LOGICAL REASONING

Direction for question 1 to 4: Answer the questions based on the following

information.

Four people of different nationalities live on the same side of a street in four houses, each of a different colour. Each person has a different favorite drink. The following additional information is also given.

I. The Englishman lives in red house.

II. The Italian takes tea.

III. The Norwegian lives in the first house on the left.

IV. In the second house from the right, they drink milk.

V. The person living adjacent to blue house drinks cocoa.

VI. The Spaniard drink fruit juice.

VII. Tea is taken in blue house.

VIII. The white house is to the right of the red house.

IX. No other description of cocoa is available.

Example 1: Milk is drunk by

(A) the Norwegian (B) the Englishman

(C) the Italian (D) None of these

Example 2: The Norwegian drinks

(A) milk (B) cocoa

(C) tea (D) fruit juice

Example 3: The colour of the Norwegian’s house is

(A) white (B) red

(C) blue (D) Cannot be determined

Example 4: Which of the following is not true?

A. Milk is drunk in the red house

B. The Italian lives in blue house

C. The Spaniard lives in a corner house

D. The Italian lives next to the Spaniard

Using the given information, try to draw a diagram. In this case, a table would be more apt and it might look like,

We would see now, how easy it is solve the questions.

Solution1: Ans (B) (Straight from table)

Solution2: Ans (B) (Straight from table)

Solution: Ans (D) (Fourth colour is not mentioned in the data)

Solution: Ans (D) ((Straight from table))

As seen above, logical reasoning problems don’t involve any complex mathematical calculations. If we are able to visualize the problem in any suitable figure, 99% job is done. Rest is to read the question carefully and answer them

Direction for the question 5 to 8: Answer the questions based on the following information.

Four friends – Manas, Kailash, Shashidev and Bhagwan – have different preferences for watches and bike. Each person prefers one exclusive watch and bike. Bikes are Passion, Pulsar, Enticer and Fiero. Watches are radio, Omega, Cartier and Tissot. One who likes Enticer like Cartier, and one who likes Tissot also likes Pulsar. Bhagwan likes Fiero and Rado. Manas does not like either Omega or Enticer.

Example 5: Which of the following are Manas choices?

(A) Tissot and Pulsar (B) Pulsar and Cartier

(C) Passion and Cartier (D) None of these

Example 6: The one who likes Omega likes

(A) Passion (B) either Passion or Fiero

(C) Fiero (D) Cannot be determined

Example 7: What is Shashidev’s choice for the watch?

(A) Omega (B) Cartier

(C) Tissot (D) Cannot be determined

Example 8: What is Kailash’s preference for the bike?

(A) Pulsar (B) Passion

(C) Enticer (D) Either (b) or (c)

Using the given information, try to draw a diagram. In this case, a table would be more apt and it might look like,

Now, all the questions can be cracked easily.

Solution5: Ans (A) (Straight from table)

Solution6: Ans (D) (As seen from table, it can be Shashidev or Kailash, so can’t be determined)

Solution7: Ans (D) (As seen from table, it can be Omega or Cartier, so can’t be determined)

Solution8: Ans (D) ((As seen from table, it can be passion or enticer, so can’t be determined)

Directions for Examples 9-10: Study the following information: (CAT 2001)

Elle is three times Yogesh

Zahir is half Wahida

Zahir is younger than Yogesh.

Example 9: Which of the following are necessary to find the age of each?

(A) Wahida is same age as that of Yogesh

(B) Age of Zahir is ten

(C) Both are required

(D) None of these.

Solution9: Given , E=3Y, Z=1/2W, Z<Y

Now, From statement II, Z = 10 years

So, W = 2Z = 20 years

From Statement 1, Y=W=20

Then E = 3Y=3 x 20 = 60 years.

Hence, both the statements are necessary to find the age of each person.

Ans=(C)

Example 10: Which of the following is true?

(A) Elle is the eldest

(B) Wahida can be elder to Elle

(C) Wahida is elder to Yogesh

(D) None of these.

Solution10: Given that Z < Y

so that 2Y < 2Y or W < 2Y < 3Y = E

Hence, Elle is the eldest.

