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Barbara invests $2400 in the National Bank at 5%. How much

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by swerve » Sat Jan 26, 2019 7:59 am
We need to have the equation as follows.

Additional money=x

Therefore, (6/100)*x+144=120+(8/100)*x

Solving for x, x=1200.

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by [email protected] » Sat Jan 26, 2019 10:49 am
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

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by fskilnik@GMATH » Sun Jan 27, 2019 5:30 am
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
Let´s use ALLIGATION, one powerful technique covered in our course!

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$$? = x$$
$${{2400} \over {2400 + x}} = {{8 - 6} \over {8 - 5}} = {{2 \cdot 1200} \over {3 \cdot 1200}}\,\,\,\,\, \Rightarrow \,\,\,\,\,? = x = 3 \cdot 1200 - 2400 = 1200$$


We follow the notations and rationale taught in the GMATH method.

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Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by Brent@GMATPrepNow » Sun Jan 27, 2019 6:02 am
AAPL wrote: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
Barbara invests $2400 in the National Bank at 5%.
So, her annual income for this investment = 5% of $2400 = $120
Let x = the additional money Barbara must invest at 8%
So, her annual income for this investment = 8% of x = 0.08x
So, Barbara's TOTAL annual income = $120 + 0.08x

We want the TOTAL annual income to be equal to 6% of her entire investment.
The TOTAL amount invested = $2400 + x
So, we want her TOTAL annual income to equal 6% of ($2400 + x)
In other words, we want: Barbara's TOTAL annual income = 0.06($2400 + x)

We now have the equation: $120 + 0.08x = 0.06($2400 + x)
Expand right side: 120 + 0.08x = 144 + 0.06x
Subtract 0.06x from both sides to get: 120 + 0.02x = 144
Subtract 120 from both sides to get: 0.02x = 24
Solve: x = 24/0.02 = 2400/2 = 1200

Answer: A

Cheers,
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by Scott@TargetTestPrep » Wed Jan 30, 2019 6:03 pm
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

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