Problem Solving

Hi All,

We're told that Barbara invests $2400 in the National Bank at 5%. We're asked how much additional money she must invest at 8% so that the TOTAL annual income will be equal to 6% of her entire investment. This question can be approached in a number of different ways, including by TESTing THE ANSWERS.

To start, IF Barbara invested another $2400 at 8%, then the percentage return would be equal to the average of the two percents: (5% + 8%)/2 = 13%/2 = 6.5%. This is too high though (it's supposed to be 6%). This means that Barbara would have to invest LESS than $2400 at 8%. Eliminate Answers B, D and E. With two answers remaining, we can TEST either one - if it's a match, then it's the correct answer; if it's not the match, then the remaining answer is the correct answer.

Let's TEST Answer C: $1000
IF... Barbara invests $1000 at 8%, then she'll receive (.08)($1000) = $80
$2400 at 5% = (.05)($2400) = $120
Total Interest = $80 + $120 = $200
Total Invested = $2400 + $1000 = $3400
$200/$3400 = 1/17 = a little less than 6%. This is NOT a match (we need 6% exactly), so the final Answer must be A. You can still prove that Answer A is correct with the same general arithmetic that we did above...

IF.. Barbara invests $1200 at 8%, then she'll receive (.08)($1200) = $96
$2400 at 5% = (.05)($2400) = $120
Total Interest = $96 + $120 = $216
Total Invested = $2400 + $1200 = $3600
$216/$3600 = 24/400 = 6/100 = 6%

Final Answer: A

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

AAPL wrote:GMAT Paper Tests

Barbara invests $2400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?

A. 1200
B. 3000
C. 1000
D. 3600
E. 2400

OA A

We can let x = the amount of money invested at 8%, making her entire investment equal to (2,400 + x).

We can create the following equation:

0.05(2,400) + 0.08x = 0.06(2,400 + x)

120 + 0.08x = 144 + 0.06x

0.02x = 24

2x = 2400

x = 1,200

Answer: A