Each Question given below has a problem and two statements numbered I and II giving certain information. You have to decide if the information given in the statements is sufficient for answering the problem.

1. How is D related to A?

I. B is the brother of A.

II. B is D’s son.

(a) if the data in statement I alone are sufficient to answer the question;

(b) if the data in statement II alone are sufficient to answer the question;

(c) if the data either in I or II alone are sufficient to answer the question;

(d) if the data even in both the statements together are not sufficient to answer the question;

(e) if the data in both the statements together are needed;

2. Who is C’s partner in a game of cards involving four players A, B, C and D?

I. D is sitting opposite to A.

II. B is sitting right of A and left of D.

(a) if the data in statement I alone are sufficient to answer the question;

(b) if the data in statement II alone are sufficient to answer the question;

(c) if the data either in I or II alone are sufficient to answer the question;

(d) if the data even in both the statements together are not sufficient to answer the question;

(e) if the data in both the statements together are needed;

3. What day is the fourteenth of a given month?

I. The last day of the month is a Wednesday.

II. The third Saturday of the month was seventeenth.

(a) if the data in statement I alone are sufficient to answer the question;

(b) if the data in statement II alone are sufficient to answer the question;

(c) if the data either in I or II alone are sufficient to answer the question;

(d) if the data even in both the statements together are not sufficient to answer the question;

(e) if the data in both the statements together are needed;

Each Question given below has a problem and three statements numbered I,II and III giving certain information. You have to decide if the information given in the statements is sufficient for answering the problem. Remember out of the three statements, each of them alone can also be sufficient to answer the question. In such cases for example, your answer should be taken as Only I or Only II or Only III and not Only I.

4. Five persons- A, B, C, D and E are sitting in a row. Who is sitting in the middle?

I. B is between E and C

II. B is to the right of E

III. D is between A and E.

(a) I and II together.

(b) II and III together.

(c) I and III together.

(d) I, II and III together.

(e) None of these

5. In which year was Sanjay born?

I. Sanjay is six years older than Gopal.

II. Gopal’s brother was born in 1982.

III. Sanjay’s brother is two years younger than Gopal’s brother who was eight years younger

a) I and II together.

b) II and III together.

c) I and III together.

d) I, II and III together.

e) None of these

6. How many sons does X have?

I. Q and U are brothers of T.

II. R is sister of P and U.

III. R and T are daughters of X.

(a) I and II only.

(b) II and III together.

(c) I, II and III together.

(d) I, II and III together are not sufficient

(e) None of these

**Answer & Explanations**

1. Ans: e. From both the statements together, we find that D is the father of B and B is the brother of A. So, D is the father of A. Thus, both the given statements are needed.

2. Ans: c. Clearly, each of the given statements shows that B is sitting opposite to C or B is the partner of C.

3. Ans: b. Statement II reveals that 17^{th} was a Saturday and therefore, 14^{th} was Wednesday. So, only statement II is needed.

4. Ans: d. From I, the order is E, B, C or C, B, E.

From II, the order is E, B

From III, the order is A, D, E.

Combining the above three, we get the order as: A, D, E, B, C.

Clearly, E is sitting in the middle. So, all the three statements are required.

5. Ans: d. From II, we know that Gopal’s brother was born in 1982.

From III, we find that Gopal’s brother was 8 years younger to him ie, Gopal was born in 1974.

From I, we find that Sanjay is 6 years older than Gopal. Thus, Sanjay was born in 1968.. So, all the three statements are required.

6. Ans: d. The information given in the three statements together is also not sufficient to answer the given question.

**Data Sufficiency Aptitude basics, practice questions, answers and explanations **

**Prepare for companies tests and interviews**

**Introduction: **This section consists of problems in which a question on any topic such as Coding-Decoding, Puzzle Test, Blood Relations, Mathematical calculations etc. is put forward followed by certain statements containing facts providing clues to solve the question.

I. Each Question given below has a problem and two statements numbered I and II giving certain information. You have to decide if the information given in the statements is sufficient for answering the problem. Indicate your answer as

(a) if the data in statement I alone are sufficient to answer the question;

(b) if the data in statement II alone are sufficient to answer the question;

(c) if the data either in I or II alone are sufficient to answer the question;

(d) if the data even in both the statements together are not sufficient to answer the question;

(e) if the data in both the statements together are needed;

**Example:**

1. What is Reena’s rank in the class?

I. There are 26 students in the class.

II. There are 9 students who have scored less than Reena.

Exp: Option (e).

From I and II, we conclude that there are 16 students above Reena in rank. Thus, Reena’s rank is 17th in the class. So, both the statements are necessary.

II. Each Question given below has a problem and three statements numbered I,II and III giving certain information. You have to decide if the information given in the statements is sufficient for answering the problem. Remember out of the three statements, each of them alone can also be sufficient to answer the question. In such cases for example, your answer should be taken as Only I or Only II or Only III and not Only I.

**Example:**

1. How many sons does X have?

I. Q and U are brothers of T.

II. R is sister of P and U.

III. R and T are daughters of X.

(a) I and II only.

(b) II and III together.

(c) I, II and III together.

(d) I, II and III together are not sufficient

(e) None of these

Exp: Option (d).

The information given in the three statements together is also not sufficient to answer the given question.