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Investment of d dollars at k percent simple annual interest?

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by phoenixhazard » Sat Dec 11, 2010 12:51 pm
An investment of d dollars at k percent simple annual interest yields $600 interest over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 interest over a 3-year period?
A) 2d/3
B) 3d/4
C) 4d/3
D) 3d/2
E) 8d/3

OA: E
explain please
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by GMATGuruNY » Sat Dec 11, 2010 2:33 pm
phoenixhazard wrote:An investment of d dollars at k percent simple annual interest yields $600 interest over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 interest over a 3-year period?
A) 2d/3
B) 3d/4
C) 4d/3
D) 3d/2
E) 8d/3

OA: E
explain please
$600 interest over 2 years means 600/2 = 300/year.
Plug in d = 3000, k = 10.
This works because 10% of 3000 = 300.

$2400 over 3 years means 2400/3 = 800/year.
Now we plug d=3000 into all the answer choices to which will yield $800 interest at an annual rate of 10%:

Only answer choice E works:
8d/3 = 8*3000/3 = 8000
10% of 8000 = 800.

The correct answer is E.
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by phoenixhazard » Sat Dec 11, 2010 4:39 pm
GMATGuruNY wrote:
phoenixhazard wrote:An investment of d dollars at k percent simple annual interest yields $600 interest over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 interest over a 3-year period?
A) 2d/3
B) 3d/4
C) 4d/3
D) 3d/2
E) 8d/3

OA: E
explain please
$600 interest over 2 years means 600/2 = 300/year.
Plug in d = 3000, k = 10.
This works because 10% of 3000 = 300.

$2400 over 3 years means 2400/3 = 800/year.
Now we plug d=3000 into all the answer choices to which will yield $800 interest at an annual rate of 10%:

Only answer choice E works:
8d/3 = 8*3000/3 = 8000
10% of 8000 = 800.

The correct answer is E.
How did you know to backsolve? I have trouble determining when to solve using the answers and not trying to find an equation and solve.
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