GRE Quantitative Comparison Tip #5 – Approximation with a Twist

The fourth post in the GRE Quantitative Comparison series showed how to use estimation techniques to compare values quickly. We were able to solve the problem below:

Column A                                            Column B

(221)/(400)  +  (3090)/(9060)      (720)/(1450) + (200)/(603)

Comparing Parts: Recap

We estimated the values of each fraction:

Column A                     Column B

1/2⁺   +   1/3⁺            1/2^-   +   1/3^-

The answer was Choice (A) Quantity A is greater. We do have to be careful. Let’s see what would have happened if we had rounded these values.

Column A                    Column B

1/2   +   1/3               1/2   +   1/3

If we hadn’t estimated carefully, we could have assumed that the columns were equal and gotten an incorrect answer.

Approximation Strategy

Now we’ll use a similar strategy to solve another type of problem. Try to use an approximation method for this question:

Column A                         Column B

639,709 x 449,202         898,190 x 311,977

(A) Quantity A is greater.

(B) Quantity B is greater.

(C) The two quantities are equal.

(D) The relationship cannot be determined from the information given.

Aside: These values are too large to fit into the onscreen calculator.

Using our estimation strategies from the last post, we can think of ways to make these numbers easier to use.

Column A                            Column B

640,000^- x 450,000^-      900,000^- x 310,000⁺

Dividing both sides by 1,000 will reduce the numbers even more.

Column A                  Column B

640^- x 450^-           900^- x 310⁺

We can apply a useful trick to help our approximation: A x B = 2A x ½ B. This says that multiplying two numbers is equal to the product of twice the first number and half of the second number. 450 is half of 900 and 640 is two times 320: we can use those numbers to simplify Column A.

Column A                Column B

320^- x 900^-          900^- x 310⁺

Both columns include the term 900^-, so we only have to compare the other values. 320 is greater than 310, so Column A has a larger value.

Calculator Approach

Instead of using logic to finish the problem, we could have used our onscreen calculator. Let’s look at the problem again after approximating the values:

Column A                   Column B

640^- x 450^-            900^- x 310⁺

All of these numbers are small enough to fit into the onscreen calculator, so we can use it to multiply the values on both sides.

Column A               Column B

288,000                 279,000

The value in Column A is larger, and we get answer A again.

Decimal Approach

We can use a fast adjustment to make these values fit into the onscreen calculator. Starting with the original problem, let’s divide all the values by 1,000:

Column A                       Column B

639.709 x 449.202       898.190 x 311.977

These values are small enough to type into the calculator, so we can solve the problem without any other steps.

Column A                   Column B

287,358.56             280,214.62

Clearly Column A has the larger value, so we choose Choice A.