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Difficulty:
25%
(medium)
Question Stats:
84% (02:20) correct
16%
(02:50)
wrong
based on 626
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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
2024-01-25_23-19-12.png [ 47.05 KiB | Viewed 7592 times ]
A. $100
B. $200
C. $300
D. $500
E. $600
Attachment:
2024-01-25_23-19-12.png [ 47.05 KiB | Viewed 7592 times ]
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guddo
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
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General Discussion
guddo
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.
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KarishmaB , gmatophobia , Can this question be solved using the method of alligation or any quick short cut ?
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.
+ 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.
Attachments
alligatation_profitNdloss_800.png [ 12.83 KiB | Viewed 6808 times ]
Posts: 6
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
0.96x+1.12×800−1.12x=848
0.96x+896−1.12x=848
−0.16x+896=848
−0.16x=−48
x=300
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Posts: 132
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.
$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.
guddo
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
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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