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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 ##### Most Helpful Expert Reply Math Expert V Joined: 02 Sep 2009 Posts: 60644 Re: What's the fastest way to asnwer this problem? [#permalink] ### Show Tags 8 9 GMATFIGHTER 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

Strange wording. Anyway:

Cost of the profitable stock: x=96/1.2=80, so profit from it 96-80=16. Total profit 50*16=800
Cost of the non-profitable stock: y=96/0.8=120, so loss from it 96-120=-24. Total loss 50*(-24)=-1200

Total loss: 800+(-1200)=-400.

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Re: What's the fastest way to asnwer this problem?  [#permalink]

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GMATFIGHTER 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 Would you guys please show me a short cut to answer this problem? A much faster approach would be appreciated! Thanks! 50 shares for 20 % loss and 50 share for 20 % profit. For profit - > 96 = 120 % of x hence x = 80 , total profit = 50 x (96-80) = 50 x 16 For Loss - > 96 = 80 % of y hence y = 120, total loss = 50 x (120-96) = 50 x 24 Net loss = 50 x24 - 50 x 16 = 50 (8) = 400 answer should be c Director  Joined: 03 Sep 2006 Posts: 602 Re: What's the fastest way to asnwer this problem? [#permalink] ### Show Tags GMATFIGHTER 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

Would you guys please show me a short cut to answer this problem? A much faster approach would be appreciated!
Thanks!

Total Selling Price = $9600 For 50 shares it is 20% profit and for other 50 it is 20% Loss. For 20% profit 6/5*cost = 9600 cost=$80

For 20% Loss
4/5*cost = 9600

cost= $120 Total cost =$80*50 + $120*50 = 10,000 Therefore Loss = 10,000 - 9600 =$400
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Re: What's the fastest way to asnwer this problem?  [#permalink]

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2
20% profit and 20% loss = $$\frac{6}{5}*\frac{4}{5} = \frac{24}{25}$$ OR 4% loss

$$\frac{24}{25}x=9600$$ .... [where x is the cost]

total loss [4% of cost] = $$9600*\frac{25}{24x}*\frac{4}{100} = 400$$

ans: 400
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Re: What's the fastest way to asnwer this problem?  [#permalink]

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Sure...

S.P of 1 share = 96
S.P of 50 shares = 50 * 96 = 4800

C.P of 1 share = x
C.P of 50 shares = 50x

Profit = 4800 - 50x --------------------[S.P - C.P] = 20 % profit

20% profit = 4800 - 50x

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Re: What's the fastest way to asnwer this problem?  [#permalink]

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enigma123 wrote:
Sure...

S.P of 1 share = 96
S.P of 50 shares = 50 * 96 = 4800

C.P of 1 share = x
C.P of 50 shares = 50x

Profit = 4800 - 50x --------------------[S.P - C.P] = 20 % profit

20% profit = 4800 - 50x

First of all, John sold ALL 100 shares of stock for $96 per share, not only 50 of them. Next, cost (CP) of the profitable stock was 96/1.2 =$80 and the cost of the non-profitable stock was 96/0.8 = $120. Thus the profit was 50*(96-80) =$800 and the loss was 50*(120-96) = $1,200, which give s the overall loss of$400.

Hope it's clear.
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1
One will always have loss in such case;

Direct formula:

Total loss amount = $$\frac{2 X P^2}{(100^2 - P^2)$$

Total loss % = $$\frac{P^2}{100^2}$$

X = common sales price of two different items = in this case 96x50
P = % loss = % gain = in this case 20
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sabrina3509 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 Could you show a simple step by step for solving and then also show the most efficient method for solving? 50 shares for$96 gave 20% profit.
This means Cost of each share = $80. Net cost of 50 shares =$4000

50 shares for $96 gave 20% loss. This means cost of each share =$120
Net cost of 50 shares = $6000 Total net cost = 6000 + 4000 =$10000
Total net seeing price = 96*100 = 9600

