# GRE Quantitative Comparison Example Problem: Percent Change Problems

Testmasters helps students to increase their score on the GRE. While many students are interested in only improving their scores by a certain number of points, others want to see how their scores increase as a percentage of their original score. Such a skill also helps when solving some of the quantitative comparison questions on the GRE, which require you to know how to calculate the original value when given the percent change and the new value. One such problem is below.

If a cell phone is purchased with a contract calling and data plan, the cost of the phone is marked down 60% off its original price. Mel signs up for a data and calling plan when he purchased his phone, and he paid \$300 for the phone.

Quantity A

The full cost of the phone without signing up for a data and calling plan.

Quantity B

The cost of a second phone that costs \$800 without a calling and data plan.

To find the full cost of the phone for quantity A, use the percent change formula:

New Value = (100%-% Change)(Original Value)

The new value is the price of the phone after the discount has been taken, which is \$300. The percent change is -60% because it is a discount and should be subtracted from 100%.

300 = (100%-60%)(Original)

Convert the percents to decimals by moving the decimal to the left twice in each value.

300 = (1-0.6)(Original)

300 = (0.4)(Original)

Divide both sides by 0.4 to find the original value of the phone for quantity A.

300/0.4=\$750=Original

Compare this to quantity B, which is \$800, and quantity B is larger, which makes the answer (B).

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