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Bobby bought two shares of stock, which he sold for $96 each. If he had a profit of 20 percent on the sale of one of the shares but a loss of 20 percent on the sale of the other share, then on the sale of both shares combined Bobby had (A) a profit of$10
(B) a profit of $8 (C) a loss of$8

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I may not be understanding the formula for the 'Cost of the stock' do you mind elaborating on this?

i.e. 96/1.2?
Math Expert V
Joined: 02 Sep 2009
Posts: 59236
Re: Bobby bought two shares of stock, which he sold for $96 each. If he [#permalink] ### Show Tags 2 Yellow22 wrote: I may not be understanding the formula for the 'Cost of the stock' do you mind elaborating on this? i.e. 96/1.2? He had a profit of 20% on the sale of the first stock, so if he bought it for$x then x+0.2x=1.2x=96 --> x=96/1.2=80 --> profit 96-x=96-80=16;

He had a loss of 20% on the sale of the second stock, so if he bought it for $y then y-0.2y=0.8y=96 --> y=96/0.8=120 --> loss y-96=120-96=24; Overall loss: 24-16=8. Hope it's clear. _________________ Intern  Joined: 19 Oct 2010 Posts: 6 Re: Bobby bought two shares of stock, which he sold for$96 each. If he  [#permalink]

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That helps! Thank you so much!
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Yellow22 wrote:
Bobby bought 2 shares, and which he sold for $96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares Bobby had... A) a profit of 10 B) a profit of 8 C) a loss of 8 D) a loss of 10 E) neither a profit nor a loss I am no fan of formulas, especially the unintuitive ones still, this little formula has proved useful because of the tedious calculations involved otherwise. When two items are sold at the same price, one at a profit of a% and other at a loss of a%, there will always be a loss of $$\frac{(a^2)}{100} %$$. e.g. Here a = 20, so loss % = $$\frac{(20)^2}{100} %$$ = 4%. Total Sale Price = Cost Price - Loss% of Cost Price 192*(100/96) = Cost Price Cost Price =$200
Loss = $200 -$192 = $8 Get back to me if you need the derivation of the formula above. _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Manager  Joined: 16 Feb 2011 Posts: 172 Re: Bobby bought two shares of stock, which he sold for$96 each. If he  [#permalink]

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VeritasPrepKarishma wrote:
Yellow22 wrote:
Bobby bought 2 shares, and which he sold for $96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares Bobby had... A) a profit of 10 B) a profit of 8 C) a loss of 8 D) a loss of 10 E) neither a profit nor a loss I am no fan of formulas, especially the unintuitive ones still, this little formula has proved useful because of the tedious calculations involved otherwise. When two items are sold at the same price, one at a profit of a% and other at a loss of a%, there will always be a loss of $$\frac{(a^2)}{100} %$$. e.g. Here a = 20, so loss % = $$\frac{(20)^2}{100} %$$ = 4%. Total Sale Price = Cost Price - Loss% of Cost Price 192*(100/96) = Cost Price Cost Price =$200
Loss = $200 -$192 = $8 Get back to me if you need the derivation of the formula above. Hi Karishma, Thanks for letting us know the formula...i wasnt aware of it...nonetheless, can you pls help me understand the usage of the formula in this particular question.. Thanks. Veritas Prep GMAT Instructor V Joined: 16 Oct 2010 Posts: 9799 Location: Pune, India Re: Bobby bought two shares of stock, which he sold for$96 each. If he  [#permalink]

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DeeptiM wrote:
VeritasPrepKarishma wrote:
Yellow22 wrote:
Bobby bought 2 shares, and which he sold for $96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares Bobby had... A) a profit of 10 B) a profit of 8 C) a loss of 8 D) a loss of 10 E) neither a profit nor a loss I am no fan of formulas, especially the unintuitive ones still, this little formula has proved useful because of the tedious calculations involved otherwise. When two items are sold at the same price, one at a profit of a% and other at a loss of a%, there will always be a loss of $$\frac{(a^2)}{100} %$$. e.g. Here a = 20, so loss % = $$\frac{(20)^2}{100} %$$ = 4%. Total Sale Price = Cost Price - Loss% of Cost Price 192*(100/96) = Cost Price Cost Price =$200
Loss = $200 -$192 = $8 Get back to me if you need the derivation of the formula above. Hi Karishma, Thanks for letting us know the formula...i wasnt aware of it...nonetheless, can you pls help me understand the usage of the formula in this particular question.. Thanks. The formula is that when two items are sold at the same selling price, one at a profit of a% and the other at a loss of a%, there is an overall loss. The loss% = $$\frac{(a^2)}{100} %$$. Bobby bought 2 shares, and which he sold for$96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares Bobby had...

Here the two shares are sold at the same selling price. One at a profit of 20% and the other at a loss of 20%.
So loss % = $$\frac{(20)^2}{100} %$$ = 4%.
But we need the amount of loss.

