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Worked Examples

Example-1

Bharat’s mother says to Bharat, ‘My mother has a son whose son is Amar.’ How is Amar related to Bharat?

  1. Cousin
  2. Father
  3. Brother
  4. Grandfather

Solution

Bharat’s mother’s mother’s son is Bharat’s uncle. So, Amar is the son of Bharat’s uncle. Hence, Amar is Bharat’s cousin.

 

Answer: (1)
 

 

Example-2

Anil introduces Mohan saying, ‘He is the husband of the granddaughter of the father of my father and my father is the only son to his father’. How is Mohan related to Anil?

  1. Son
  2. Nephew
  3. Brother-in-law
  4. Son-in-law
  5. Brother

Solution

The relationship can be analysed as follows:

  1. Father’s father is grandfather.
  2. Grandfather’s granddaughter is sister.
  3. Sister’s husband is brother-in-law.

Hence, Mohan is Anil’s brother-in-law.

 

Answer: (3)
 

 

Example-3

Pointing to a man in a photograph, a woman said, ‘His brother’s father is the only son of my grandfather’. How is the woman related to the man in the photograph?

  1. Aunt
  2. Daughter
  3. Grandmother
  4. Mother
  5. Sister

Solution

Presume the name of the woman showing the photograph as X and the name of the man in the photograph as Y.

 

Y’s brother’s father means Y’s father and he is the only son of X’s grandfather. This clearly indicates that Y’s father and X’s father is one and the same. So, X is Y’s sister.

 

Answer: (5)
 

 

Example-4

Directions: Six members of Kapoor’s family, A, B, C, D, E and F, are travelling in a sumo.

  1. B is the son of C, but C is not the mother of B.
  2. A and C are married couple.
  3. E is the brother of C.
  4. D is the daughter of A.
  5. F is the brother of B.
 
  1. How many children does A have?
    1. One
    2. Three
    3. Four
    4. Two
    5. None of these
  2. How is E related to B?
    1. Brother
    2. Uncle
    3. Father
    4. Cannot be determined
    5. None of these
  3. Who is the mother of B?
    1. A
    2. E
    3. D
    4. F
    5. None of these
  4. Which of the following is a pair of females?
    1. B, D
    2. A, E
    3. A, D
    4. D, F
    5. None of these
  5. How many males are there in Kapoor’s family?
    1. 3
    2. 5
    3. 2
    4. 1
    5. 4
  6. Who is the wife of E?
    1. A
    2. F
    3. B
    4. Cannot be determined
    5. None of these

Solution

In this example, we are required to establish the relationship within the whole family and not just between two individuals. If we construct a family tree, it enables us to answer all the questions quickly and accurately.

 

All the statements in this example are actual information. Statements (i) and (iv) provide information regarding parent–child relationship. We can start analysing with either of these two statements. We shall start with statement (iv). D is the daughter of A. On representing this relation, the family tree starts as given below:

 

Description: 101905.png

 

Next go to the statement (ii). A and C are married couple.

 

Description: 101922.png

 

Now, statement (i) states that B is the son of C, but C is not the mother of B. From this it is clear that C is the father of B. This means C is a male and hence, A must be female.

 

Description: 101946.png

 

According to statement (iii), E is the brother of C and according to statement (v), F is the brother of B. The final family tree now appears as shown below.

 

 

Description: 102020.png

 

With the help of the above family tree, we can answer all the questions.

 

Following are the answers to the questions.

 

Answers:

  1. (2)
  2. (2)
  3. (1)
  4. (3)
  5. (5)
  6. (4)
 

Example-5

Directions:

  1. A, B, C, D, E and F are six members of Mehta’s family.
  2. There are two married couples.
  3. B is an engineer and the father of E.
  4. F is the paternal grandfather of C and is a doctor.
  5. D is the paternal grandmother of E and is a housewife.
  6. There is one engineer, one doctor, one teacher, one housewife and two students in the family.
 
  1. Who is the sister of E?
    1. C
    2. D
    3. A
    4. Data inadequate
    5. None of these
  2. Who among the following members are the males?
    1. F and D
    2. B, F and A
    3. B and F
    4. B, F and D
    5. None of these
  3. Who is the husband of A?
    1. C
    2. F
    3. B
    4. E
    5. D
  4. What is A’s profession?
    1. Student
    2. Teacher
    3. Housewife or teacher
    4. Housewife
    5. Engineer or teacher
  5. Which of the following are the two married couples?
    1. FD; BE
    2. FD; CA
    3. FD; BA
    4. ED; CF
    5. None of these

Solution

The first two statements (i) and (ii) and the last one (vi) are USI, whereas the statements (iii), (iv) and (v) are the actual information.

 

Let us begin with statement (iii), which states the parent–child relationship.

