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

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31 Jan 2010, 13:29

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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

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

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

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31 Jan 2010, 13:53

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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

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

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31 Jan 2010, 22:48

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.

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

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14 Dec 2013, 13:14

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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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?

Can you please elaborate or show your work? Thank you.
_________________

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.

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

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14 Sep 2014, 07:56

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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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Piyush K ----------------------- Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison Don't forget to press--> Kudos My Articles: 1. WOULD: when to use?| 2. All GMATPrep RCs (New) Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".

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

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13 Dec 2015, 03:03

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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

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

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13 Dec 2015, 03:08

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Bluefalkon wrote:

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

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

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/

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

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29 Aug 2016, 07:36

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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29 Aug 2016, 09:41

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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