# Ch.20 :- Analytical Reasoning :- Introduction & Formula

Example 1

Ex.1 Read the following information carefully and answer the questions given below: Five cities A, B, C, D and E are famous for their lovely garden, fancy jewellery, educational institute, blue pottery and scents but not in the same order.
(i) it and C are neither educational institutes nor have gardens.
(ii) Band E are not famous for jewellery or pottery.
(iii) Scents and jewellery have nothing to do with A.
(iv) D and E are not famous for garden and jewellery.
(v) D is not famous for educational institutes.

I. which of the following city is famous for gardens?
(a) A
(b) C
(c) D
(d) B
(e) E

II. Blue pottery is available in which of the following cities?
(a) A
(b)C
(c)E
(d)B
(e)D

III. City E IS famous for which of the following?
(a) Jewellery
(b) Educational institutes
(C) Blue pottery
(d) Scent
(e)Garden

Sol. These questions can be solved easily with the help of a truth table. Truth table is an arrangement of the components given in a matrix form with one component in row and other component in column. In our question, components given are city and the feature for which each city is famous. The first arrange the components in matrix form with cities in column and features in row.
→ From (i), cross the possibility of garden and
education institute in front of cities A and C
→ Also the possibility of jewellery and pottery is ruled
out for cities B and E, from information (ii).Similarly, city A is crossed for scent and jewellery as
given in information (iii).
→ After using first three informations in the table, we see that only block uncrossed in front of city A is the
one related with blue pottery. So we know from here that city A. :city famous s for blue pottery. In this block
mark (✓)and row cross me row and column of this block because one city in famous only for one feature.

→  Using information (iv) in the table we know that city. B is famous for garden and city C for jewellery. Cross
row and column of each symbol (✓) obtained each time. This helps to determine one to one matching.
→ Last information helps us to know that city E is famous for educational institutes and city D for scent
The final order of matching of cities and their features is as under

On the basis of the table, all the questions can be answered:
I. City B is famous for garden, hence correct answer is (d).
II. City A is famous for blue pottery, hence correct answer is (a).
III. City E is famous for educational institute, hence correct answer is (b).

Example 2

Ex. 2. Read the following information carefully and answer the questions given below:
Four young men Raj, Sunder, Tarun and Upal are married to Rekha, Sunita, Tara and Uma and the couples live in
Rarnpur, Sanchi, Tirupati and Udhampur.

(i) The 1S( letter of names of men, their wives and cities is not the same
(ii) Sunita is not Raj’s wife.
(iii) Sunder does not live in Rampur or Udhampur and is not Rekha’s husband.
(iv) Upal and Tara do not live in Sanchi.

I. Which pair given below is the right combination of wife and city for Tarun ?
(a) Sunita, Tirupati
(b) Tara, Sanchi
(d) Rekha, Sanchi
(c) Uma, Rampur
(d) Rekha, Sanchi
(e) None of these

II. Who among the following is the wife of Upal ?
(a) Rekha
(b) Sunita
(c) Tara
(d) Uma
(e) Cannot be determined

III. Which of the following is the correct pair of husband and wife?
(a) Upal, Sunita,
(b) Raj, Tara
(c) Sunder, Uma
(d) None of these
(e) All of the above

Sol. This question is the same as the previous one but here in this question has three components husband, wife and city are given instead of two components as in the previous question. First, arrange these components in truth table with husband in column and wife and city in row as under:

→ With the help of information (i), it can be concluded that Raj can’t be married with Rekha and does not live in Rampur, Sunder can’t be married with Sunita nor does he live in Sanchi, Tarun can’t be married with Tara and nor does he  live in Tirupati and Upal can’t be married with Uma nor does he live in Udhampur. On the basis of these informations, cross the respective blocks.
→ Using information (ii), cross the possibility of matching of Sunita with Raj.
→ Information (iii) rules out the matching of Sunder with Rampur, Udhampur and Rekha.
→ Information (iv) denies the matching of Upal with Sanchi. The part of this information, which denies the matching of Tara and Sanchi, can’t be used in the table now unless the husband of Tara is known. So keep the information to be used later on.
→ After using all these informations, we see that only
city left in front of Sunder is ‘Tirupati’. So, mark
(✓) in this block crossing row and column of city to
ensure one to one matching. As a result, we know
that Upallives in Rampur.
→ Using informations (iv) and (i) we get the matching of husbands, wives and cities as under:

On the basis of the above table, we can answer the questions:
I. The correct matching of pairs is Rekha and Sanchi. Therefore, the answer is (d).
II. The wife of Upal is Sunita. Therefore, the answer is (b).
III. All the combinations given in the alternatives are correct. Therefore, the answer is (e).

Example 3

Ex. 3. Study the following information to answer the given question:
(i) J, K, L, M, N and 0 are six family members having different professions.
(ii) There are two married couples in the family.
(iii) M is a doctor and his wife is an engineer.
(iv) J is the grand daughter of 0 and sister of L, who is a typist.
(v) K is the grandfather of L and is married to a teacher.
(vi) J’s mother, who is an engineer, is the daughter-in-law of a lawyer.

