M47-165

Question

A craft store sold 40 handmade lamps. Each lamp was sold for either $120 or $180. If for each lamp, the selling price was either 25% greater than its cost or 50% greater than its cost, what was the store’s total profit from the 40 lamps?

(1) 16 lamps were sold for $120 each.
 
(2) 24 lamps were sold at a selling price that was 50% greater than cost.

Bunuel · Answer

Official Solution:

A craft store sold 40 handmade lamps. Each lamp was sold for either $120 or $180. If for each lamp, the selling price was either 25% greater than its cost or 50% greater than its cost, what was the store’s total profit from the 40 lamps? 
 
Before evaluating the statements, find the profit for each possible case.
 
 For a $120 lamp: 
 
 25\%  markup:
 
 120 = 1.25 * 	ext{cost} 
 
 	ext{cost} = 96 
 
 	ext{profit} = 120 - 96 = 24 
 
 50\%  markup:
 
 120 = 1.5 * 	ext{cost} 
 
 	ext{cost} = 80 
 
 	ext{profit} = 120 - 80 = 40 
 
 For a $180 lamp: 
 
 25\%  markup:
 
 180 = 1.25 * 	ext{cost} 
 
 	ext{cost} = 144 
 
 	ext{profit} = 180 - 144 = 36 
 
 50\%  markup:
 
 180 = 1.5 * 	ext{cost} 
 
 	ext{cost} = 120 
 
 	ext{profit} = 180 - 120 = 60 
 
So the possible profits are 24, 40, 36, and 60, depending on the selling price and markup.
 
(1) 16 lamps were sold for $120 each.
 
Then 24 lamps were sold for $180 each. But we do not know how many lamps in each price group were sold at a  25\%  markup and how many were sold at a  50\%  markup.
 
Not sufficient.
 
(2) 24 lamps were sold at a selling price that was  50\%  greater than cost.
 
Then 16 lamps were sold at a selling price that was  25\%  greater than cost. But we do not know how many lamps in each markup group were sold for $120 and how many were sold for $180.
 
Not sufficient.
 
(1)+(2) Even together, the statements are not sufficient.
 
For example, suppose all 16 lamps sold for $120 were sold at a  25\%  markup, and all 24 lamps sold for $180 were sold at a  50\%  markup.
 
Then the total profit would be:
 
 16 * 24 + 24 * 60 = 1,824 
 
But suppose all 16 lamps sold for $120 were sold at a  50\%  markup. Then, since 24 lamps total were sold at a  50\%  markup, 8 of the $180 lamps were sold at a  50\%  markup and the remaining 16 were sold at a  25\%  markup.
 
The total profit would be:
 
 16 * 40 + 8 * 60 + 16 * 36 = 1,696 
 
Both cases satisfy both statements, but they give different total profits.
 
Not sufficient.
 
Answer: E

M47-165

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