Problem Solving

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Tue Dec 21, 2021 6:52 pm

GMAT Prep

Bobby bought two shares of stock, which he 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 a profit nor a loss

OA C

Let x = the ORIGINAL purchase price of the stock that had a PROFIT of 20%
So, 1.2x = the SALE price when Bobby sold the stock for a profit of 20%
Since Bobby sold that stock for $96, we can write: 1.2x = 96
Solve to get: x = $80

Let y = the ORIGINAL purchase price of the stock that had a LOSS of 20%
So, 0.8x = the SALE price when Bobby sold the stock for a loss of 20%
Since Bobby sold that stock for $96, we can write: 0.8x = 96
Solve to get: y = $120

This means the total cost of Bobby's ORIGINAL purchase = $80 + $120 = $200
The total SALE price of the two stocks = $96 + $96 = $192

So, Bobby lost a total of $8 in this transaction.

Answer: C