Total Sale price of the two shares = 2*96 = 192
Since there is a loss of 4%, the 96% of the total cost price must be the total sale price

(96/100)*Cost Price = 192
Cost Price = $200 Loss =$200 - $192 =$8
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Re: Bobby bought two shares of stock, which he sold for $96 each. If he [#permalink] ### Show Tags lets say cost of each shares are x and y respectively. Selling price = 120x/100 and 80y/100 respectively = 96 120x/100 = 96 => x=80 80y/100 = 96 => y =120 => together cost = x+y = 200 together selling price = 2*96 = 192 => loss of$8

Math Expert V
Joined: 02 Sep 2009
Posts: 59236

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Total SP = 2*96
Total CP = CP1

The formula for calculating loss % when SP is same = (x/10) ^2
So here x = 20
%loss = (20/10)^2 = 2^2 = 4% loss

We know SP = 92*2 ( 2 items)
loss % = 4
Now calc CP => SP = CP(1-loss/100) = CP (1-4/100) = CP*96/100

2*96 = CP * 96/100 => CP = 200
Total loss is 4% of CP => 4*200/100 = 8
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Yellow22 wrote:
I may not be understanding the formula for the 'Cost of the stock' do you mind elaborating on this?

i.e. 96/1.2?

SP= 100% of CP + profit
SP= 100% of CP + 20% of CP
SP= 120% of CP

therefore CP= SP/120%
= 96*100/120
= 80

Similarly,

SP= 100% of CP - Loss
= 100% of CP - 20% of CP
= 80% of CP

CP = SP*100/80
=96*100/80
=120
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Re: Bobby bought two shares of stock, which he sold for $96 each. If he [#permalink] ### Show Tags Yellow22 wrote: Bobby bought 2 shares, and which he sold for$96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares Bobby had...

A) a profit of 10
B) a profit of 8
C) a loss of 8
D) a loss of 10
E) neither a profit nor a loss

(Common) Assumption: although not explicitly mentioned, we are dealing with profit of 20% over the cost on the corresponding sale. The same for the loss.

$$?\,\,\,:\,\,\,{\text{profit/loss}}\,\,\left( \ \right)$$

$$1{\text{st}}\,\,{\text{share}}:\,\,\,\,\,96 = \,\,\left( {1 + \frac{1}{5}} \right)\,\,{\text{cost}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{cost}} = \frac{5}{6}\left( {96} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{profit}} = \frac{1}{6}\left( {96} \right) = \underleftrightarrow {\frac96{6}} = 16\,\,\,\left( \ \right)$$

$$2{\text{nd}}\,\,{\text{share}}:\,\,\,\,\,96 = \,\,\left( {1 - \frac{1}{5}} \right)\,\,{\text{cost}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{cost}} = \frac{5}{4}\left( {96} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{loss}} = \frac{1}{4}\left( {96} \right) = \underleftrightarrow {\frac96{4}} = 24\,\,\left( \ \right)$$

$$?\,\, = \,\,\,16 + \left( { - 24} \right) = - 8\,\,\left( \ \right)$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Bobby bought two shares of stock, which he sold for $96 each. If he [#permalink] ### Show Tags Hi All, We're told that Bobby bought 2 shares, which he sold for$96 each, he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share. We're asked to find the TOTAL profit or loss on the sale of the two shares. This question essentially comes down to creating two equations and then solving for the original purchase price of each share.

The 20% profit share --> X + .2X = 96
The 20% loss share --> Y - .2Y = 96

1.2X = 96
12X = 960
X = 960/12 = $80 For the first share, the PROFIT was$96 - $80 =$16

.8Y = 96
8Y = 960
Y = 960/8 = $120 For the second share, the LOSS was$120 - $96 =$24

$16 profit -$24 loss = Total LOSS of $8 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ Intern  B Joined: 09 Apr 2018 Posts: 34 Location: India Schools: IIMA PGPX"20 GPA: 3.5 Re: Bobby bought two shares of stock, which he sold for$96 each. If he  [#permalink]

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Gain = (S.P.) - (C.P.)

Loss = (C.P.) - (S.P.)

Loss or gain is always reckoned on C.P.

Gain Percentage: (Gain %)

Gain % = Gain x 100
C.P.
Loss Percentage: (Loss %)

Loss % = Loss x 100
C.P.
Selling Price: (S.P.)

SP = (100 + Gain %) x C.P
100
Selling Price: (S.P.)

SP = (100 - Loss %) x C.P.
100
Cost Price: (C.P.)

C.P. = 100 x S.P.
(100 + Gain %)
Cost Price: (C.P.)

C.P. = 100 x S.P.
(100 - Loss %)
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Re: Bobby bought two shares of stock, which he sold for 96$[#permalink] ### Show Tags Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: Bobby bought two shares of stock, which he sold for 96$   [#permalink] 15 Oct 2019, 04:06
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