McGraw-Hill Education GRE 2019

After a 20% increase, the price of a computer is $3,000. What was the

original price of the computer?

SOLUTION: Let o = the original price. Thus

(100% + 20%) × o = $3,000

120% × o = $3,000

1.2o = $3,000

o = $3,0001.2 = $2,500

In this example, many test-takers make the mistake of subtracting 20%

from $3,000 to determine the original price. This approach is wrong

because it confuses which whole the 20% is a piece of: adding 20% to

$2,500 is not the same as taking 20% away from $3,000.

If a quantity decreases by p percent, the new quantity will equal (100 – p)% × the

original quantity.

After a 25% decrease, the price of a car was $24,000. What was the original

price?

SOLUTION: Let p = the original price of the car. Thus

(100% – 25%) × p = $24,000

75% × p = $24,000

0.75p = $24,000

p = $24,0000.75

p = $32,000

Consecutive Percentages

Certain GRE questions will involve more than one percent change to a value.

For example:

On January 1, the price of a certain stock was $400. On January 2, the price

of the stock was 20% greater than it was on January 1. On January 3, the

price was 20% less than it was on January 2. What was the price of the stock

on January 3?

SOLUTION: To answer these questions, you should use the preceding formulas,

but keep the following point in mind: Each successive percent change relates

to the quantity that immediately precedes it, not to the starting quantity.

230 PART 4 ■ MATH REVIEW

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