## Data Sufficiency

Data sufficiency covers many different topics of quantitative aptitude. In data sufficiency, usually, a question is followed by two or three statements. You need to determine whether any of the statements individually or together are required to find the answer. You are not required to do the calculation, you just have to check whether with the help of given data you can find the answer or not. Data sufficiency has many types of questions. And today we will be discussing on CI and SI-based data sufficiency.

In compound interest and simple interest you just have to calculate the rate of interest based on the number of years given to you. The rate of interest and the total amount has to be calculated on the based of the formulas.

### The formula to calculate simple interest

**I = P x R x N/100**, where p is the principal amount, r is the rate of interest, and n is the number of years

### The formula to calculate compound interest

**A = P (1 + R/100) ^{n}**

Here, A is the total amount i.e. principal + interest, P is the principal amount, R is the rate of interest, and N is the number of years. There are other two formulas as well to calculate compound interest quarterly and half-yearly.

Compound interest for quarterly, **A = P(1 + R/100 x 2)² ^{n}**

Compound interest for half-yearly, **A = P(1 + R/100 x 4)^{4n}**

Before solving the questions, here are the directions for the questions:

Each question given will be followed by two statements.

- If statement I alone is sufficient, but statement II alone is not sufficient mark (A)
- Statement II alone is sufficient, but the statement I alone is not sufficient mark (B).
- If both the statements I and II together are sufficient, but neither statements alone is sufficient mark (C).
- Each statement alone is sufficient mark (D).
- If statement I and II together are not sufficient mark (E).

### Solved Examples

1. Find the total worth of Ram’s assets.

The statement I: A compound interest at 10% on his assets, followed by a tax of 4% on the interest, fetches Ram Rs. 1500 this year.

Statement II: The interest is compounded once every four months.

So, as per the data are given to us in this question, we need to find the total worth of Ram’s assets and for that two statements are given to us. We will start solving the question using statements alone and if we are not able to find the answer then we will solve the question using both the statements.

Using statement I, we can see that the compound interest i.e. 10% is given to us. Than 4% interest on this compound interest is also given to us. And this interest will be a total of Rs. 1500. But to calculate the total worth we need to have a duration of the compound interest as well as total amount or the principal amount given to us. This data cannot be found in statement I. Thus, a statement I is insufficient to determine the answer.

In statement II only the duration on which compound interest can be calculated is given to us. But there is no other information or data given which can be useful to find the answer. Thus, statement II is also insufficient to determine the answer. So, both the statements alone cannot determine the answer. But when you combine statement I and II than you can see that all the information is given to us and you can determine the total worth of Ram’s assets. So, the correct answer is option C.

## Practice Questions

Directions for the question are same as above.

1. If today the price of the item is Rs. 3500, what was the price of the item exactly 3 years ago?

The statement I: Today the price of the item is exactly 1.21 times its price exactly 3 years ago.

Statement II: The price of the item increased by 10% during these 3 years.

The correct answer is D.

2. What was Ajay’s yearly income on government bonds of the face value Rs? 50000?

The statement I: The certificates yielded half-yearly interest at 10% per year.

Statement II: Ajay had the bond for 10 years.

The correct answer is A.

3. Find the investment of shopkeeper on 200 antique pieces in Rs.

The statement I: Out of 200 pieces, 38 were broken and he sold the remaining at Rs. 480 per piece.

Statement II: He gained 8% on the investment.

The correct answer is C.

4. Hari decided to lend Manoj a sum of Rs. 5000 at the end of some years. The simple interest charged is 12% per annum. Thus, find the number of years Hari lends the sum of money to Manoj.

Statement I: The total interest at the end of 5 years is Rs.2500.

Statement II: Because of money returned by Manoj t0 Hari, Hari will be able to buy a television of Rs. 9999.

The correct answer is B.