Victor invested a total of $800 in 2 stocks. At the end of 1 year, one

Question

Victor invested a total of $800 in 2 stocks. At the end of 1 year, one stock had gained 12% in value, the other stock had lost 4% in value, and the total value of the 2 stocks was $848. How much did Victor invest in the stock that decreased in value?

A. $100
B. $200
C. $300
D. $500
E. $600

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KarishmaB · Accepted Answer

Yes, overall return from the stocks was  \frac{48}{800} * 100 = 6%

Now use weighted averages:

\frac{w1}{w2} = \frac{(-4 - 6)}{(6 - 12)} = \frac{5}{3}  (or draw the scale)

So $500 was invested in the stock that gave 12% and $300 was invested in the stock that gave -4%.

Answer (C)

Weighted Averages video:
 https://www.youtube.com/watch?v=_GOAU7moZ2Q

Bunuel · Answer

Let's denote the amount Victor invested in the stock that decreased in value as x. Therefore, the amount he invested in the stock that increased in value is 800 - x.

The total net gain of both stocks is $48, as the total value went from $800 to $848. Therefore, we'd have:

0.12(800 - x) - 0.04x = 48

12(800 - x) - 4x= 4800

3(800 - x) - x = 1200

2400 - 3x - x = 1200

1200 = 4x

x = 300

Answer: C.

VivekSri · Answer

sayan640 · Answer

KarishmaB  ,  gmatophobia  , Can this question be solved using the method of alligation or any quick short cut ?

sayan640 · Answer

Many thanks  KarishmaB  ...kudos

Posted from my mobile device

sayan640 · Answer

For the sake of others , I am attaching the alligation diagram herewith.
+ 6 % is the overall gain . +12% is to be placed on one side. -4% is to be placed on another side. ( Refer to the diagram attached herewith)
 KarishmaB  , Kindly check.

chillblade · Answer

0.96x+1.12(800−x)=848
0.96x+1.12×800−1.12x=848
0.96x+896−1.12x=848
−0.16x+896=848
−0.16x=−48
x=300

msignatius · Answer

This was doable with a bit of mental maths, so I'll highlight how I did that.

$800 in two stocks - one rises by 12%, the other falls by 4%. The total profit was $48.

The stock that decreased in value - can be quickly found going through the choices.

$100 - If this one lost 4% in value, it lost $4; we'd need the positive-return stock, which will naturally be of the remaining value ($800 - $100) to make 52 (-4 + 52 = 48) and reach the profit amount. Clearly, $700 at 12% profit will exceed 70, so this can't be it.

$200 - at a 4% loss, we have the double of $4, $8 as a loss, requiring the positive-return stock to make us $56; but that won't work when 12% of 600, we clearly know, is above $60.

$300 - at a 4% loss, have have the triple of $4, $12 as loss, requiring the positive-return stock to make us $60; and that's exactly what $500 at 12% makes us. Hence, the answer.

tanvi0915 · Answer

I used algebra to solve this question
x + y = 800
1.12x + 0.96 y = 848
Multiplying eqn 1 by 1.12 and solving to find y
therefore y = 300

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