LOGICAL REASONING

Directions for problems 1-4: In a group of 7 people, there are two ladies Fiza and Kavita and five men Ram, Rahim, Peter, David and Shyam. (CAT 2001)

                        A group of 3 or 4 has to be selected.

                        If Fiza goes, she wants David.

                        David wants Kavita.                 

Shyam and Rahim insist on going together.

David and Peter do not go together.

Ram and Shyam do not go together.

Problem 1:        Can both the females be there is a group of four?

(A)   Yes

(B)   No

(C)   Uncertain

(D)   Cannot be determined.

Problem 2:        Which is a feasible group of three

(A)   Ram, David, Fiza

(B)   Shyam, David, Peter

(C)   Kavita, David Shyam

(D)   None of these.

Problem 3:        Which is a feasible group of four?

(A)   Ram, David, Fiza, Shyam

(B)   Shyam, David, Kavita, Rahim

(C)   Fiza, David, Ram, Peter

(D)   None of these.

Problem 4:        Which of the following will be true ?

(A)   A group of four can be formed with only the men

(B)   Both women can be included in a group of four

(C)   Feasible groups of three and four cannot be made simultaneously.

(D)   None of these.

Directions for problem 5: Amti wants to see some plays. There are six plays going on. Amit wants to see all to them, as well as take a lunch break for one hour from 12.30 p.m. to 1.30 p.m. The names of the plays, their durations and timings are all mentioned in the following table. (CAT 2001)

Problem 5 :       Which is the best possible plan for Amit.

(A)  Sundar Kand first, Jhansi ki Rani third, Tipu Sultan fifth.

(B)   Sati Savitri first, Nagamandala third, Sundar Kand fifth.

(C)   Jhansi ki Rani, Nagamandala third, Sundar Kand fifth.

(D)  None of these.

Direction for Problem 6 to 9: Answer the questions based on the following information. A parking space has seven parallel rows that is occupied by cars of different models. These rows are numbered consecutively from 1 to 7. In each row, a different model of car – Palio, Siena, Baleno, Escort, Accent, Astra and Indica – is to be parked according to the following conditions.

I.                    If Astra is next to only one other row of cars, that row must be Siena.

II.                 Neither Palio nor Siena can be in a row next to the row Indica is in.

III.               Baleno must be parked in a row next to a row containing either Accent or Indica or in a row that is the only row between the rows containing Accent and Indica.

IV.              Escort must be parked in either row 1 or row 7.

Problem 6:        If Astra is in row 1 and Palio is in 6 row, which car must be parked in row 4?

(A) Indica                                 (B) Siena

(C) Baleno                                (D) Escort

Problem 7:        If Indica is next to Escort and Astra is in row 7, then in which row must Indica be placed?

(A) 6                                        (B) 4

(C) 2                                        (D) 5

Problem 8:        If Palio, Baleno, Siena, Accent and Indica are parked in the inner five rows, then which of the following is the correct and possible order of arrangment of these cars in the row?

A.     Palio, Siena, Baleno, Indica, Accent

B.     Palio, Accent, Baleno, Indica, Siena

C.     Siena, Accent, Indica, Baleno, Palio

D.     Baleno, Palio, Sina, Accent, Indica

Problem 9:        Which of the following is possible order for the parking of these cars in the parking space, beginning with row1?

A.     Accent, Indica, Baleno, Palio, Escort, Astra, Siena

B.     Escort, Indica, Baleno, Accent, Palio, Siena, Astra

C.     Escort, Accent, Baleno, Indica, Siena, Palio, Astra

D.     Baleno, Palio, Siena, Accent, Indica, Astra, escort

Problem 10:       Consider the facts given below.

I.                    Sushma finished her graduation five years ago form today.

II.                 Geeta did her graduation three years before Sushma and joined the teaching profession the same year that Sushma entered college.

III.               Aarti did her graduation three years after Sushma.

IV.              Geeta taught both Sushma and Aarti during their graduation. If Geeta is still teaching, for how many years has Geeta been a teacher?

(A) 3 years                               (B) 5 years

(C) 8 years                               (D) 10 years

Direction for the Problem 11 to 14: Answer the question based on the following on the following information.

A group of three persons must be selected from six individuals – Keshto, Omprakash, Sanjiv Kumar, Tuntun, Vijayendra and Wahid, according to the following conditions.

