Strategy 5: Simplify an Arithmetic or Algebraic Representation

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.

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?

Give your answer to the nearest whole percent.

%

Explanation

The percent profit is  percent, which is 33%, to the nearest whole percent. Thus, the correct answer is 33% (or equivalent).

If you use the calculator and the Transfer Display button, the number that will be transferred to the answer box is 33.333333, which is incorrect since it is not given to the nearest whole percent. You will need to adjust the number in the answer box by deleting all of the digits to the right of the decimal point.

Also, since you are asked to give the answer as a percent, the decimal equivalent of 33 percent, which is 0.33, is incorrect. The percent symbol next to the answer box indicates that the form of the answer must be a percent. Entering 0.33 in the box would give the erroneous answer 0.33%.