Hence there is a loos of $400 Correct Option: C Veritas Prep GMAT Instructor V Joined: 16 Oct 2010 Posts: 10011 Location: Pune, India Re: John sold 100 shares of stock for$96 per share. For half  [#permalink]

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GMATFIGHTER 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 With the same selling price, if we have a profit of a% on one and a loss of a% on another, in all we always have a loss of (a^2/100)%. This is discussed in detail here: http://www.veritasprep.com/blog/2014/04 ... n-another/ So here, we have a loss of (20^2/100)% = 4% Cost Price * 96/100 = Selling Price = 96 *100 Cost Price = 10,000 Amount of Loss = 4% of 10,000 =$400

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Re: John sold 100 shares of stock for $96 per share. For half [#permalink] ### Show Tags GMATFIGHTER 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

Very tricky question, consider this question as A person sold the same product for 4800 and on one product he gained 20% and on another product he lost 20%.
In such cases there will always be overall loss and never gain.
So, you can use formula Loss = (2x^2s)/(100^2-x^2)
where x = common profit/loss %
s = Selling price

Applying the formula you will get Loss = 2*20*20*4800/(120*80) = 400
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Meenakshi13 wrote:
The direct formula in such cases is : a+b+ab/100 where a and b are profit and loss.
so here a=+20 and b =-20
+20-20+20(-20)/100=4%loss

Hi Meenakshi 13,

Because a and b are equal in the scenario I explained your formula will eventually become x^2/100 which is the formula for OVERALL LOSS %.
The question asks for amount so we will use 2x^2s/(100^2-x^2)
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Re: John sold 100 shares of stock for $96 per share. For half [#permalink] ### Show Tags 1.2x = 96$
x=80
so he purchased 50 shares at the price of 80$/share 0.8y = 96$
y=120 - so he purchased the other 50 at the price of 120

now
50*80 = 4000$50*120 = 100*60 = 6000$
total spent - 10,000$total received - 9,600$
net loss - 400$Current Student B Status: DONE! Joined: 05 Sep 2016 Posts: 347 Re: John sold 100 shares of stock for$96 per share. For half  [#permalink]

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50 shares:

x+0.20x=96
1.2x=96
x=80

Orig: 50x$80/each =$4000
New: 50x$96/each =$4800
------------------------
$800 gain 50 shares: x-0.20x=96 0.80x=96 x=120 Orig: 50x$120/each=$6000 New: 50x$96/each = $4800 -------------------------$1200 loss

Net loss/profit = 800-1200 = 400 loss

C.
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Re: John sold 100 shares of stock for $96 per share. For half [#permalink] ### Show Tags GMATFIGHTER 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.

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Re: John sold 100 shares of stock for $96 per share. For half [#permalink] ### Show Tags Top Contributor GMATFIGHTER 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

Let x be the ORIGINAL price of each share that sold for a 20% PROFIT
So, 1.2x = price of each share that sold for a 20% profit
In other words, 1.2x = $96 So, x = 96/1.2 =$80
So, these shares ORIGINALLY cost $80 each Let y be the ORIGINAL price of each share that sold for a 20% LOSS So, 0.8x = price of each share that sold for a 20% loss In other words, 0.8x =$96
So, x = 96/0.8 = $120 So, these shares ORIGINALLY cost$120 each

Let's first determine how much money John spent to BUY the 100 shares
50 shares at $80 apiece cost$4000
50 shares at $120 apiece cost$6000
TOTAL cost to BUY = $4000 +$6000 = $10,000 Now determine how much money John RECEIVED when we SOLD the 100 shares Since he sold all 100 shares for$96 each, the TOTAL amount received = $9600 So, John SPENT$10,000 and he RECEIVED $9600 This represents a LOSS of$400

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Re: John sold 100 shares of stock for $96 per share. For half [#permalink] ### Show Tags GMATFIGHTER 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

CP of first 50 shares is 96/120*100 = 80 each
CP of next 50 shares is 96/80*100 = 120 each

Total CP of 100 Shares is 80*50 + 1200*50 = 10000

SP of 100 Shares is 9600

Net Loss is 400 , Answer must be (C)
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