Mixtures Problem

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prachi18oct: Master | Next Rank: 500 Posts; Posts: 269; Joined: Sun Apr 27, 2014 10:33 pmFollowed by: 5 members; Thanked: 8 times

by prachi18oct » Mon Jul 13, 2015 7:47 pm

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

How to solve by alligation and other quicker methods?

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Source: Beat The GMAT — Problem Solving | Mon Jul 13, 2015 7:47 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jul 13, 2015 8:17 pm

prachi18oct wrote: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

A -15% loss is MIXED with a +12% profit to yield an AVERAGE profit of +4%.
The following approach is called alligation -- a very good way to handle MIXTURE PROBLEMS.

Let F = the first investment and S = the stock.

Step 1: Plot the 3 percentages on a number line, with the percentages for F and S on the ends and the percentage for the mixture in the middle.
F -15% ------------ +4% ----------- S +12%

Step 2: Calculate the distances between the percentages.
F -15% -----19----- +4% -----8----- S +12%

Step 3: Determine the ratio in the mixture.
The required ratio of F to S is equal to the RECIPROCAL of the distances in red:
F : S = 8:19.

Since the actual value of F = 10,000, we can set up the following proportion:
8/19 = 10,000/S
8S = 190,000
S = 23,750.

The correct answer is A.

For a similar problem, check here:
https://www.beatthegmat.com/ratios-fract ... 15348.html

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by [email protected] » Tue Jul 14, 2015 9:54 am

Hi praci18oct,

This question is perfect for TESTing THE ANSWERS.

Since the initial $10,000 lost 15%, and the new investment is only a 12% gain, then far MORE than $10,000 must be invested in this new investment for the entire portfolio to have a net GAIN of 4%. Among the answer choices, I would TEST Answer B first....

The LOSS on the first $10,000 is (.15)(10,000) = $1,500

IF....the second investment was $15,833...
the 12% of $15,833 is approximately a $1,900 gain

The NET gain is $400 on $25,833
4% of $25,833 is approximately $1,000, so this net gain is TOO SMALL
Eliminate B.

Given the patterns involved, there's only one answer left that makes sense...

Final Answer: A

Here's the proof though....

12% of $23,750 is $2850
The NET gain is $1350
4% of 33,750 is $1350
This is a MATCH, so this MUST be the correct answer.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Jim@StratusPrep: MBA Admissions Consultant; Posts: 2279; Joined: Fri Nov 11, 2011 7:51 amFollowed by: 266 members; Location: New York; Thanked: 660 times; GMAT Score:770

by Jim@StratusPrep » Wed Jul 15, 2015 4:56 am

The distance from -15% to +4 percent is 19 and the distance from +12% to +4% is 8. You can flip the distances and this gives you a ratio of the dollar amounts of 8 : 19 for the loss : gain.

The loss was 10,000, which means the gain must be more than twice this amount. Only A is large enough.

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nikhilgmat31: Legendary Member; Posts: 518; Joined: Tue May 12, 2015 8:25 pm; Thanked: 10 times

by nikhilgmat31 » Tue Jul 28, 2015 4:57 am

Please make it a simple equation of this problem.

additional money invested = $x on top of $10000

4% of (10000 + x) = 12 % of x - 1500
400 + 4% of x = 12% of x -1500

1900 = 8 % of x

x = 1900 *100/8

solving for x gives 23750

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