 

B is an engineer and the father of E.

 

Description: 102096.png

 

Now, check a statement which gives data on relationship involving B or E. Statement (v) gives the relationship of E with D. It states that D is the paternal grandmother of E. Hence, the son of D must be E’s father and thus B is the son of D.

 

On plotting the above information, the family tree appears as under.

 

Description: 102115.png

 

Consider statement (iv). F is the paternal grandfather of C and is a doctor.

 

Description: 102150.png

 

Now, we have to analyse and correlate both the components. Let us check the USI. Statement (ii) states that there are two married couples in the family. It is obvious that the possible pairs are grandfather, grandmother and father, mother. By taking this information into account, if both the diagrams are combined, we get the final family tree as shown below:

 

Description: 102167.png

 

In the above diagram, we are unable to make out the professions of A, E and C. However, by applying a bit of logical thinking and by considering statement (vi), we can conclude that mother A is a teacher and the two children E and C are students. Further, the sex of E and C cannot be determined.

 

Following are the answers to the question.

 

Answers:

  1. (4)
  2. (3)
  3. (3)
  4. (2)
  5. (3)
  6. (3)

 

 

Example-6

Directions:

  1. P, Q, R, S, T and U are six members of a family and each of them is in a different profession, namely, philosopher, manager, advocate, businessman, dentist and a contractor.
  2. In this group, there are two married couples.
  3. The dentist is the grandfather of U who is a philosopher.
  4. The manager S is married to P.
  5. R, the businessman is married to the advocate.
  6. Q is the mother of U and T.
 
  1. What is the profession of P?
    1. Dentist
    2. Businessman
    3. Manger
    4. Advocate
    5. None of these
  2. How many male members are there in the family?
    1. Three
    2. Two
    3. Four
    4. One
    5. Cannot be determined
  3. Which of the following is one of the two pairs of couples in the family?
    1. P, R
    2. P, S
    3. P, Q
    4. Cannot be determined
    5. None of these
  4. What is the profession of T?
    1. Businessman
    2. Philosopher
    3. Dentist
    4. Manger
    5. Contractor
  5. What is the relation of P to T?
    1. Uncle
    2. Grandfather
    3. Brother
    4. Father
    5. None of these

Solution

In the above example, statements (i) and (ii) are USI.

 

Let us consider statement (vi), which states that Q is the mother of U and T.

 

Description: 102217.png

 

Next, let us search for a statement which gives a clue on the relationship involving Q, U or T.

 

In statement (iii), it is given that the dentist is the grandfather of U, who is a philosopher.

 

Since, Q is the mother of U, she must be the daughter-in-law of the dentist.

 

Description: 102241.png

 

The other two remaining statements are (iv) and (v).

 

S (? Manager)

P (??)

(The manager S is married to P)

R (Businessman)

? (− Advocate)

(R, the businessman, is married to the advocate)

 

Now, try to correlate all the above three diagrams.

 

Since all the actual information are made use of, let us read statement (ii), which states that there are two married couples in the family. It implies that the dentist’s wife is alive. She must be the manager S and the dentist must be P because the other couple is businessman and advocate. Now, only R is remaining, who must be the husband of Q, and hence Q must be an advocate.

 

The final family tree appears as under:

 

Description: 102306.png

 

Observe that the sex of T and U can’t be determined. But the profession of T must be contractor based on the USI [statement (i)].

 

Following are the answers to the question.

 

Answers:

  1. (1)
  2. (5)
  3. (2)
  4. (5)
  5. (2)

 

Example-7

A woman walking with a boy to a market meets another woman and when asked how the boy is related to her, she says, ‘My maternal uncle and his maternal uncle’s maternal uncle are brothers’. How is the boy related to the woman?

  1. Brother
  2. Brother-in-law
  3. Grandson
  4. Son
  5. Husband

Solution

Boy’s maternal uncle is the brother of boy’s mother. So, boy’s maternal uncle’s maternal uncle means boy’s mother’s maternal uncle. Boy’s mother’s maternal uncle and the woman’s maternal uncle are brothers. Hence, the woman is either boy’s mother or boy’s mother’s sister. Thus, the boy is either woman’s son or her nephew. Since nephew is not in the given options, we can conclude that the boy is woman’s son.

 

Answer: (4)
 

 

Example-8

Directions:

  1. A + B means A is the mother of B.
  2. A ÷ B means A is the father of B.
  3. A − B means A is the brother of B.
  4. A × B means A is the sister of B.
 
