Some of the topics are commonly asked in all the competitive exams. One of that common topic is data sufficiency. Data sufficiency consists of different types of questions from number system to profit and loss of arithmetic aptitude and geometry. Any question can be asked in data sufficiency.

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## Data Sufficiency

In data sufficiency, there are two options given to you in the form of the statements and you need to determine whether the given statements are enough to find the answer. You need to start by solving the question using the statements one by one and then if you cannot find the answer you need to combine the statements to find the answer.

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).

### Examples Based on Age

1. How old is Ajay in 1997?

Statement I: Ajay is 11 years younger than Sanjay whose age will be a prime number in 1998.

Statement II: Sanjay’s age was a prime number in 1996.

Now, in this question, we can see that in statement I and II it is given that Sanjay’s age was a prime number in 1996 as well as 1998. So, it can be determined that the prime numbers will be consecutive. Thus, there are many pairs that can be formed by having two consecutive prime numbers. These pairs are (3,5), (5,7), (11,13), (17,19), and so on. Thus you cannot find a definite answer.

One thing we can determine that the first two pairs are not possible, because Ajay is 11 years younger than Sanjay. But after that, there are many pairs that can be possible. So, there is not a unique pair that can be determined with the use of the given two statements. Thus, E is the correct option.

### Examples Based on Average

1. What is a student’s overall average in the 4 subjects?

Statement I: The weight of the subjects is as follows: English 4, maths 3, physics 3, and chemistry 1.

Statement II: The student receives 90 in English, 84 in maths, 75 in physics, and 76 in chemistry.

In order to find the average, you need to find the total marks in all the subjects and divide it by the total number of subjects. We will start solving the question by using statements individually. Let’s start with the first statement. In the first statement, the weight of the individual subjects is given to us. Each subject has an individual weight but in order to find the average, we all need the actual marks of the subjects. Thus, the statement I is not enough to answer the question.

In statement II the marks of the individual subjects of the students are given to us. But once again you cannot find the average without the wieghtage of each individual subjects. Thus statement II is also insufficient to determine the answer. Now we will combine both the statements and see whether the required answer can be obtained or not. In the statement, I individual weight of the subjects is given, so the total of the weight age will be 11. We will put this in the denominator. And from statement II we can find the total marks of all the subjects.

Thus, average = (Total marks/total weight) = (90 x 4 + 84 x 3 + 75 x 3 + 76 x 1)/11. So, we can find the required answer using both the statements. The correct answer is C.

## Practice Questions

1. How much did Rahul earn in 1980?

The statement I: Rahul earned Rs. 6500 in 1981 which is 12.5 % more than what he earned in 1980.

Statement II: His wife(who earned half of what he earned) and he earned Rs. 8666.62 together in 1980.

Ans: The correct answer is D.

2. What will be the average speed of the two cars?

Statement I: One car completes 60 kilometers.

Statement II: The other car travels 4 km in one hour.

Ans: The correct answer is A.

3. In a school, there were 82 students who attend class A or class B or both. How many students attend each class?

Statement I: 50 students attend class A only.

Statement II: 32 students attend class B.

Ans: The correct answer is E.

4. Who is the youngest among Rahul, Ramesh, Suresh, and Ajay?

Statement I: Rahul is elder to Ramesh.

Statement II: Suresh and Ramesh are younger than Ajay.

Ans: The correct answer is E.

5. The first term of the sequence is 8. What will be the tenth term?

Statement I: The 11th term is 256.

Statement II: The third term of the sequence is 512.

Ans: The correct answer is E.