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

I'm confused how to set up the formulas here. Can any experts help?

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ardz24 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 I'm confused how to set up the formulas here. Can any experts help? If he made a 20% profit, then we know that the selling price, 96, was 20% greater than the cost, which we can call C. Algebraically: 96 = C + .2C --> 96 = 1.2C ---> 96/1.2 = C --> 960/12 = C --> 80 = C So, for half the shares, he earned a profit of 96 - 80 = 16. If he incurred a 20% loss, we know that the selling price, 96 was 20% less than the cost, which we can call X. Algebraically: 96 = C - .2C --> 96 = .8C ---> 96/.8 = C --> 960/8 = C --> 120 = C So half the shares he suffered a loss of 96-120 = -24. The average of the profit and loss = [16 + (-24)]/2 ---> -8/2 = -4. At 100 shares: -4 * 100 = -400. The answer is C. (Note you could also say that his total profit is 16*50 = 800. His total loss is 24*50 = 1200. His net is 800-1200 = -400.) _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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ardz24 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 I'm confused how to set up the formulas here. Can any experts help? You can also immediately see that he must have suffered a loss. In order to have earned a profit, the cost must be less than the revenue, so the profit is 20% of some number less than 96. Call this value P. In order to have incurred a loss, the cost be greater than the revenue, so the loss is 20% of some number greater than 96. Call this value L. Clearly, L > P, leaving you with C and E. And E ends up being the trap you fall into if you simply take the difference of P and L and multiply that value by 100. _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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ardz24 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. Answer: C _________________ Jeffrey Miller Head of GMAT Instruction jeff@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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