Question

A designer purchased 20 mannequins that each cost an equal amount and then sold each one at a constant price. What was the designer's gross profit on the sale of the 20 mannequins?
(1) If the selling price per mannequin had been double what it was, the gross profit on the total would have been $2400.
(2) If the selling price per mannequin had been $2 more, the store's gross profit on the total would have been $440.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are NOT sufficient.

Hint:

In Data Sufficiency, always write down the algebraic expression you need to find. Then, analyze each statement to see if it allows you to solve for that specific expression, even if you can't solve for the individual variables.

Answer 1

The Correct Option is B

Step 1: Understanding the Question
Let the cost per mannequin = \(C\) and the selling price per mannequin = \(S\).
Number of mannequins = 20.
Total cost = \(20C\).
Total revenue = \(20S\).
Gross profit (GP) = Revenue – Cost = \(20S - 20C = 20(S - C)\).
We need to determine \(GP\).

Step 2: Analysis of Statement (1)
If the selling price were doubled (i.e., \(2S\)), then:
\[ \text{New Revenue} = 20 \times (2S) = 40S \] \[ \text{New Profit} = 40S - 20C = 2400 \] Simplify:
\[ 2S - C = 120 \] This is a single equation in two variables \(S\) and \(C\).
Different values of \(S, C\) can satisfy this, giving different profits.
Hence, Statement (1) alone is not sufficient.

Step 3: Analysis of Statement (2)
If the selling price were \(S+2\), then:
\[ \text{New Revenue} = 20(S+2) \] \[ \text{New Profit} = 20(S+2) - 20C = 440 \] Expanding:
\[ 20S + 40 - 20C = 440 \] \[ 20S - 20C = 400 \] This directly gives the gross profit.
Thus, Statement (2) alone is sufficient.

Step 4: Final Answer
Statement (1) alone → Not sufficient.
Statement (2) alone → Sufficient.

Correct Option: (B) Statement (2) alone is sufficient.