If a merchant purchased a sofa from a manufacturer for $400

Hi All,

We're told that a merchant purchased a sofa from a manufacturer for $400 and then sold it. We're asked for the selling price of the sofa. This question is based around a mix of basic Arithmetic and Algebra.

(1) The selling price of the sofa was greater than 140 percent of the purchase price.

Fact 1 tells us that the selling price was GREATER than 140% of $400, so there's clearly a limitless number of possibilities. There's no way to determine the exact selling price, although we know that it would be MORE than (1.4)($400) = $560.
Fact 1 is INSUFFICIENT

(2) The merchant's gross profit from the purchase and sale of the sofa was 1/3 of the selling price.

Based on the information in Fact 2, we can create the following equation:
Profit = (Selling Price) - (Cost)
(1/3)(P) = (P) - 400

This is one variable and one equation, so you CAN solve for P (and there will be just one answer. If you did the extra steps, you would come up with the following:

P = 3P - 1200
1200 = 2P
600 = P
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

AbeNeedsAnswers wrote: ↑

Fri May 03, 2019 4:09 pm

If a merchant purchased a sofa from a manufacturer for $400 and then sold it, what was the selling price of the sofa?

(1) The selling price of the sofa was greater than 140 percent of the purchase price.
(2) The merchant's gross profit from the purchase and sale of the sofa was 1/3 of the selling price.

B

Source: Official Guide 2020

Solution:

Question Stem Analysis:

We need to determine the selling price of the sofa, given that the purchase price of the sofa from the manufacturer was $400.

Statement One Alone:

With statement one, we see that the selling price of the sofa was greater than 400 x 1.4 = $560. However, since we can’t determine the exact selling price of the sofa, statement one alone is not sufficient.

Statement Two Alone:

If we let s be the selling price of the sofa, we can create the equation:

s - 400 = s/3

2s/3 = 400

s = 400 x 3/2 = 600

We see that the selling price of the sofa was $600. Statement two alone is sufficient.

Answer: B