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John sold 100 shares of stock for $96 per share. For half hi

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John sold 100 shares of stock for $96 per share. For half hi

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John sold 100 shares of stock for $96 per share. For half his shares, this represented a 20% profit; for the other half, this represented a 20% loss. What was the net gain or net loss on this sale of stock?

A. No loss or gain
B. Gain of $400
C. Loss of $400
D. Gain of $800
E. Loss of $800

I'm confused how to set up the formulas here. Can any experts help?

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ardz24 wrote:
John sold 100 shares of stock for $96 per share. For half his shares, this represented a 20% profit; for the other half, this represented a 20% loss. What was the net gain or net loss on this sale of stock?

A. No loss or gain
B. Gain of $400
C. Loss of $400
D. Gain of $800
E. Loss of $800

I'm confused how to set up the formulas here. Can any experts help?
If he made a 20% profit, then we know that the selling price, 96, was 20% greater than the cost, which we can call C. Algebraically: 96 = C + .2C --> 96 = 1.2C ---> 96/1.2 = C --> 960/12 = C --> 80 = C

So, for half the shares, he earned a profit of 96 - 80 = 16.

If he incurred a 20% loss, we know that the selling price, 96 was 20% less than the cost, which we can call X. Algebraically: 96 = C - .2C --> 96 = .8C ---> 96/.8 = C --> 960/8 = C --> 120 = C

So half the shares he suffered a loss of 96-120 = -24.

The average of the profit and loss = [16 + (-24)]/2 ---> -8/2 = -4. At 100 shares: -4 * 100 = -400. The answer is C.

(Note you could also say that his total profit is 16*50 = 800. His total loss is 24*50 = 1200. His net is 800-1200 = -400.)

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ardz24 wrote:
John sold 100 shares of stock for $96 per share. For half his shares, this represented a 20% profit; for the other half, this represented a 20% loss. What was the net gain or net loss on this sale of stock?

A. No loss or gain
B. Gain of $400
C. Loss of $400
D. Gain of $800
E. Loss of $800

I'm confused how to set up the formulas here. Can any experts help?
You can also immediately see that he must have suffered a loss.

In order to have earned a profit, the cost must be less than the revenue, so the profit is 20% of some number less than 96. Call this value P.

In order to have incurred a loss, the cost be greater than the revenue, so the loss is 20% of some number greater than 96. Call this value L.

Clearly, L > P, leaving you with C and E. And E ends up being the trap you fall into if you simply take the difference of P and L and multiply that value by 100.

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ardz24 wrote:
John sold 100 shares of stock for $96 per share. For half his shares, this represented a 20% profit; for the other half, this represented a 20% loss. What was the net gain or net loss on this sale of stock?

A. No loss or gain
B. Gain of $400
C. Loss of $400
D. Gain of $800
E. Loss of $800
For the 20% profit we have:

Profit = 0.2c

r - c = 0.2c

r = 1.2c

Since r = 96, we have:

96 = 1.2c

80 = c

So the profit was 96 - 80 = 16 dollars per share for 50 shares of stocks.

For the 20% loss we have:

Profit = -0.2c

r - c = -0.2c

r = 0.8c

Since r = 96, we have:

96 = 0.8c

120 = c

So the loss was 120 - 96 = 24 dollars per share for the other 50 shares of stocks

Thus, the total net loss is 24(50) - 16(50) = (24 - 16)(50) = 8(50) = 400 dollars.

Answer: C

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