Ans=(A)

Directions for Examples11-13: Read the following passage and answer the questions which follow.

Two union representative and one management representative are seated together at an octagonal table with only one seat to a side of the table. No pair of either union or management representatives may be seated together. Two additional management representatives are seated. (CAT 2001)

Example 11: Seated between the two union reps are

(A) at most two management people.

(B) only two management people.

(C) no more than one management person.

(D) three management people.

Solution: At most, two management people can be seated between the two union representatives.

<<Logical Reasoning Solved 1>>

Ans=(A)

Example 12: Seated opposite the first management representative

(A) must be a union person.

(B) may be a union person.

(C) may be a management person.

(D) must be a management person.

Solution: Seated opposite the first management representative may be a

management person. (The only other alternative is that the seat

would be empty).

Ans=(C)

Example 13: If two more union reps are seated without causing any changes of

seats, then there is (are)

(A) no empty seat next to a union person.

(B) no empty seat next to a management person.

(C) two empty seats between union people.

(D) at most one empty seat between union reps.

Solution: If two more union representatives are seated without causing any

changes of seats, then there is at most one empty seat between union

representatives.

<<Logical Reasoning Solved 2>>

Ans=(D)

Example 14: There are six houses in a row. A has B and C as neighbours. D has E and F neighbours. E’s house is not next to B or C, and F does not be next to C. Who are B’s next door neighbours?

(A) A and F (B) C and F

(C) D and E (D) F and D

Solution14: According to given conditions:

A is in between B and C and D is in between E and F. But E is not

neighbour of B and F is not neighbour of C. So the sequence will be

EDFBAC. Hence B neighbours are F and A

Ans=(A)

Directions for example 15 to 19: Refer to the data below and answer the questions that follow.

There are five events A, B, C, D and E that can happen. The occurrence of every event is governed by few rules, which are:

- If A occurs then either of B or C or both must occur.

- If B occurs then D cannot occur.

- If C occurs then E must occur.

- If D occurs then C must occur.

- If E occurs then A must occur and B cannot occur.

- If D has not occurred then A will also not occur.

Example 15: If C has occurred, then which of the events must happen?

(A) A (B) B

(C) D (D) A and D

Example 16: If E has not occurred, then which of the statements must be true?

I. C has not occurred. II. B has occurred.

III D has not occurred. IV. A has not occurred.

(A) I and II (B) III and IV

(C) I, III and IV (D) I and IV

Example 17: If B has occurred, then which statement will be definitely false?

(A) D has not occurred. (B) C has not occurred.

(C) E has not occurred. (D) A must occur.

Example 18: If A has occurred, then which event(s) will definitely occur?

(A) B (B) C and D

(C) B and E (D) C, D and E

Example 19: If D occurs, then any of the events can occur except:

(A) A (B) B

(C) A and E (D) Cannot say

Solution

Let us first draw the figure of the information given. As this is a logical problem, an arrow diagram would best describe. Let us symbolize the given conditions..

1.) A > B or C or both

When A occurs, then either B., C or both would occur so, If both of B or C not occurred then A will not occur. (Logical inference) But it may happen that B or C has occurred and still A hasn’t occurred.

2)B > - D (- sign means can’t occur)

3) C > E

4) D > C

5) E > A

6) E > - B

7) A > D (Last statement actually means that if A happens then D must happen)

Now read all the questions and check all the options for the information given.

Solution 15:

<<Logical Reasoning Solved 3>>

If C happens, then E must happen. If E happened then A must happen and B would not happen and If A happens then D must happen Also either B or C should happen. As B can’t happen then C would happen and it is happening.Thus E, A and D must occur.

Ans=(D)

Solution 16:

<<Logical Reasoning Solved 4>>

If E doesn’t occurs, then C can’t occur. If C doesn’t occur then D can’t occur. If D doesn’t occur, then A can’t occur. So if E doesn’t occur, then C, D and A can’t occur. We don’t know about B. So

Ans=(C)

Solution 17:

<<Logical Reasoning Solved 5>>

If B occur, then D can’t occur. If D doesn’t occur then A can’t occur.

