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

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John sold 100 shares of stock for $96 per share. For half [#permalink]

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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
[Reveal] Spoiler: OA
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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


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.

Answer: C.
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New post 31 Jan 2010, 14:53
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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
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New post 31 Jan 2010, 20:16
ayeshan wrote:
answer should be C


ayeshan - you look like a spammer to me who is in a rush to grab gmatclub test .

Bunuel/bb - please check his profile
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Re: What's the fastest way to asnwer this problem? [#permalink]

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New post 31 Jan 2010, 23:48
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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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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New post 14 Dec 2013, 14:14
Bunuel - apologies. But, I am struggling on this question from Veritas Arithmetic guide. See, Profit = S.P - C.P and after taking C.P as x for 1 item, I am not getting it right. Can you please explain?
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New post 22 Dec 2013, 15:29
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

After this I struggle. can you please help?
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New post 22 Dec 2013, 23:55
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

After this I struggle. can you please help?


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

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New post 23 Dec 2013, 02:24
simple percetage question...


96=5/4 of x (its better to write in fraction rather in percentage, I have tried in both way, bt it tuk me longer time with decimals)

x=80.

profit is of 16 dollar per share. so 16*50=800.

4/5 of x=96

x=120 (this is the value on which he purchased 50 stocks)

loss of 24 dollar per share....24*50=1200..... so 1200 loss-800 profit=net loss of 400.
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John sold 100 shares of stock for $96 per share. For half [#permalink]

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

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

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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
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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

Answer (C)
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Re: John sold 100 shares of stock for $96 per share. For half [#permalink]

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New post 29 Aug 2016, 08:36
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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Re: John sold 100 shares of stock for $96 per share. For half [#permalink]

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

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New post 29 Aug 2016, 10:41
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]

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New post 16 Oct 2016, 14:32
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$
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Re: John sold 100 shares of stock for $96 per share. For half [#permalink]

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New post 06 Dec 2016, 19:42
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.
Re: John sold 100 shares of stock for $96 per share. For half   [#permalink] 06 Dec 2016, 19:42
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