Jackson invested $300,000, dividing it all unequally between Account P

Answer = A. $115,384

Let "x" be invested in scheme P

\(\frac{12x}{100} + \frac{25}{100}(300000-x) = 60000\)

\(x = \frac{15*10^5}{13} = 115***\)

Hi All,

This question is essentially just a Weighted Average question that involves deposits into 2 bank accounts.

We're given a set of facts to work with:
1) The interest on Account P is 12%
2) The interest on Account Q is 25%
3) The total deposit was $300,000
4) The total interest was $60,000

We're asked for the APPROXIMATE amount that was deposited into Account P.

Since the total interest is $60,000, that represents a 20% overall return (since 60,000/300,000 = .2)

P = dollars deposited into Account P
Q = dollars deposited into Account Q

Now we can set up a Weighted Average formula

(.12P + .25Q)/(P+Q) = .20

.12P + .25Q = .2P + .2Q
.05Q = .08P
5Q = 8P
5/8 = P/Q

This means that for every 5 dollars deposited into Account P, 8 dollars was deposited into Account Q. By extension, for every 13 dollars deposited in total, 5 of those dollars were deposited into Account P.

5/13 = X/300,000

13X = 1,500,000

While this calculation will not be "nice", the answer choices are sufficiently 'spread out' that we won't have to do the entire calculation:

1,500,000/13 = 11 _ , _ _ _

At this point, we can stop working. The correct answer must begin with 11......

Final Answer:

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

(300-a)0.25+a0.12=60
75-0.25a+0.12a=60
a=-15/-.13=1500/13~115

Ans (A)

We can let p = the amount in Account P and q = the amount in Account Q. We can create the equations:

p + q = 300,000

and

0.12p + 0.25q = 60,000

Multiplying the second equation by 4, we have:

0.48p + q = 240,000

Subtracting this equation from the first equation, we have:

0.52p = 60,000

p = 60,000/0.52 ≈ 115,384

Answer: A

could not we solve this one with weighted average?

Hi, Camach700,

Yes, you can set up the following Weighted Average formula (where P is the amount of money invested in account P and Q is the amount of money invested in Account Q):

(.12P + .25Q)/(P+Q) = .20

.12P + .25Q = .2P + .2Q
.05Q = .08P
5Q = 8P
5/8 = P/Q

This means that for every 5 dollars deposited into Account P, 8 dollars was deposited into Account Q. By extension, for every 13 dollars deposited in total, 5 of those dollars were deposited into Account P.

5/13 = X/300,000

13X = 1,500,000

While this calculation will not be "nice", the answer choices are sufficiently 'spread out' that we won't have to do the entire calculation:

1,500,000/13 = 11 _ , _ _ _

At this point, we can stop working. The correct answer must begin with 11......

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

We can solve the question using 1 variable or 2 variables. Let's use 1.

Let x = the money (in dollars) placed in Account P
So, $300,000 - x = the money placed in Account Q

Account P earned 12% interest and Account Q earned 25% interest, and Jackson earned a total of $60,000 in interest between the two accounts
We can write: (12% of x) + (25% of 300,000 - x) = 60,000
In other words: 0.12x + 0.25(300,000 - x) = 60,000
Expand: 0.12x + 75,000 - 0.25x = 60,000
Simplify: -0.13x + 75,000 = 60,000
Subtract 75,000 from both sides: -0.13x = -15000
Solve: x = 15,000/0.13 ≈ 115,000

Answer: A

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