# Logical Reasoning Capsules - Edwin Jose, CAT DILR 100 Percentiler - Set 6

• Directions: Answer the questions on the basis of the information given below.

The following data pertains to the profiles of 100 students who have appeared for the 'Selection Process' of a B-School, ISW College in the year 2009.

1. Each student has written exactly one of the two tests LAT or BAT, and every one of them has at least one of the two features - Good Academic Record (GAR) or Extra Curricular Activities (ECA).
2. No student who has written LAT has both GAR and ECA.
3. Sixty percent (60%) of the students who have appeared for the Selection Process have written LAT, of which 40% have Work Experience.
4. Fifty percent (50%) of the students who have appeared for the Selection Process have Work Experience, of which 30 students have GAR.
5. The number of students who have written BAT and also have both Work experience and GAR is 20.
6. The number of students who have written LAT and also have GAR is 25.
7. The number of students who have ECA but have no Work Experience is 35.
Note: The questions that follow are for the year 2009 only.

(1) Out of all the students who have appeared for the Selection Process of ISW College, how many have written BAT and have Work Experience and GAR, but no ECA?
(a) 10
(b) 15
(c) 20
(d) Cannot be determined

(2) Out of all the students who have appeared for the Selection Process of ISW College, what is the maximum possible number of students who have GAR and who have also written BAT but have no Work Experience?
(a) 10
(b) 12
(c) 14
(d) Cannot be determined

(3) Out of all the students who have appeared for the Selection Process of ISW College, what is the total number of students who have written LAT and have ECA?
(a) 31
(b) 35
(c) 28
(d) Cannot be determined

Solutions:

We can make the following figure based on the information given in the question.

(1) d
From the figure it can be inferred that the answer must be ‘20 – x’. As we don’t know the exact value of x the answer cannot be determined.
(2) c
From the figure it can be inferred that the answer must be the maximum possible value of ‘y’. As the number of students who have ECA and who have also written BAT but have no Work Experience is ‘14 – y’, we can say that the maximum possible value of ‘y’ must be 14.
(3) b
Answer = 21 (No Work Experience) + 14 (Work Experience) = 35

DIRECTIONS: Answer the questions on the basis of the information given below.

In the data given below, Table - 1 indicates the number of fruit bearing trees planted by six friends on three days - Day1, Day 2 and Day 3. Table - 2 shows the number of trees of each of the six types planted on these three days. The following conditions must be valid:

1. On any given day, each of them planted only one type of tree.
2. From among Ashish, Dinesh and Farhan exactly two people planted the same type of tree(s) on Day 2 and Day 3 as they planted on Day 1.
3. The person who planted exactly one Orange tree on Day 3 had also planted Orange trees on each of the first two days.
4. Dinesh did not plant a Banana tree on Day 2.

(1) Who planted Orange trees on all the three days?
(a) Dinesh
(b) Ekant
(c) Ekant or Farhan
(d) Dinesh or Ekant

(2) For how many friends can the number of trees planted of each type be conclusively determined?
(a) 3
(b) 4
(c) 5
(d) None of these

(3) What can be the maximum number of Guava trees planted by Farhan in all the three days collectively?
(a) 1
(b) 3
(c) 5
(d) None of these

Solutions:

From Table-2 the number of Orange trees planted on Day 3 is 7. Therefore, Bobby (B) and Chetan (C) must have planted Orange trees on Day 3. From Table-1 and Table-2, Ashish (A) planted Coconut trees on Day 1 and Day 2. Dinesh (D) planted a Mango tree on Day 1. Therefore, A and D could not have planted Orange trees on all the three days. Farhan (F) could not have planted Orange trees on all the three days as only 1 Orange tree was planted on Day 2, while he had planted 2 trees on Day 2. Therefore, only Ekant (E) is left who must have planted 1 Orange tree on Day 3 and also planted Orange trees on Day 1 and Day 2.

Exactly two people out of A, D and F planted the same type of tree on all the three days; the possible person-tree combinations in such a case could be: A-Coconut, D-Mango, F-Guava. Exactly 2 out of the given 3 combinations are true. On Day 3, they definitely planted these types only, as otherwise the given condition could not be true. So A is definitely one of the persons who planted the same type of tree on all the three days.

On Day 2, D did not plant Apple, Banana, Coconut or Orange tree. D could not have planted a Guava tree on Day 2 as in that case even F would not be able to plant Guava trees on all the three days. Therefore, D must have planted 1 Mango tree on Day 2. Therefore, D is the other person to have planted the same type of tree on all the three days.

(1) Option b
(2) Option a
(3) Option b
Farhan plants 1 Guava tree on Day 3. He cannot plant Guava trees on all the three days as then there will be three persons who plant the same type of tree on all

DIRECTIONS: Answer the questions on the basis of the information given below.

Alok, Bharti, Chaman, Dinu, Ekant and Faisal are the only people available for selection in a team. The team should have at least two people subject to the following conditions.

1. If Bharti is selected, then Dinu should also be selected while Ekant should be rejected.
2. If Alok is selected, then exactly one from Bharti and Chaman should also be selected.
3. If Chaman is selected, then Ekant should also be selected while Faisal should be rejected.
4. If the size of the team is less than 4 then Dinu and Faisal cannot be selected together.

(1) If Bharti and Faisal are not selected in the team then who should definitely be selected?
(a) Chaman
(b) Ekant
(c) Dinu
(d) Alok

(2) Which of the following pairs of two people cannot be selected along with anyone else out of the remaining 4 people?
(a) Bharti and Dinu
(b) Chaman and Ekant
(c) Dinu and Ekant
(d) Ekant and Faisal

(3) If the team selected is of the maximum possible size, then who is/are definitely selected in the team?
(a) Alok
(b) Dinu
(c) Bharti
(d) Both Alok and Dinu

Solutions:

Let’s first form as many teams as possible out of the six people Alok (A), Bharti (B), Chaman (C), Dinu (D), Ekant (E) and Faisal (F).

Teams with 2 members:
A cannot be in any such team as otherwise at least one of B and C must be selected and then subsequently one of D and E must be selected as well (hence exceeding 2-member size).
Possible teams are:

1. B, D
2. C, E
3. D, E
4. E, F

Teams with 3 members:

1. A, C, E
2. A, B, D
3. C, E, D

Teams with 4 members:

1. A, B, D, F
2. A, C, E, D

(1) Option B
Possible teams without B and F are:

1. C, E
2. D, E
3. A, C, E
4. C, E, D
5. A, C, E, D
We can see that Ekant (E) should definitely be selected.

(2) Option D
Ekant (E) and Faisal (F) (team number 4) appeartogether only once and their pair is not selected with any one else out of the remaining 4 people.

(3) Option D
Team selected must be either
A, B, D, F (team number 8 ) or
A, C, E, D (team number 9 )
We can see that Alok (A) and Dinu (D) both are definitely selected in the team.

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