smartass666 wrote:

M07-Q33

A shop purchased a pair of sunglasses for $120 and was selling it at a price that equaled the purchase price of the sunglasses plus a markup that was 25 percent of the selling price. After some time a shop owner decided to decrease the selling price by 20 percent. What was the shop's gross profit on this sale?

$0

$2

$4

$6

$8

Since the markup is equal to \(\frac{1}{4}\) of the original selling price, and the original selling price is discounted by \(\frac{1}{5}\), the original selling price must be a multiple of 4 and 5 -- in other words, a MULTIPLE OF 20 -- that is greater than the $120 purchase price:

140,

160, 180...

The answer choices indicate that the discounted selling price yields a profit between $0 and $8, inclusive.

Implication:

Reducing one of the values above by \(\frac{1}{5}\) must yield a discounted selling price between $120 and $128, inclusive.

Only the green option is viable:

\(160 - \frac{1}{5}*160 = 160 - 32 = 128.\)

Since the discounted selling price = 128, the profit = 128-120 = 8.

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