# Common Misconceptions Involving Percents – Part I

In this article, we’ll examine a common misconception that the GRE often tests. To start things off, try the following question:

Hank bought a bike from a wholesaler and then assigned it a retail price that is 40% greater than the wholesale price. For a sale, Hank reduced the retail price by 15%. The net result is the same as increasing the wholesale price by what percent?

(A) 6

(B) 19

(C) 25

(D) 34

(E) 60

Here, the GRE is testing the common misconception that the net effect can be found by subtracting the percent decrease from the percent increase. Students who fall for this trap subtract 15% from 40% to get a net increase of 25% (answer choice C). This answer is incorrect.

Calculating the Net Effect

An easy approach to calculating net effect is to begin with 100, the most convenient value possible when it comes to percent questions. So, we’ll begin with \$100 as the original wholesale price.

The retail price is 40% greater than the wholesale price.40% of \$100 equals \$40, so the retail price = \$100 + \$40 = \$140.

For the sale, the retail price is reduced by 15%. 15% of \$140 equals \$21, so the sale price = \$140 - \$21 = \$119.

So, if the wholesale price was \$100, and the final sale price is \$119, the net effect is a 19% price increase. The correct answer is B.

This next question doesn’t necessary involve net effect, but it can be solved using the same approach. For an extra challenge, try solving it in your head.

Jan’s annual salary is 60% greater than Sam’s. Pat’s annual salary is 25% greater than Jan’s. Kelly’s annual salary is 10% less than Pat’s. Kelly’s annual salary is what percent greater than Sam’s?

(A) 5

(B) 13.5

(C) 69

(D) 75

(E) 80

It looks like Sam has the lowest salary, AND the question asks for Kelly’s salary in relation to Sam’s. So, let’s say that Sam’s annual salary is \$100

Jan’s annual salary is 60% greater than Sam’s. 60% of \$100 is \$60. So, Jan’s salary = \$100 + \$60 = \$160

Pat’s annual salary is 25% greater than Jan’s. 25% of \$160 is \$40. So, Pat’s salary = \$160 + \$40 = \$200

Kelly’s annual salary is 10% less than Pat’s. 10% of \$200 is \$20. So, Kelly’s salary = \$200 - \$20 = \$180

If Sam’s salary is \$100, and Kelly’s salary is \$180, then Kelly’s salary is 80% greater then Sam’s.