Ans=(D)

Solution 18:

<<Logical Reasoning Solved 6>>

Ans=(D)

Solution 19:

<<Logical Reasoning Solved 7>>

Ans=(B)

Example 20: There are 3 families…. Bannerjees, Guptas and Sharmas. Each family has a feast every Sunday at different timings of 12:00, 1:00 and 2:00. Each family eats different dishes and uses different coloured dinner sets. (CAT 2001)

The Bannerjees eat sambhar but not in the red dinner set.

The last family does not eat karela or brinjal.

The other dinner sets are yellow and blue in colour.

Which of the following is true?

(A) The Bannerjees eat at 12

(B) The last family eats sambhar in the blue dinner set

(C) The Guptas eat karela in the yellow dinner set

(D) None of these

Solution20: Given information may be put in the tabular form as

So, option (A) of definitely false. Both options B and C can be true but we are not sure.

Ans=(D)

Direction for examples 21-24 :Answer the questions on the basis on the following information.

Four families decided to attend the marriage ceremony of one of their colleagues. One family has no kids, while the others have at least one kid each. Each family with kids, has at least one kid attending the marriage. Given below is some information about the families, and who reached when to attend the marriage. (CAT 2003)

The family with 2 kids came just before the family with no kids.

Shanthi who does not have any kids reached just before Sridevi’s family.

Sunil and his wife reached last with their only kid.

Anil is not the husband of Joya.

Anil and Raj are fathers.

Sridevi’s and Anita’s daughters go to the same school.

Joya came before Shanthi and met Anita when she reached the venue.

Raman stays the farthest from the venue.

Raj said his son could not come because of his exams.

Example 21:Which woman arrived third?

A. Shanthi

B. Sridevi

C. Anita

D. Joya.

Example 22:Name the correct pair of husband and wife.

A. Raj and Shanthi

B. Sunil and Sridevi

C. Anil and Sridevi

D. Raj and Anita.

Example 23:Of the following pairs, whose daughters go to the same school?

A. Anil and Raman

B. Sunil and Raman

C. Sunil and Anil

D. Raj and Anil.

Example 24:Whose family is known to have more than one kid for certain?

A. Raman’s

B. Raj’s

C. Anil’s

D. Sunil’s

Solution for Examples 21-24

The key to cracking this question is to follow the simple fundamentals in logical

reasoning. Read all the data and try to draw a picture. In this question, a table would best represent the data.

Let us interpret all the data one by one:

Sentence 1- Family with 2 kids came just before no kids. ( they should be together)

Sentence 2 – Shanthi with no kids came just before Sridevi

Sentence 3 - Sunil and wife came last with only kid

Sentence 4 – Anil and Joya not husband and wife.

Sentence 5 – Anil and Raj are fathers – hence cannot be the family with no kids.

Sentence 6 – Sridevi and Anita cannot be the persons with no kid

Sentence 7 – Joya came before Shanthi and Anita was already present.

Sentence 8-- Raman stays the farthest from the venue. (Useless information)

Sentence 9- Raj said his son could not come because of his exams.

Using the above into – Anil and Raj cannot be married to Shanthi as Shanthi has no kids whereas Anil and Raj are fathers. Also, Sunil and wife came last but Shanthi can’t come last as she came before Sridevi so she can’t be wife of Sunil.

So, Shanthi is married to Raman. Also from Sentence 7 and Sentence 2, Sridevi has to come last and is wife of Sunil.

As Anil and Joya are not spouses, so Anil is married to Anita and Raj is married to Joya.

Now, combing all the information, the data can be summarized as

Solution21 : Straight from table

Ans=(A)

Solution 22 : Straight from table

Ans=(B)

Solution 23: Straight from table

Ans=()

Solution 24: As Raj said that his son can’t come and he came with atleast one kid,

he surely have two or more kids.

Ans=(B)

Directions. for Examples 25-28: Answer the questions on the basis of the following information.

