# Strategy 5: Simplify an Arithmetic or Algebraic Representation

Arithmetic and algebraic representations include both expressions and equations. Your facility in simplifying a representation can often lead to a quick solution. Examples include converting from a percent to a decimal, converting from one measurement unit to another, combining like terms in an algebraic expression and simplifying an equation until its solutions are evident.

• This strategy is used in the following two sample questions.

This is a Quantitative Comparison question.

1. Quantity A Quantity B y

(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.

Explanation

Set up the initial comparison: Then simplify:

Step 1: Multiply both sides by 5 to get Step 2: Subtract 3y from both sides to get Step 3: Divide both sides by 2 to get The comparison is now simplified as much as possible. In order to compare 1 and y, note that you are given the information (above Quantities A and B). It follows from that or so that in the comparison the placeholder represents less than (<): .

However, the problem asks for a comparison between Quantity A and Quantity B, not a comparison between 1 and y. To go from the comparison between 1 and y to a comparison between Quantities A and B, start with the last comparison, and carefully consider each simplification step in reverse order to determine what each comparison implies about the preceding comparison, all the way back to the comparison between Quantities A and B if possible. Since step 3 was "divide both sides by 2," multiplying both sides of the comparison by 2 implies the preceding comparison thus reversing step 3. Each simplification step can be reversed as follows:

• Reverse step 3: multiply both sides by 2.
• Reverse step 2: add 3y to both sides.
• Reverse step 1: divide both sides by 5.

When each step is reversed, the relationship remains less than (<), so Quantity A is less than Quantity B. Thus, the correct answer is Choice B, Quantity B is greater.

This is a Numeric Entry question.

1. A merchant made a profit of \$5 on the sale of a sweater that cost the merchant \$15. What is the profit expressed as a percent of the merchant's cost? %
The percent profit is percent, which is 33%, to the nearest whole percent. Thus, the correct answer is 33% (or equivalent).