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John bought 2 shares and sold them for $96 each...

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John bought 2 shares and sold them for $96 each...

by BTGmoderatorLU » Sun Jan 14, 2018 6:51 am

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John bought 2 shares and sold them for $96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John 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

The OA is C.

I'm really confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
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by DavidG@VeritasPrep » Sun Jan 14, 2018 11:07 am
LUANDATO wrote:John bought 2 shares and sold them for $96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John 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

The OA is C.

I'm really confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
Say the cost of the shares on which John had a 20% profit was 'C.' Thus the cost was C and the profit was .20C. If we add the profit to the cost, we'll have our revenue, thus .20C + C = 96
1.2C = 96
C = 96/1.2 = 80.
Profit = 96 - 80 = 16

Similarly, if the shares on which John had a 20% loss had a cost of X, then the profit would have been -.20X. Now X + (-.20X) = 96
..80X = 96
X = 96/.80
X = 120
Profit = 96 - 120 = -24.

Net: 16 + (-24) = -8. The answer is C
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by DavidG@VeritasPrep » Sun Jan 14, 2018 11:09 am
Note also that when John earns a profit, it means that the initial cost of the stock would have been some value less than the 96 he sold it for. So he's earning 20% of some value LESS than 96.

When John incurs a loss, it means the initial cost of the stock would have been some value greater than 96, so he's losing 20% of some value GREATER than 96.

Taken together, we see that he must have suffered a loss, allowing us to immediately eliminate A, B, and E.
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by Scott@TargetTestPrep » Mon Aug 05, 2019 6:17 pm
BTGmoderatorLU wrote:John bought 2 shares and sold them for $96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John 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

The OA is C.

I'm really confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

For the one share earning a 20% profit, we can set up the following equation in which c = cost:

Profit = 0.2c

96 - c = 0.2c

96 = 1.2c

80 = c

Thus, John made 96 - 80 = 16 dollars on the sale.

For the share with a 20% loss, we can set up the following equation in which c = cost:

Profit = -0.2c

96 - c = -0.2c

96 = 0.8c

120 = c

Thus, John lost 120 - 96 = 24 dollars on the sale.

So, overall he lost 8 dollars.

Answer: C

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