Investment of d dollars

[alex.gellatly]

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

2d/3
3d/4
4d/3
3d/2
8d/3

[Anurag@Gurome]

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

Tricky Approach:
The interest becomes (2400/600) = 4 times
And the time period is (3/2) of the previous time period

Hence, investment must be d*4*(2/3) = 8d/3

The correct answer is E.

[Anurag@Gurome]

Algebraic Approach:
Interest of d dollars at k% simple interest in 2 year = d*k*2/100 = dk/50
Hence, dk/50 = 600 ---> k = 50*600/d

Let s assume we need to invest D dollars.
Hence, interest of D dollars at k% simple interest in 3 year = D*k*3/100 = 3Dk/100
Hence, 3Dk/100 = 2400

Therefore, D = (800*100)/k = (800*100)/(50*600/d) = 800d/(50*6) = 800d/300 = 8d/3

The correct answer is E.

[sandeep_thaparianz]

+1 for E

[alex.gellatly]

Therefore, D = (800*100)/k = (800*100)/(50*600/d) = 800d/(50*6) = 800d/300 = 8d/3

I'm not following your step here. Where did the 800*100 come from?

[Anurag@Gurome]

Therefore, D = (800*100)/k = (800*100)/(50*600/d) = 800d/(50*6) = 800d/300 = 8d/3

I'm not following your step here. Where did the 800*100 come from?

As, 3Dk/100 = 2400
--> 3Dk = 2400*100
--> D = (2400*100)/(3k) = (800*100)/k

Hope that clears you confusion.

[GMATGuruNY]

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

2d/3
3d/4
4d/3
3d/2
8d/3

PLUG AND CHUG:
1. Choose a good value for k.
2. Use the value of k to determine the value of d.
3. Answer the question and get a target.
4. Determine which answer choice yields the target.

Step 1:
Let the interest rate = 100%:
k=100.

Step 2:
Since $600 is earned over 2 years, $300 is earned each year.
To earn $300 at an interest rate of 100%, the amount invested = $300:
d=300.

Step 3:
To earn $2400 over 3 years, $800 must be earned each year.
To earn $800 at an interest rate of 100%, the amount invested = 800.
This is the target.

Step 4:
Now plug d=300 into the answers to see which yields the target of 800.
A quick scan of the answers reveals that only E works:
8d/3 = 8(300)/3 = 800.

The correct answer is E.