IP Practice DS SET – 1
DS: Interest & Growth – Level 1
Directions: Choose the correct option (A-E) based on sufficiency.
1.
What is the simple interest earned on a certain sum?
(1) The principal amount is $2,000.
(2) The annual interest rate is 5% and the time period is 2 years.
(1) The principal amount is $2,000.
(2) The annual interest rate is 5% and the time period is 2 years.
Solution (C):
Formula: \( I = P \times r \times t \).
(1) Gives \( P=2000 \). Missing \( r \) and \( t \). Not sufficient.
(2) Gives \( r=0.05 \) and \( t=2 \). Missing \( P \). Not sufficient.
Combined: We have \( P, r, t \). \( I = 2000 \times 0.05 \times 2 = 200 \). Sufficient.
2.
Is the population of Town X greater than 15,000?
(1) The current population is 12,000 and it will grow by 30% in one year.
(2) The current population is 8,000 and it will double in one year.
(1) The current population is 12,000 and it will grow by 30% in one year.
(2) The current population is 8,000 and it will double in one year.
Solution (D):
(1) New Pop = \( 12000 \times 1.3 = 15600 \). Is \( 15600 > 15000 \)? Yes. Sufficient.
(2) New Pop = \( 8000 \times 2 = 16000 \). Is \( 16000 > 15000 \)? Yes. Sufficient.
3.
How long will it take for an investment to double at simple interest?
(1) The annual interest rate is 10%.
(2) The principal amount is $5,000.
(1) The annual interest rate is 10%.
(2) The principal amount is $5,000.
Solution (A):
To double, Interest must equal Principal (\( I = P \)).
\( P = P \times r \times t \implies 1 = rt \).
(1) \( r = 0.1 \). \( 1 = 0.1t \implies t=10 \). Sufficient.
(2) \( P = 5000 \). Without rate, we can’t find time. Not sufficient.
4.
What is the compound interest accrued in 2 years?
(1) The interest rate is 5% per annum.
(2) The interest is compounded annually.
(1) The interest rate is 5% per annum.
(2) The interest is compounded annually.
Solution (E):
To find the dollar amount of interest, we need the **Principal**.
(1) Gives rate. No Principal. Not sufficient.
(2) Gives compounding frequency. No Principal. Not sufficient.
Combined: We still don’t know if we invested $10 or $1,000,000. Not sufficient.
5.
Did the bacteria population increase by more than 1000?
(1) The initial population was 500.
(2) The population tripled over the time period.
(1) The initial population was 500.
(2) The population tripled over the time period.
Solution (C):
(1) Initial = 500. We don’t know the growth rate. Not sufficient.
(2) Tripled means New = \( 3 \times \text{Initial} \). Increase = \( 2 \times \text{Initial} \). Without knowing Initial, we can’t say if \( 2 \times \text{Initial} > 1000 \). Not sufficient.
Combined: Initial = 500. Increase = \( 2 \times 500 = 1000 \).
Is 1000 **more than** 1000? No, it is equal. We have a definite answer (No). Sufficient.
Score: 0 / 0