer. Instead you are asked to find the relationship between two quantities. This tends to really test your knowledge of more abstract mathematical concepts like number properties and the definitions of mathematical operations. With a little review and practice, though, these questions are no more difficult than the more usual ones.

This question tests your knowledge of exponents. Remember that exponents are just a shorthand way of multiplying a number by itself a certain number of times. For instance, 8^6 = 8*8*8*8*8*8. To find out if Column A is greater than, less than, or equal to Column B (we know we must be able to determine the relationship since we could actually solve the expressions found in each column), let’s start by writing out these multiplications the long way:

(8^6)/(4^4) = (8*8*8*8*8*8)/(4*4*4*4)

(2^4)*(4^3) = (2*2*2*2)*(4*4*4)

If only we could make the two Columns look more alike. Well, remember that 8 = 4*2, so if we replace each 8 in Column A with 4*2, then we can cancel out all of the 4s in the denominator:

(4*2*4*2*4*2*4*2*4*2*4*2)/(4*4*4*4) = 4*4*2*2*2*2*2*2

Now, remember that 4 = 2*2. This means that 4*4*(2*2)*2*2*2*2 = 4*4*4*2*2*2*2 = (2^4)*(4^3).
Thus, without using a calculator and without actually solving either expression, we have discovered that Column A and Column B are in fact equal. On the test, you would grid choice (C) as your answer. In case you were curious, both expressions equal 1024.
