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 C be the cost per mannequin and S be the selling price per mannequin. The number of mannequins is 20. The total cost is \(20 \times C\). The total revenue is \(20 \times S\). The gross profit (GP) is Total Revenue - Total Cost. We need to find the value of \(GP = 20S - 20C = 20(S - C)\).

Step 2: Analysis of Statement (1)
Statement (1) presents a hypothetical situation. If the selling price were 2S, the new gross profit would be \$2400. The new total revenue would be \(20 \times (2S) = 40S\). The cost remains \(20C\). So, the equation is: \[ 40S - 20C = 2400 \] Dividing by 20 gives: \[ 2S - C = 120 \] This is one equation with two variables, S and C. We cannot use this single equation to find the value of \(20(S - C)\). For example, if S=70, C=20, then 2(70)-20=120. Profit = 20(70-20)=1000. If S=80, C=40, then 2(80)-40=120. Profit = 20(80-40)=800. We don't get a unique answer.
Therefore, Statement (1) ALONE is not sufficient.

Step 3: Analysis of Statement (2)
Statement (2) presents another hypothetical. If the selling price were S + \$2, the new gross profit would be \$440. The new total revenue would be \(20 \times (S + 2)\). The cost remains \(20C\). So, the equation is: \[ 20(S + 2) - 20C = 440 \] Let's expand the equation: \[ 20S + 40 - 20C = 440 \] We can rearrange this to isolate the expression for the actual gross profit: \[ 20S - 20C = 440 - 40 \] \[ 20(S - C) = 400 \] This equation directly gives us the value of the designer's gross profit, which is \$400.
Therefore, Statement (2) ALONE is sufficient.
Step 4: Final Answer
Since Statement (2) alone is sufficient and Statement (1) alone is not, the correct answer is (B).