Tricks to Data Sufficiency Problems and Solutions

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In Data Sufficiency problems, a question has two statements labeled A and B, which contain certain data. In these questions, the important point is that you are not required to solve the question but to check that whether the data given in the statements are sufficient to solve the question or not. The statement will be considered sufficient if the answer you obtain is unique. If a question cannot be solved with the help of the statement or it has multiple answers, then the given statement will be insufficient.

Steps to follow while solving Data Sufficiency questions

The first step for solving these questions is that you should take both the statements as individual statements i.e. there is no relation in the statements. To solve the question, take the first statement and check whether the question can be solved by using this statement or not. If you get answer from first statement then it is sufficient.
In the Second Step you need to solve the question with the help of the information given in the second statement. If you are able to solve the question with the second statement as well then this statement is also valid and mark your answer accordingly. There is possibility that first statement has the required information to solve the question but not the second and vice a versa. In this case you will mark the answer as only one statement is sufficient.
Third step; There is still a chance that you are not able to solve the question with the help of given statements individually. In this case, try to solve the question by combining the information given in both the statements together. If you get the answer then mark your answer as both statements are required. If you do not get the answer, then mark your answer as data is insufficient.

Keep one thing in mind that you cannot combine the information given in the statements as long as at least one of the statements is sufficient.

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Data Sufficiency: Solved Questions

DIRECTIONS for the following questions:

Mark (1) if the question can be answered by A alone but cannot be answered by B alone

Mark (2) if the question can be answered by B alone but cannot be answered by A alone

Mark (3) if the question cannot be answered by A or B alone but can be answered by combining the two statements.

Mark (4) if the question can be answered by A alone and B alone

Mark (5) if the question cannot be answered by A or B alone and cannot be answered even by combining the two statements.

Example 1: If n is a prime number between 10 and 20, what is the value of n?

A. n>12

B. n<17

Solution: In this question, you are being asked to determine the value of n. If you know the definition of a prime number, then you can quickly figure out that there are four prime numbers between 10 and 20 ; 11, 13, 17 and 19.

Now consider the two statements and see whether either or both can give you the information you need.

Firstly statement A, it tells you that n is greater than 12, which does not enable you to answer the question uniquely. It still leaves three possible answers (13, 17 and 19). Hence statement A alone is not sufficient.
Now statement B by itself is also not sufficient as if n is less than 17, there are still two possible answers (11 and 13).
Finally, if you combine both the statements, you know that n is greater than 12 and that n is less than 17, only one possible number that fits in these conditions is 13.
Hence the question can be solved with the help of both statements together. So the answer is 3^rd option.

Example 2: In which year was Sohan born?

A. Sohan at present is 25 years younger to his mother.

B. Sohan's Sister, who was born in 1964, is 35 years younger to his mother.

Solution: From both I and II, we find that Sohan is (35 - 25) = 10 years older than his sister, who was born in 1964. So, Sohan was born in 1954.

Since, we are getting unique answer from both statements when combined, so the answer is 3^rd option.

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Data Sufficiency: Key Learning

In this article, you learned how a Data Sufficiency question is asked and what steps are to be followed in order to solve these questions systematically.
In order to get hold on such questions you need to solve variety of questions in order to get exposure to different kind of Data Sufficiency questions. Read the question carefully and then solve for each statement individually and then combine them if required.

Still doubtful about any concept mentioned in the article? Feel free to post in the comment section below.