# Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation

When a figure is given in a problem, it may be effective to express relationships among the various parts of the figure using arithmetic or algebra.

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

This is a Quantitative Comparison question.

1. Quantity A Quantity B PS SR

(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

From the figure, you know that PQR is a triangle and that point S is between points P and R, so and You are also given that However, this information is not sufficient to compare PS and SR. Furthermore, because the figure is not necessarily drawn to scale, you cannot determine the relative sizes of PS and SR visually from the figure, though they may appear to be equal. The position of S can vary along PR anywhere between P and R. Following are two possible variations of the figure, each of which is drawn to be consistent with the information ##### Variation 2  Note that Quantity A is greater in Variation 1 and Quantity B is greater in Variation 2. Thus, the correct answer is Choice D, the relationship cannot be determined from the information given.

This is a Numeric Entry question.

1.

Results of a Used-Car Auction

Small Cars Large Cars
Number of cars offered 32 23
Number of cars sold 16 20
Projected sales total for cars offered (in thousands) \$70 \$150
Actual sales total (in thousands) \$41 \$120

For the large cars sold at an auction that is summarized in the table above, what was the average sale price per car?

\$ Explanation

From the table above, you see that the number of large cars sold was 20 and the sales total for large cars was \$120,000 (not \$120). Thus the average sale price per car was The correct answer is \$6,000 (or equivalent).

(In numbers that are 1,000 or greater, you do not need to enter commas in the answer box.)