GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 11 Nov 2019, 14:56 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  ### Show Tags

4
13 00:00

Difficulty:   55% (hard)

Question Stats: 66% (02:12) correct 34% (02:15) wrong based on 497 sessions

### HideShow timer Statistics

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 ##### Most Helpful Expert Reply Math Expert V Joined: 02 Sep 2009 Posts: 58954 Re: What's the fastest way to asnwer this problem? [#permalink] ### Show Tags 8 9 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.

_________________
##### General Discussion
Manager  Joined: 25 Jun 2009
Posts: 226
Re: What's the fastest way to asnwer this problem?  [#permalink]

### Show Tags

2
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

### Show Tags

1
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
_________________
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".
Intern  Joined: 25 Mar 2015
Posts: 8
Schools: ISB '16

### Show Tags

1
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 Intern  Joined: 28 Aug 2016 Posts: 1 Re: John sold 100 shares of stock for$96 per share. For half  [#permalink]

### Show Tags

1
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
Director  Joined: 03 Sep 2006
Posts: 625
Re: What's the fastest way to asnwer this problem?  [#permalink]

### Show Tags

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 Senior Manager  Status: Finally Done. Admitted in Kellogg for 2015 intake Joined: 25 Jun 2011 Posts: 439 Location: United Kingdom Concentration: International Business, Strategy GMAT 1: 730 Q49 V45 GPA: 2.9 WE: Information Technology (Consulting) Re: What's the fastest way to asnwer this problem? [#permalink] ### Show Tags 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? _________________ Best Regards, E. MGMAT 1 --> 530 MGMAT 2--> 640 MGMAT 3 ---> 610 GMAT ==> 730 Math Expert V Joined: 02 Sep 2009 Posts: 58954 Re: What's the fastest way to asnwer this problem? [#permalink] ### Show Tags 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. _________________ Senior Manager  Joined: 06 Aug 2011 Posts: 317 Re: John sold 100 shares of stock for$96 per share. For half  [#permalink]

### Show Tags

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 !
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9764
Location: Pune, India
Re: John sold 100 shares of stock for $96 per share. For half [#permalink] ### Show Tags 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) _________________ 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 > Intern  Status: Vice President Joined: 16 May 2016 Posts: 12 Location: India Concentration: Finance, Strategy GMAT 1: 700 Q48 V38 GPA: 2 WE: Operations (Other) Re: John sold 100 shares of stock for$96 per share. For half  [#permalink]

### Show Tags

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 _________________ Route to 700+ Intern  Status: Vice President Joined: 16 May 2016 Posts: 12 Location: India Concentration: Finance, Strategy GMAT 1: 700 Q48 V38 GPA: 2 WE: Operations (Other) Re: John sold 100 shares of stock for$96 per share. For half  [#permalink]

### Show Tags

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)
_________________
Route to 700+
Board of Directors P
Joined: 17 Jul 2014
Posts: 2498
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: John sold 100 shares of stock for $96 per share. For half [#permalink] ### Show Tags 1.2x = 96$
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$Current Student B Status: DONE! Joined: 05 Sep 2016 Posts: 355 Re: John sold 100 shares of stock for$96 per share. For half  [#permalink]

### Show Tags

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.
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2812
Re: John sold 100 shares of stock for $96 per share. For half [#permalink] ### Show Tags 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

For the 20% profit we have:

Profit = 0.2c

r - c = 0.2c

r = 1.2c

Since r = 96, we have:

96 = 1.2c

80 = c

So the profit was 96 - 80 = 16 dollars per share for 50 shares of stocks.

For the 20% loss we have:

Profit = -0.2c

r - c = -0.2c

r = 0.8c

Since r = 96, we have:

96 = 0.8c

120 = c

So the loss was 120 - 96 = 24 dollars per share for the other 50 shares of stocks

Thus, the total net loss is 24(50) - 16(50) = (24 - 16)(50) = 8(50) = 400 dollars.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4055
Re: John sold 100 shares of stock for $96 per share. For half [#permalink] ### Show Tags Top Contributor 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

Let x be the ORIGINAL price of each share that sold for a 20% PROFIT
So, 1.2x = price of each share that sold for a 20% profit
In other words, 1.2x = $96 So, x = 96/1.2 =$80
So, these shares ORIGINALLY cost $80 each Let y be the ORIGINAL price of each share that sold for a 20% LOSS So, 0.8x = price of each share that sold for a 20% loss In other words, 0.8x =$96
So, x = 96/0.8 = $120 So, these shares ORIGINALLY cost$120 each

Let's first determine how much money John spent to BUY the 100 shares
50 shares at $80 apiece cost$4000
50 shares at $120 apiece cost$6000
TOTAL cost to BUY = $4000 +$6000 = $10,000 Now determine how much money John RECEIVED when we SOLD the 100 shares Since he sold all 100 shares for$96 each, the TOTAL amount received = $9600 So, John SPENT$10,000 and he RECEIVED $9600 This represents a LOSS of$400

Cheers,
Brent
_________________
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4829
Location: India
GPA: 3.5
Re: John sold 100 shares of stock for $96 per share. For half [#permalink] ### Show Tags 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

CP of first 50 shares is 96/120*100 = 80 each
CP of next 50 shares is 96/80*100 = 120 each

Total CP of 100 Shares is 80*50 + 1200*50 = 10000

SP of 100 Shares is 9600

Net Loss is 400 , Answer must be (C)
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Re: John sold 100 shares of stock for $96 per share. For half [#permalink] 15 Aug 2018, 02:00 Go to page 1 2 Next [ 21 posts ] Display posts from previous: Sort by # John sold 100 shares of stock for$96 per share. For half  