I. What is the profession of J ?
(a) Teacher
(b) Lawyer
(c) Engineer
(d) Cannot be determined
(e) None of these

II. Which of the following is one of the married couples?
(a) KN
(b) MO
(c) KM
(d) Cannot be determined
(e) None of these

III. Who is the wife of M ?
(a) N
(b) 0
(c) J
(d) Cannot be determined
(e) None of these

IV. How many male members are the~e in the family?
(a) Two
(b) Three
(c) Four
(d) Cannot be determined
(e) None of these

Sol. For solving this type of questions, where persons engaged in different professions are in relatives of one another, the truth-table is not of much help. Students are advised to draw a family tree of three generations. Information given in the question can be then analysed and inserted in this structure.
→ From information (v), we can place K and his wife, a teacher, in 1st generation. Also L can be placed in 3rd generation.
→ From information (iv), J can be placed in 3rd generation. From this information we further know the profession of L (Typist), sex of J (Female) and name of teacher as O.

→ Information (vi) helps us to know that engineer- a female, can be placed in second generation. From this information we get the profession of K as lawyer.
→ Now 3rd information can easily be inserted in the family tree. The only place left for doctor engineer. combination is 2nd generation. However, the sex of L and profession of J is not known, On the basis of information as given by the family tree, we can answer the questions easily.

I. Profession of J can’t be determined. Hence, the correct answer is (d)
II. From the family tree we get two married couples as KO and MF. Hence the correct answer is (e).
III. The wife of Mis N. Hence, the correct answer is (a).
IV. Since the sex ofL is not known, we can’t answer that how many male members are there in the family. Hence, the correct answer is (d).

Example 4

Ex. 4. Read the following information carefully and answer the questions below it.
(i) Six friends P, 0. R, S, T and U are members of a club and play different game of Football (F), Cricket (e), Tennis (T), Basketball (Bb) , Badminton'(Bm)” and Volleyball (V) each.
(ii) T, who is taller than P and S, plays Tennis.
(iii) The tallest among them plays Basketball.
(iv) The shortest among them plays Volleyball.’
(v) R plays Volleyball.
(vi) Q and S neither play Volleyball nor Basketball.
(vii) T is between Q, who plays Football and P in order of height.

Sol. For solving this problem, draw truth-table between persons and games they play, and ranking of order of their heights, separately.
→ Information (ii) and (vii) together give ranking of heights of four persons in descending order, as Q. T, P, S,
Q. T, P, S,
→ All the information from (i) to (vii) help us to complete our table as given below.

→ Now from the information (iii), we get that the tallest person plays basketball. From the table, P and U can play basketball. But P can’t be the tallest as he is between T and S as given in ranking order. Hence, we conclude ‘from here that U is the tallest and plays football.
→ From information (v), we conclude, that R is the shortest,

On the basis of the conclusions we have derived, the final
→ form of ranking order and truth-table can be sketched as below: Ranking order in descending order.
U, Q, T, P, S, R
Q. 1. Which game does Splay?
(a) Football
(b) Either Cricket or Badminton
(c) Cricket
(d) Badminton
(e) None of the above

From the table, it can be concluded that S either plays
cricket or badminton, Hence, the correct answer is (b).

Q. 2.Who among them is taller than R but shorter than P ?
(a) T
(b) Data inadequate
(c) Q
(d) U
(e) None of these

Sol. From the ranking order, we observe that S is taller than R but shorter than P. However, this is not available in the options. Hence, the correct answer is (t).

Q. 3. Who will be at 3rd place if they are-arranged in the descending order of their, heights ?
(a) T
(b) Q
(c) P
(d)S.
(e) None of these

Sol. Clearly, T will be at 3rd position. Hence, the correct our
answer is (a) .

Example 5

Ex. Each question is based on a passage or a set of conditions. Read the information carefully and select the best answer choice given : A combination of three colours is being chosen to decorate a room. The colour must be chosen from a group of seven colours-A, B, C, D, E, F and G according to the following conditions:
(i) If A or B is chosen, the other must also be chosen.
(ii) C and D can’t be chosen together.
(iii) Either Cor A or both must be chosen.

Q.1. Which of the following combination of colours conforms to the conditions ?
(a) A,C,D
(b) A,E,F
(c) B,C,G
(d) G, D, F
(e) C, E, G

Q.2. If D is chosen, which of the following pair of colours must also be chosen ?
(a) A and B
(b) A and G
(c) B and C
(d) C and E
(e) E and F

Q.3. If E is chosen, which of the following pair of colours could also be chosen ?
(a) A and C
(b) A and F
(c) B and C
(d) C and F
(e) F and D.

Sol.This question is entirely different from the earlier questions of this type and therefore, methods for solution discussed so far will not provide much help for its solution. The main difference in this question is that, according to set of conditions given in the questions. there may be more than one valid combination which may conform to the given condition. Hence.our answer will vary according to the question asked.
1. In this question, option (a) violates condition en, option (b) violates condition (i), option (C) violates condition (i), option (d) violates condition (ii), option (e) complies with all the conditions, hence the correct answer is (e).
2. If D is chosen, C can’t be chosen. So alternatives (c) and (d) are rejected. If A is chosen, B has to be chosen, so alternative (b) is rejected. (e) is not the answer as it violates condition (iii). Hence, the correct answer is (a).
3. Alternatives (a), (b), (c) violates condition (i) .Alternative (e) violates condition (iii). Hence, the correct answer is (d).