The plan above shows an office block for six officers, A, B, C, D, E, and F. Both B and C occupy offices to the right of the corridor (as one enters the office block) and A occupies an office to the left of the corridor. E and F occupy offices on opposite sides of the corridor but their offices do not face each other. The offices of C and D face each other. E does not have a corner office. F’s office is further down the corridor than A’s, but on the same side. (CAT 2003)

<<Logical Reasoning Solved 8>>

Example 25: If E sits in his office and faces the corridor, whose office is to his

left?

A. A

B. B

C. C

D. D.

Example 26: Whose office faces A’s office?

A. B

B. C

C. D

D. E.

Example 27: Who is/are F’s neighbour(s)?

A. A only

B. A and D

C. C only

D. B and C.

Example 28: D was heard telling someone to go further down the corridor to the

last office on the right. To whose room was he trying to direct that

person?

A. A

B. B

C. C

D. F.

Solutions to Examples 25-28

Like last example, let us comprehend the data and try to draw a suitable diagram. As the examiner himself has given the diagram let us try to fill it by placing different people in appropriate positions.

<<Logical Reasoning Solved 9>>

This is the only combination possible given all the constrains. Why, let us explain

F is further down the corridor from A, so F can take 2 or 3 position on left. As F is on left, so E would be on right. As E can’t be take corner office, he would take middle one on right. So E is fixed. Now F can’t face E, F would take 3 on Left as 2 on left would face E. So Now E and F are fixed. C and D have to face each other that are possible now only at poison 1. Hence, C takes 1 position on right and D takes 1 position on left. Now, A has to take 2 position on left and B would take 3 position on right.

Understood, As said many times before, logical reasoning don’t involve any mathematical calculations or formulas to remember. Simple logic application.

Solution 25 : From the figure, If E faces the corridor, person to his left is C.

Ans=(C)

Solution 26 : According to figure, E face A’s office.

Ans=(D)

Solution 27 :According to figure, F’s neighbour is A.

Ans=(A)

Solution 28 : According to figure, B’s room is last on the right.

Ans=(B)

This Question appeared in CAT’05. (In Quantitative section)

But we believe it should be in Data Analysis Section.

Question: A telecom service provider engages male and female operators for

answering 1000 calls per day. A male operator can handle 40 calls per day whereas a female operator can handle 50 calls per day. The male and the female operators get a fixed wage of Rs. 250 and Rs. 300 per day respectively. In addition, a male operators get a male operator gets Rs.15 per call he answers and a female operator gets Rs. 10 per call she answers. To minimize the total cost, how many male operators should the service provider employ assuming he has to employ more than 7 of the 12 female operators available for the job?

(1) 15 (2) 14

(3) 12 (4) 10

Solution: By the condition given in question.

Each male operator get Rs. 250/40 = Rs. 6.25 for one call as fixed wage

Similarly, Each female operator fixed cost is Rs. 300/50 = Rs. 6 for one call.

Also the variable cost for male is Rs 15 per call amd for female is Rs 10 per call. So total cost per call

For Male=6.25+15=Rs 21.25

For female=6+10=Rs 16

So, female operator is cheaper than man to minimize one should use the maximum possible number of female operators. The telecom service

provider engages maximum 12 female operator, which will answer 12 x 50 = 600 calls. The remaining 400 calls will be answered by 10 operators.

Ans (4)

The Answer was rather simple. Only common sense and logic was required to answer the above question.

This Question appeared in CAT’05 (In Quantitative section)

But we believe it should be in Data Analysis Section.

Question: Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets. None of the Frenchmen knows English, and only one Englishman knows French. What is the minimum number of phone calls needed for the above purpose?

(1) 5 (2) 10

(3) 9 (4) 15

Solution: The key to answer lies in drawing the below figure.

<<Logical Reasoning Solved 10>>

For min number of phone calls let

E2 & E3 converse to E1 --2 calls

F2 & F3 converse to F1 --2 calls

E1 & F1 interchange their code --1 call

Now F1 calls F2 & F3 --2 calls

& E1 calls to E2 & E3 -- 2 calls

Total calls = 2 + 2 + 1 + 2 + 2 = 9

Ans (3)

Once again, No permutation-combination was required. Just draw the diagram and the logic would flow.