neer.king wrote:Bobby bought two shares of stock, which sold for $96 each. If he had a profit of 20 percent on the sale of one of the shares but a loss of 20 percent on the sale of the other share, then on the sale of both shares combined bobby had:
a: a profit of $ 10
b: a profit of $ 8
c: a loss of $8
d: a loss of $ 10
e: neither profit nor loss
Many students struggle with this type of question.
An efficient way to solve that involves very little algebra is to GUESS AND CHECK.
Since all of the values in the problem and in the answer choices are integers, the purchase prices are almost certainly each a multiple of a 10.
Stock sold at a 20% profit:
Since this stock is sold at a PROFIT, the purchase price = a multiple of 10 LESS than 96.
90 + .2(90) = 108. Too big.
80 + .2(80) = 96.
Success!
The purchase price = 80.
Profit = 96-80 = 16.
Stock sold at a 20% loss:
Since this stock is sold at a LOSS, the purchase price = a multiple of 10 GREATER than 96.
100 - .2(100) = 80. Too small.
110 - .2(110) = 88. Too small.
120 - .2(120) = 96.
Success!
The purchase price = 120.
Loss = 96-120 = -24.
Profit + loss = 16 + (-24) = -8.
A loss of $8.
The correct answer is
C.
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