I.                    Either Omprakash or Vijayendra must be selected but neither Vijayendra nor Sanjiv Kumar can be selected with Omprakash.

II.                Either Sanjiv Kumar or Keshto or both must be selected.

Problem  11:      If Vijayendra is not selected, which pair of individuals must be among those selected?

(A) Omprakash and Wahida                  (B) Tuntun and Keshto

(C) Tuntun and Omprakash                                (D) Omprakash and Keshto

Problem 12:       Which of the following is an acceptable selection of persons?

A.     Omprakash, Vijayendra and Tuntun

B.     Keshto, Tuntun and Sanjiv Kumar

C.     Keshto, Omprakash and Snajiv Kumar

D.     Keshto, Sanjiv Kumar and Vijayendra

Problem 13:       If Sanjiv Kumar is selected, which of the following individuals must also be among the people selected?

(A) Wahida                                                       (B) Vijayendra

(C) Omprakash                                     (D) Tuntun

Problem 14:       Which of the following pairs of persons cannot both be among the persons selected?

(A) Vijayendra and Wahida       (B) Omprakash and Wahida

(C) Keshto and Omprakash                   (D) Tuntun and Wahida

Direction for the Problem  15 to 19: Answer the question based on the following on the following information.

In a typical college day at IIM, Bangalore, exactly seven lecturers A, B, C, D, E, F and G were to give their lecturers in a first year class. In the schedule for the day, seven-time slots are available for the speakers and they are numbered from 1 to 7. Only one speaker is assigned one time slot, according to the following conditions.

I.                    C must speak in the either time slot 1 or time slot 7

II.                 A must speak immediately before or immediately after D speaks.

III.               F must speak in the fourth time slot.

IV.              D must speak sometime before B speaks.

Problem 15:       If G speaks at position 7, any of the following pairs of speakers could speak in time slots immediately adjacent to each other except

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

(C) A and B                              (D) C and D

Problem 16:       Which of the following must be true?

A.     G speaks sometime before F speaks

B.     C speaks sometime  before D speaks

C.     A speaks sometime before F speaks

D.     A speaks sometime before B speaks

Problem 17:       If E wants to speak in the second time slot, then there will be a total of how many scheduling possibilities from which to select the schedule of speakers?

(A) 6                                        (B) 1

                        (C) 2                                        (D) 4

Problem 18:       If B speaks immediately before F speaks, which of the following could be true?

A.     D speaks in the third time slot

B.     G speaks in the sixth time slot

C.     C speaks in the first time slot

D.     A speaks in the fifth time slot

Problem 19:       If E speaks sometime before A speaks, which of the following must be true?

A.     G speaks sometime before C speaks

B.     E speaks sometime before G speaks

C.     D speaks sometime before F speaks

D.     F speaks sometime before B speaks

Problem 20: Peter owned a butcher’s shop. In Peter’s absence, a dog ran away with a piece of meat. When Peter returned, the other shopkeepers, who were jealous of him, gave two statements each, one of which was a lie. (CAT 2001)

1^st shopkeeper: The dog was black. It had no collar.

2^nd shopkeeper: The dog was black. It had a short tail.

3^rd Shopkeeper: The dog was white. It had a collar.

Therefore the dog was

(A)   white with a short tail and no collar.

(B)   black with a long tail and a collar.

(C)   black with a short tail and a collar.

(D)   white with a long tail and no collar.
Solutions

Solutions 1-4

Let us put together all the constrains in a diagram

Fi>Da  (if Fiza goes, she wants David)

Da>Kv  (if David goes, he wants Kavita)

Sh<>Rh  (Shyam and Rahim want to go together)

Ra>Pe    (if Ram goes, he wants Peter)

Da><Pe (David and Peter would not go together)

Ra><Sh   (Ram and Shyam don’t go together)

Solution 1:         Both the ladies – Fiza and Kavita can go only with David. But when

David goes then none of Ram, Shyam, Rahim or Peter can go. Hence, such a combination is not possible.

Ans=(B)

Solution2:          Checking the options, all the groups fail one or more constraints.

Ans=(D)

Solution3:          Checking the options ,Only feasible group of four Shyam, David, Kavita and Rahim.

Ans=(B)

Solution4:          Checking the options , option (C) is true.