  1. If P + Q ÷ R − S, then how is P related to S?
    1. Grandfather
    2. Father
    3. Grandmother
    4. Sister
    5. None
  2. Given P × Q ÷ R − S + T; then how is P related to T?
    1. Brother
    2. Great-aunt
    3. Maternal uncle
    4. Mother
    5. None
  3. Which of the following shows that P is the aunt of T?
    1. P + Q − R × S ÷ T
    2. P ÷ Q × R + S − T
    3. P − Q + R ÷ S × T
    4. P × Q ÷ R × S − T
    5. None of these

Solution

Following the directions, P + Q ÷ R – S implies the following information.

 

P is the mother of Q;

 

Q is the father of R; and

 

R is the brother of S.

 

Q is S’s brother’s father, which means Q is S’s father. So, P is the mother of S’s father. Thus, P is the grandmother of S.

 

Answer: (3)

 

Statement 2 implies the following information.

 

P is the sister of Q;

 

Q is the father of R;

 

R is the brother of S and;

 

S is the mother of T.

 

Q is the father of S’s brother, which means Q is the father of S. So, Q is T’s maternal grandfather. P is the sister of T’s maternal grandfather. Thus, P is the great-aunt of T.

 

Answer: (2)

 

On analysing the statements given in question 23, we observe that statement 4 in the options implies the following information.

 

P is the sister of Q;

 

Q is the father of R;

 

R is the sister of S; and

 

S is the brother of T.

 

From the above relations, we notice that P is the sister of T’s father. So, P is the aunt of T.

 

Answer: (4)

 

Following are the answers to the questions.

 

Answers:

  1. (3)
  2. (2)
  3. (4)

 

Example-9

Directions:

  1. A family consists of seven persons, A, B, C, D, E, F and G. They all appeared for an I.Q. test.
  2. There are two married couples and three females in the family.
  3. G, a female is the most intelligent.
  4. B, the father of E is more intelligent than his son.
  5. C has one son and one daughter. She is more intelligent than her husband.
  6. The father of B is more intelligent than B.
  7. E, the grandson of F is the least intelligent.
  8. F, the grandfather is the second most intelligent in the family.
  9. The mother of B is less intelligent than B.
  10. None among the married topped the I.Q. test.
  11. The grandmother of G has two sons, one of whom is D, who is more intelligent than his brother but less intelligent than his brother’s wife.
  12. Nobody is a widow or a widower in the family.
 
  1. How are C and A related?
    1. Daughter-in-law and mother-in-law
    2. Daughter-in-law and father-in-law
    3. Daughter-in-law and father-in-law
    4. Mother and daughter
    5. Cannot be determined
  2. Who is B’s spouse?
    1. A
    2. D
    3. C
    4. Cannot be determined
    5. None of these
  3. Who among the following are married couple?
    1. A, E
    2. A, C
    3. A, D
    4. A, F
    5. None of these
  4. Who is the third most intelligent in the family?
    1. C
    2. D
    3. A
    4. B
    5. Cannot be determined
  5. Who is less intelligent than all but E?
    1. D
    2. A
    3. C
    4. B
    5. Cannot be determined
  6. How is G related to D?
    1. Cousin
    2. Daughter
    3. Daughter-in-law
    4. Niece
    5. None of these

Solution

Let us analyse the data in a systematic way. First let us draw the family tree, and later analyse the order of intelligence.

 

It is given that there are three females and four males. On analysing the given statements, we can form the opinion that (i) B, F, E and D are males and (ii) C and G are females. This implies that ‘A’ is the third female in the family.

 

It is given (statement iii) that G is the most intelligent. Since none of the married persons topped the I.Q. test, it is evident that G is unmarried. It means that both A and C are married, since there are two married couples.

 

The grandmother of G has two sons (statement xi), so the grandmother cannot be C since she has one son and one daughter (statement v). It implies that A is the grandmother.

 

Since F is a grandfather (statement viii) and since A is the grandmother, A and F must be a couple (As per statement xii, nobody in the family is a widow or widower).

 

Similarly, B is a father and since C is a mother, B and C must be a couple.

 

The son of C is E, who is the grandson of F.

 

The granddaughter is G, and her grandmother A has two sons, one is B and the other D.

 

Now based on the above data, we can construct the family tree easily.

 

Description: 102746.png

 

Now analyse the information regarding the intelligence in the I.Q. test.

  1. G is the most intelligent (statement iii).
  2. B is more intelligent than his son E (statement iv).
  3. C is more intelligent than her husband B (statement v).
  4. F, the father of B is more intelligent than B (statement vi).
  5. E is the least intelligent (statement vii).
  6. F is the second most intelligent (statement viii).
  7. A, the mother of B is less intelligent than B (statement ix).
  8. D is more intelligent than his brother B but less intelligent than B’s wife C (statement xi).

Now from the above information, we can conclude:

 

G > F > C > D > B > A > E (In I.Q.)

 

Following are the answers to the questions.

 

Answers

  1. (1)
  2. (3)
  3. (4)
  4. (1)
  5. (2)
  6. (4)




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