GMAT Set 8 Q14

[Abhijit K]

$10,000 is deposited in a certain account that pays r percent annual interest compounded
annually, the amount D(t), in dollars, that the deposit will grow to in t years is given by
D(t) = 10,000 {1+(r/100)}t. What amount will the deposit grow to in 3 years?
(1) D(t) = 11,000
(2) r =10

Answer should be B or D?

[GMATGuruNY]

Statement 1 has been transcribed incorrectly.
It should read as shown below:

$10,000 is deposited in a certain account that pays r percent annual interest compounded annually, the amount D(t), in dollars, that the deposit will grow to in t years is given by D(t) = 10,000 [1+(r/100)}t. What amount will the deposit grow to in 3 years?

(1) D(1) = 11,000
(2) r =10

Disregard the given formula.
To determine the amount in the account after 3 years, we simply need to know the annual interest rate.
Question stem, rephrased:
What is the value of r?

Statement 1: D(1) = 11000
Since the $10000 deposit increases by 10% after 1 year, r=10.
SUFFICIENT.

Statement 2: r=10
SUFFICIENT.

The correct answer is D.

[Brent@GMATPrepNow]

$10,000 is deposited in a certain account that pays r percent annual interest compounded
annually, the amount D(t), in dollars, that the deposit will grow to in t years is given by
D(t) = 10,000[1+(r/100)]t. What amount will the deposit grow to in 3 years?

(1) D(1) = 11,000
(2) r =10

Target question:What amount will the deposit grow to in 3 years?
The formula tells us that, in 3 years, the deposit be worth D(3), which equals 10,000[1+(r/100)]3
To evaluate 10,000[1+(r/100)]3, we need to find the value of r.
So, let's REPHRASE the target question....
REPHRASED target question: What is the value of r?

Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: D(1) = 11,000
In other words, 10,000[1+(r/100)]1 = 11,000
Here we have a linear equation that we COULD solve for r (but we won't actually solve it because that would be a waste of time)
Since we COULD answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: r = 10
PERFECT - this answers the REPHRASED target question.
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent