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# John sold 100 shares of stock for $96 per share. For half  Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: Intern Joined: 20 Oct 2009 Posts: 40 Followers: 0 Kudos [?]: 6 [1] , given: 0 John sold 100 shares of stock for$96 per share. For half [#permalink]  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 [Reveal] Spoiler: OA Math Expert Joined: 02 Sep 2009 Posts: 23482 Followers: 3501 Kudos [?]: 26452 [2] , given: 2712 Re: What's the fastest way to asnwer this problem? [#permalink] 31 Jan 2010, 13:49 2 This post received KUDOS Expert's post 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]  31 Jan 2010, 13:53
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: 341 Followers: 1 Kudos [?]: 49 [0], given: 14 Re: What's the fastest way to asnwer this problem? [#permalink] 31 Jan 2010, 19:16 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: 893 Followers: 6 Kudos [?]: 127 [0], given: 33 Re: What's the fastest way to asnwer this problem? [#permalink] 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. 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]  28 Feb 2012, 03:27
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]  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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Re: What's the fastest way to asnwer this problem? [#permalink]  16 Dec 2013, 01:33
Expert's post
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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Re: What's the fastest way to asnwer this problem? [#permalink]  22 Dec 2013, 14:29
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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Re: What's the fastest way to asnwer this problem? [#permalink]  22 Dec 2013, 22:55
Expert's post
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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Re: John sold 100 shares of stock for $96 per share. For half [#permalink] 23 Dec 2013, 01:24 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. _________________ Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score ! Verbal Forum Moderator Joined: 22 Mar 2013 Posts: 915 Location: India GPA: 3.51 WE: Information Technology (Computer Software) Followers: 31 Kudos [?]: 329 [1] , given: 194 John sold 100 shares of stock for$96 per share. For half [#permalink]  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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