John sold 100 shares of stock for $96 per share. For half

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

John sold 100 shares of stock for $96 per share. For half

by BTGmoderatorDC » Sun Aug 12, 2018 3:10 pm

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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

OA C

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Sun Aug 12, 2018 3:10 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Tue Aug 14, 2018 6:21 am

BTGmoderatorDC 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

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

by swerve » Tue Aug 14, 2018 9:39 am

Total selling price $9,600

For 50 shares it is 20% profit and for other 50 it is 20% Loss.

For 20% profit, we have
6/5*cost=9,600
cost = $80.

Now, for 20% loss, we have
4/5*cost=9,600
cost = $120.

Thus, total cost = 80*50 + 120*50 = 10,000

Hence, Loss = 10,000 - 9,600 = $400.

Option C is the correct answer. Regards!

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Sat Aug 18, 2018 6:45 pm

BTGmoderatorDC 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's let c = cost and r = revenue. For the shares experiencing a 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 stock.

For the shares experiencing a 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 stock.

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

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]