A trader has lost 15% on a $10,000 investment. He is going to buy a st

Question

A trader has lost 15% on a $10,000 investment. He is going to buy a stock that is guaranteed a 12% gain. How much should he invest in this stock so that the net gain for the entire portfolio is 4%?

A. $23,750
B. $15,833
C. $13,750
D. $10,700
E. $10,000

0akshay0 · Answer

let x be the amount that must be invested

(-0,15*10000+0,12*x)/(10000+x)=0,04 => (-1500+0,12x)/(10000+x)=0,04 =>-1500+0,12x=400+0,04x =>0,08x=1900 => x=23750
Answer is A

kwindi · Answer

let x be the amount that must be invested

(-0,15*10000+0,12*x)/(10000+x)=0,04 => (-1500+0,12x)/(10000+x)=0,04 =>-1500+0,12x=400+0,04x =>0,08x=1900 => x=23750
Answer is A

0akshay0 · Answer

since the trader lost 15% on 10000. He was left with 8500. now 12% of x = 0.12 * 23750 (according to your answer) = 2850.... so 2850 + 8500 = 11350 (11350-10000)/10000 = 1350/10000 = 13.5% and not 4% net gain. hope its clear

Kudos if you liked it 8-)

kwindi · Answer

The portfolio consists of 2 assets: one in which we invested 10000 and the second one in which we invest x. Therefore, the net gain is 0,12*x-0,15*10000=0,12x-1500. Meaning that the return is (0,12x-1500)/(total investment=10000+x)=0,04

aniket1025 · Answer

A 23750 ✓

-1500 + 0.12x = 0.04x ( 10000+x)

Where x is the amount he decides to invest in stock that has return of 12%

Sent from my ONEPLUS A3003 using  GMAT Club Forum mobile app

Salv · Answer

Let the amount to be invested be x. So,

12% of x - 1500 = 4% of (10000 + x){the amount invested at 12% needs to make up for the $1500 loss to give an overall 4% gain}

12% of x -1500 = 400 + 4% of x 
12% of x - 4% of x = 1900
8% of x = 1900

x = 1900 *100/8 
x = 23750

0akshay0 · Answer

Understood what I was missing thanks

corrected my answer

KrishnakumarKA1 · Answer

let the investment in this stock be x
loss is 1500
profit from second stock = 0.12x
net profit = 0.12x-1500 = 0.04(10000+x)

solving for x, we get x = 23750

Option A

Fdambro294 · Answer

You can use Weighted Average concepts to solve

The Data Points are the %Returns on each investment, “weighted” by the amount invested

The overall Net Return on Investment is the Weighted Average.

We can determine the Proportion of $10,000 to $X unknown dollars at a 12% return

+12% - (-15%) = 27

+12% - 4% = 8 ———> “weighting” of the 10,000 investment

4% - (-15%) = 19 ———> “weighting” of the $X unknown investment with a 12% return

At this point, you can set up a proportion:

8 / 19 = $10,000 / $X

8X = (19) (10,000)

X = (19) (1,250) =. 23,750

(A)
$23,750

Posted from my mobile device

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A trader has lost 15% on a $10,000 investment. He is going to buy a st

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A trader has lost 15% on a $10,000 investment. He is going to buy a st

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards