percent

buoyant 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 half his shares -- 50 of the 100 shares -- this represented a 20% profit.
In other words, $96 is equal to 120% of the purchase price of each of these shares:
96 = 1.2x
960 = 12x
x = 80.
Since the selling price = 96 and the purchase price = 80, the profit per share = 96-80 = 16.
Total profit for these 50 shares= 50*16 = 800.

For the other half -- the remaining 50 shares -- this represented a 20% loss.
In other words, $96 is equal to 80% of the purchase price of each of these shares:
96 = 0.8y
960 = 8y
y = 120.
Since the selling price = 96 and the purchase price = 120, the loss per share = 120-96 = 24.
Total loss for these 50 shares= 50*24 = 1200.

Net loss = 1200-800 = 400.

The correct answer is C.

buoyant 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

[spoiler]OA: C[/spoiler]

One thing that could jump out at you on this problem is that the answer is going to be a net loss.

Why?

Because on equal numbers of shares the profit was 20 percent of a smaller number below 96 and the loss was 20 percent of bigger number greater than 96. 20 percent of a bigger number is greater than 20 percent of a smaller number. So the loss has to outweigh the profit.

Seeing this kind of relationship can be as important as knowing how to do the math, especially when doing a data sufficiency question where the relationship may be all that is really needed to determine the answer.

Lets break up the shares into the two groups.

Winning Group:
Purchase Price * (1 + % Increase) = Sale Price
Purchase Price * 1.2 = 96
Purchase Price = 80

Losing Group:
Purchase Price * (1 - % Decrease) = Sale Price
Purchase Price * 0.8 = 96
Purchase Price = 120

Each group represents half of the portfolio. As a result the average purchase price = (80+120)/2 = 100

PnL = # shares * (Average Sale Price - Average Purchase Price)
PnL = 100 * (96 - 100)
PnL = -400

Here's a quick way.

Suppose John sold one share for a 20% profit and one share for a 20% loss. Also suppose that he paid x for the share on which he profited and y for the share on which he lost.

Profit::
Cost = x
Sale = 96 = 1.2x

96 = 1.2x gives us 960 = 12x or 80 = x

Loss::
Cost = y
Sale = 96 = .8y

96 = .8y gives us 960 = 8y or 120 = y

So he PAID x + y, or $200 for the two stocks, but he only GOT 96*2 or $192 for the two stocks. Hence he LOST $8 for the two stocks, or an average of $4 per stock.

Losing $4 per stock translates to losing $400 for 100 stocks, so C.