Barbara invests $2,400 in the National Bank at 5%. How much additiona

Question

Barbara invests $2,400 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) $2,400

(B) $3,600

(C) $1,000

(D) $3,000

(E) $1,200

Bunuel · Answer

4. Percents and Iterest 
     Theory   
 Math: Number Theory - Percents 
 Percentages, Interest and More 
     Questions   
 Compound Interest Problems 
 DS Questions 
 PS Questions

For more check:
 ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

Hope it helps.

pushpitkc · Answer

If the interest earned is represented as follows
5-----------8
------6------
2-----------1

the investment must be done in the ratio 2:1

Therefore, we would need to invest  $1200(Option E)  at a rate of 8% so that the total annual income is 6%
 
 Alternate approach

Let x be the amount invested at 8%

0.05*2400 + 0.08*x = 0.06(2400 + x)  ->  120 + 0.08x = 144 + 0.06x  ->  0.02x = 24  ->  x = \frac{2400}{2} = $1200

KS15 · Answer

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
Answer E

JeffTargetTestPrep · Answer

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: E

EMPOWERgmatRichC · Answer

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 TOTAL investment. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.

To start, the $2400 invested at 5% would earn ($2400)(.05) = $120.

Since Barbara invested $2400 at 5%, IF she were to invest another $2400 at 7%, then the average return for the total investment would be exactly 6% (since the EQUAL investments at 5% and 7% would 'average out' to 6%. Here though, she's investing money at 8% - which means that she would NOT need $2400 invested there (she would need LESS than that, since the investment is at a higher rate). Thus, the answers are narrowed down to either $1000 or $1200. It's interesting that one of the two options is EXACTLY HALF of 2400....

Let's TEST Answer E = $1200 
IF... $1200 were invested at 8%, then 
that investments would earn (1200)(.08) = $96 
the total money invested would equal $2400 + $1200 = $3600 
the total return on the investment would be $120 + $96 = $216

1% of $3600 = $36 
6% of $3600 = $216 
This is an exact match for what we were told, so this MUST be the answer.

Final Answer:  E

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

fskilnik · Answer

Let´s use  ALLIGATION , one powerful technique covered in our course!

https://i.ibb.co/BZ0yxxk/27-Jan19-3z.gif

? = 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.

Regards, 
Fabio.

BrentGMATPrepNow · Answer

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,
Brent

Barbara invests $2,400 in the National Bank at 5%. How much additiona

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