__Data Sufficiency__

__Data Sufficiency__

Data sufficiency is the process of determining if the provided information is adequate for the purpose. In data sufficiency questions, you don’t have to solve the problem, you just need to check whether or not you can solve the problem using just the given data plus your knowledge of mathematics and everyday facts. These type of questions form an integral part of the competitive exam question papers as they test the understanding of the principles of arithmetic, algebra and geometry.

The questions on data sufficiency are usually divided into three parts in which the first part carries the question statement, while the second and third parts include various conditions or statements that provide clues guiding to answer the question given in first part.

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The basic format of data sufficiency questions asked in the exam is as below:

**Directions**: Each problem consists of a question and two statements numbered I and II giving certain data. You have to choose the correct answer from among the following options (1) to (5) depending on the sufficiency of data given in the statements to answer the question and mark your answer as:

- The statement (I) alone is sufficient to answer the question, but the statement (ii) alone is not sufficient to answer the question
- The statement (II) alone is sufficient to answer the question, but the statement (I) alone is not sufficient to answer the question
- The either statement (I) alone or in statement (II) alone is sufficient to answer the question
- Both statements (I) and (II) together are insufficient to answer the question
- Both statements (I) and (II) together are necessary to answer the question

**Steps to solve data sufficiency questions:**

Due to complicated directions of data sufficiency problems, they appear to be difficult at first glance, but once you get familiar with these directions, you will find these problems easy to solve. The most important thing you should keep in mind while solving the questions of data sufficiency is that you should never assume anything by your own.

The steps for solving these questions are given below:

**Step 1: **Read the question carefully and identify the required information to answer that question. Don’t assume anything except universal facts.

**Step 2:** Treat both statements separately. Combine the first statement with the main statement and try to find the answer.

**Step 3:** If you are unable to find the answer using the first step then take the second statement and combine it with the main statement and try to find the answer.

**Step 4:** If you are still unable to find the answer, add both the statements and the main statement and try to find the answer.

**Step 5:** If even now you can’t find answer, simply tick “both the statements are insufficient”.

Now let’s try to solve some examples on data sufficiency:

**Directions: **Each of the questions given below consists of a question and two statements numbered I and II. You need to decide whether the data provided in the statements are sufficient to answer the question.

- The statement (I) alone is sufficient to answer the question, but the statement (ii) alone is not sufficient to answer the question
- The statement (II) alone is sufficient to answer the question, but the statement (I) alone is not sufficient to answer the question
- The either statement (I) alone or in statement (II) alone is sufficient to answer the question
- Both statements (I) and (II) together are insufficient to answer the question
- Both statements (I) and (II) together are necessary to answer the question

**Example: **What is Rohit’s year of birth?

**Statements: **i. Rohit is 5 years older to his brother.

- Rohit’s birthday is on 25
^{th}June.

**Solution: **Both statement (i) and (ii) together are insufficient to answer the question.

Rohit’s birth year cannot be determined from the data given in both the statements.** **

**Example: **What is the ratio of the cost price to the selling price of a pen?

**Statements:** i. The pen is sold at a profit of Rs.5

- The cost price of the pen is Rs.10

**Solution: **Both statements (i) and (ii) together are necessary to answer the question.

With the data given in two statements together, we can find out both cost and selling price of a pen. So, it is possible to find the ratio using data given in statement (i) and (ii) together.

**Example: **What is the product of two numbers?

**Statements: **i. The second number is greater than the first.

- The ratio of the numbers is 2: 3.

**Solution: **Both statement (i) and (ii) together are insufficient to answer the question.

The product of the numbers cannot be determined by simply using the ratio of two numbers or by having the information that one number is greater than the other.** **

**Example: **What is the average speed of the train?

**Statements: **i. The train travelled 200 km in 4 hours.

- The train halted at two stations.

**Solution: **The statement (i) is alone sufficient to answer the question, but the statement (ii) alone is not sufficient to answer the question.

Statement (i) alone gives the information about the distance and time. Therefore we can determine the average speed while statement (ii) does not provide any distance or time.** **

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**Example: **What is the value of (*x + y*)?

**Statements: **i. *x* is the largest 3 digit number.

*x*is the opposite integer of y.

**Solution: **The Statement (ii) is alone sufficient to answer the question, but the statement (i) alone is not sufficient to answer the question.

** **Statement (i) gives the value of *x* only. Statement (ii) gives (*x = – y*) from which (*x + y*) can be calculated.** **

**Example: **A works in which of the following companies P, Q, R, S and T?

**Statements: **i. A does not work in the same company as either M or N.

- M and N work in companies Q and S respectively.

**Solution: **Both statement (i) and (ii) together are insufficient to answer the question.

** **From statement (ii) m works in Q and N works in company S and according to statement (i), A does not work in company Q or S. So, A works in company P, R or T.** **

**Example: **In a row of five children – Ahana, Maira, Shruti, Garima and Nandini – who is standing in the middle?

**Statements: **i. Garima is to the immediate left of Nandini and Maira is to the immediate right of the Nandini.

- Maira is at the extreme right of the row.

**Solution: **Both statement (i) and (ii) together are necessary to answer the question.

From statement (ii), Maira is at the extreme right of the row and from statement (i), Garima is on the left of Nandini and Nandini is on the left of Maira. So, the order is either Ahana, Shruti, Garima, Nandini and Maira or, Shruti, Ahana, Garima, Nandini and Maira. From both, we can conclude that Garima is in the middle.** **

**Example: **There are 10 identical bags and each bag has the same weight. Find out the weight of one bag.

**Statements: **i. One-fifth the weight of a bag equals 20 kg.

- The weight of three bags and two bags is equal to 100.

**Solution: **The either statement (I) alone or in statement (II) alone is sufficient to answer the question.

From statement (i), it can be derived that the weight of a bag would be 100 kg.

Similarly, from the statement (ii), if it is assumed that the weight of a bag is *x*, then according to the question,

*3x – 2x* *= 100*. So, *x* = 100g.** **

**Example: **How far is Lucknow from Kanpur?

**Statements: **i. Kanpur is 200 km from Lucknow.

- Lucknow is 400 km from Agra.

**Solution: **It is clear from statement (i) that the distance between Lucknow and Kanpur is 200 km. thus, the data in statement (i) alone is sufficient to get the answer, while the data in statement (ii) alone is not sufficient to answer the question.** **

**Example: **The monthly salary of Udit is Rs. 4000. What is the monthly salary of Tarun?

**Statements: **i. Tarun gets Rs. 500 more than Udit’s and his average salary.

- Average salary of Udit and Tarun is Rs. 4500.

**Solution: **The either statement (I) alone or in statement (II) alone is sufficient to answer the question.

From statement (ii), average salary of Udit and Tarun is Rs. 4500. That is their total salary is 9000 and Udit’s salary is 4000 (from question). So, Tarun’s salary is Rs. 5000. From statement (i), we know Tarun gets Rs. 500 more than their average salary so, from this also, we can conclude the monthly salary of Tarun.

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**Example: **Which direction is Suraj facing now?

**Statements: **i. If Suraj turns to his right and again turns to his right, he will be facing north.

- If Suraj walks some distance and turns left and again walks some distance, then his face will be towards the left of Sanket who is facing south.

**Solution: **The either statement (I) alone or in statement (II) alone is sufficient to answer the question.

From statements (i) and (ii), we can conclude that the direction which Suraj is facing now is south, A person facing south will face north on taking right turns twice and a person facing left of another person facing south is in his/her east and a person facing east on taking a left turn must be facing south.

## Author-

### Kajal Pardeshi,

Aptitude Trainer

Seven Mentor

(Banking Department)

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