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31 Jan 2010, 14:29
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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 [Reveal] Spoiler: OA Math Expert Joined: 02 Sep 2009 Posts: 34420 Followers: 6252 Kudos [?]: 79428 [4] , given: 10016 Re: What's the fastest way to asnwer this problem? [#permalink] ### Show Tags 31 Jan 2010, 14:49 4 This post received KUDOS Expert's post 5 This post was BOOKMARKED 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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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 Senior Manager Joined: 16 Apr 2009 Posts: 339 Followers: 1 Kudos [?]: 114 [0], given: 14 Re: What's the fastest way to asnwer this problem? [#permalink] ### Show Tags 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 _________________ Always tag your question Director Joined: 03 Sep 2006 Posts: 879 Followers: 6 Kudos [?]: 621 [0], given: 33 Re: What's the fastest way to asnwer this problem? [#permalink] ### Show Tags 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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28 Feb 2012, 04:27
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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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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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16 Dec 2013, 02:33
enigma123 wrote:
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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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

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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

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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14 Sep 2014, 08:56
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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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13 Dec 2015, 04:08
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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

Net loss = 50 x24 - 50 x 16 = 50 (8) = 400

Good Explanation...Thx
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09 Jun 2016, 10:42
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? Math Expert Joined: 02 Sep 2009 Posts: 34420 Followers: 6252 Kudos [?]: 79428 [0], given: 10016 Re: John sold 100 shares of stock for$96 per share. For half [#permalink]

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09 Jun 2016, 10:46
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? Merging topics. Please refer to the discussion above. _________________ Optimus Prep Instructor Joined: 06 Nov 2014 Posts: 1653 Followers: 43 Kudos [?]: 339 [0], given: 21 Re: John sold 100 shares of stock for$96 per share. For half [#permalink]

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09 Jun 2016, 11:06
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 _________________ # Janielle Williams Customer Support Special Offer:$80-100/hr. Online Private Tutoring
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09 Jun 2016, 21:46
Expert's post
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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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