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Sweater question

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by Baldini » Fri Mar 06, 2009 4:08 am
During a one day sale, a store sold each sweater of a certain type for 30$ more than the store's cost to purchase the sweater. How many sweaters were sold during the sale?

(1) During the sale, the total revenue from the sale of these sweaters was 270$
(2) During the sale, the store sold each of these sweaters at a price that was 50% greater than the store's cost to purchase each sweater.

OA is C.
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Source: — Data Sufficiency |

by pakaskwa » Fri Mar 06, 2009 4:42 am
Stmt 1 is obviously insufficient, as we don't know individual price for each sweater.

Stmt 2 alone is not sufficient either, since there's no total sales.

Combine stmt 1 and 2, AND condition from question stem, we know:
- price increased $30 from cost;
- price increased 50% from cost;
- total sales is $270.

So each sweater's cost is $60, sales price is $90, and 3 pieces were sold.

Answer is C.
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by bluementor » Fri Mar 06, 2009 4:45 am
Selling price = Cost + Profit
Profit = $30

Statement 1:
Total revenue = selling price x quantity sold

we don't know the selling price of each sweater, so insufficient.

Statement 2:
Selling price = 1.5 x Cost
So,
1.5 x cost = cost + profit
0.5 x cost = profit
0.5 x cost = 30
cost = 60

but we still can’t work out the quantity sold with knowing the total revenue.

Both statements together:
we know the cost, so selling price = $60 + $30 = $90.
and we know the total revenue = $270

So total quantity sold = total revenue/selling price

Sufficient. Choose C.

-BM-
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