Ans=(C)

Solution 5:         The best possible plan for Amit is

Ans=(D)

Solutions 6 to 9

We can put a linear arrangement like below based on data given.(From I and II)

Now see the information in each question

Solution6:          Under the given conditions, the arrangement would be

So Indica would be in Row 4.

Ans=(A)

Solution7:          Using the given conditions, see main table. If Astra is in Row 7 then, Escort would be in Row 1 and Indica in Row 2.

Ans=(C)

Solution 8:         In this question, remember first not to use any information from Problem 6 or 7. Use only the basic common data in problem, thus the main table above. As no other info is given, the best way is to check the various options and see which one satisfy the constrains of the problem

So, According to the given conditions, the only valid possible option would be Siena, Accent, Indica, Baleno and Palio

Ans=(C)

Solution9:          Following same approach as in Problem 8, Undre the given conditions, the only valid option out of the given ones is: Escort, Indica, Baleno, Accent, Palio, Siena, Astra.

Ans=(B).

Solution10:        Sushma finished her graduation 5 years back from today. Geeta started teaching from the year Sushma entered college, i.e. 3 years before Sushma finished her graduation. So Geeta started teaching 8 years back from today.

Ans=(C)

Did you notice one thing? Data in points 3 and 4 was totally useless and is called Superfluous data. The idea is to fool student and make him think where to use it.

Solutions 11 to 14

Using abbreviations for various names and classifying the given conditions, we get the following.

I.                          Either O or V must be selected but neither V or S with O, i.e. VO and SO is possible.

II.                        Either S or K or both SK must be selected.

Solution 11:       Using the given conditions, we get:

If V is not selected, then O must be selected (according to condition I).

Now using condition II V, S or K or SK must be selected along with O, but as given S cannot be with O. Therefore, K has to be there with O. Hence, Om Prakash and Keshto must be selected.

Ans=(D)

Solution12:        In type of questions, we have to explore all the choices with the conditions given. So, Using the given conditions, the combination of K, V and S is the only acceptable combination form the given choices.

Ans=(D)

Solution13:        According to the given conditions, if S is selected, then V must be selected and not Q. Therefore, V must be selected if S is selected

Ans=(B).

Solution 14:       As, one from O and P have to be selected and one from S and K have to be selected, we can never select T and W together.

Ans=(D)

Solution15:        As G speaks in time slot 7, and then C will be first slot (according to condition I). and F always speak in slot 4. So 1-4-7 is taken.

                        Now, as A has to speak adjacent to D, and D has to speak before B, AD would speak in 2-3slots. Now we have to check the options.

In any case, AB can never speak together.

Ans=(C)

Solution16:        Remember not to take any info from problem 15. We know only what is given in common directions.

We have to check the options first.

In every combination, A speaks sometimes before B speaks, will always be true. (As A and D speak adjacent and D speaks before B)

Ans=(D)

Solution17:        If E wants to speak in the second time slot, then according to the given conditions, we have these restrictions.

                        As A and D have to speak together, they can speak   in 5-6 or 6-7 positions. But As D have to speak before B, A and D Have share 5-6. So B would speak at 7 and thus C would speak at 1.

                        So we have C at 1, E at 2, G at 3, F at 4, A and D at 5 or 6 and B at Seven            So, only two combinations are possible.

(i)                  C/1, E/2, G/3, F/4, D/5, A/6, B/7.

(ii)                C/1, E/2, G/3, F/4, A/5, D/6, B/7.

Ans=(C)

Solution18:        If B speaks before F (slot 4), we have these restrictions.

                        As D has to speak before B and A and D are adjacent, B would speak at a slot 3. A and D at 1 and 2 slots and so C at 7.

                        Now, check for various options,

then only statement which would be true out of the given options is G speaks in the sixth time slot and one of that arrangement can be

A/1, D/2, B/3, F/4, E/5, G/6, C/7.

Ans=(B)

Solution19:        Using the given conditions that E speaks sometime before A speaks, we get the condition, F speaks sometime before B speaks, must be true.

Ans=(D)

Solution20:        Based on the statements, only two possibilities are there.

If 1^st shopkeeper is correct about color, then dog would be Black with collar.

if Ist shopkeeper lies about color, then dog would be white with no color and short tail

Checking the options now, Option A is correct   

Ans=(A)