# Question Bank (2) - Logical Reasoning - Hemant Malhotra

• Number of Sets -
Topic - Logical Reasoning
Answer Key available ?
Source - EliteGrid forum.

• Q1) A, B, C and D were distributed with 12 shirts, each bearing a different no among 1 to 12. No two persons got the same number of shirts. All the prime numbered shirts are owned by B. Both the shirts owned by A bear even nos. THe sum of the numbers on two shirts of C is the same as the sum of numbers on all the shirts of A. Also the no on any of the shirts that C got is not the square of a prime no. Neither the shirt numbered 1 nor the shirt numbered 9 is with B. C received shirt no 12.

1. What is the maximum possible difference b/w the sum of numbers on all the shirts of any two persons ?
a) 22
b) 23
c)21
d)30

2. What is the minimum possible difference b/w the sum of nos on all the shirts of any two persons ?
a) 5
b) 6
c) 1
d)10

3. If a shirt numbered 14 is given to anyone except the person having the maximum no of shirts without violating any of the earlier conditions. The sum of the nos all the shirts of C is more than that of B, then what is the sum of all the nos on the shirt of A ?
a) 18
b) 14
c) 32
d) CBD

4. Which of the following conditions is required to get the unique solution for the distribution ?
a) The sum of all the nos on all the shirts of one of the person is a perfect cube
b) The sum of nos on all the shirts of C is 19
c) Twice the total of nos on all the shirts of A is equal to the total of numbers on all the shirt of B
d) Any of the above

• Q2) It is possible to arrange eight of the nine numbers
2, 3, 4, 7, 10, 11, 12, 13, 15
in the vacant squares of the 3 by 4 array shown below so that the arithmetic average of the numbers in each row and in each column is the same integer. Specify which one of these nine numbers must be left out when completing the array

• Q3) A group of six persons - Babar, Humayun, Akbar, Jahangir, Shahjahan and Aurangzeb, visited angel world, where there were six rides - R1 through R6, among which two were for children, two for adults and two were common for all. There were three children and three adults in the group. Each of them went for atleast three rides. The cost of each ride is Rs. 10 per person. Before going for any adult's or any children's ride, one must go for atleast one of the common rides. Before going for R6, one must go for R3. Four persons went for both R1 and R2. Akbar did not go for R1 or R6. Shahjahan went for both R6 and R3. R4 is a children's ride. No adult went for children's ride and no child went for an adult's ride. They spent a total amount of Rs. 200 on these rides. No two of them have same combination.

1. What percentage of total expenditure did they spend on common rides?
(1) 40
(2) 50
(3) 55
(4) 25

2. If Humayun was an adult, which of the following rides he must have went for?
(1) R3
(2) R6
(3) R5
(4) R2

3. If Aurangzeb and Babar were children, then what was the least number of rides which were rode by both of them?
(1) 0
(2) 1
(3) 2
(4) 3

4. If Jahangir did not go for R2, then Humayun must have went for ______
(1) R2
(2) R3
(3) R4
(4) Cannot be determined

5. Which of the following statements will give us a clear distribution?
(1) Both Shahjahan and Aurangzeb went for four rides each.
(2) Babar, Akbar and Shahjahan were children.
(3) No ride was visited by both Akbar and Jahangir.
(4) None of the above.

• Cost of each ride is Rs 10
Total Amount =200
So Total Rides=20
Now Each one ride atleast 3
No adult went for children's ride and no child went for an adult's rde so 2 persons will ride 4 & 4 persons will ride 3 Rides
Now Four persons went for both R1 and R2 So they must be common rides
Now R4 is a children's ride & Shahzan went for R6 & R3 so R6 & R3 must be adult Rides & R5 will be children's ride
So R1,R2 -- Common rides
R4 & R5 - Children's Ride

1. Four persons went for both R1 and R2 So they must be common rides so 8 persons now in remaining 2 persons will ride one of R1 & R2 so total 10 common rides so 10/20 *100=50
2. Humayun was an adult and he will ride 3 rides atleast so R1,R2 & R3 will be combo or R1,R3,R6 or R2,R3,R6 in all cases he will ride R3 bcz R3 must come before R6
3. Now Aurangajeb & Babar were Children so common part will be 2 .. You can give one common between R1 & R2 & One common from children side
4. Jahangir did not go for R2 & Akar already didn't go for R1 & we need exact 4 persons to ride R1 & R2 so Humayun must went for R2

• Q4) During a political rally, seven leaders of a party – Ajeet, Ambika, Azad, Kamal, Kapil, Mukul and Pranab – are sitting on seven chairs arranged in a row, not necessarily in the same order. It is also known that:
(i) Ambika is sitting beside Kapil.
(ii) Pranab is the party president and so he is sitting in the middle of the row.
(iii) Either Ajeet or Kamal, but not both, is sitting at one of the ends of the row.
(iv) Azad and Mukul are sitting as far as possible from each other, without violating other conditions.

1. If ‘n’ represents the number of leaders sitting between Ajeet and Azad, which of the following is not a possible value of ‘n’?
(a) 0
(b) 2
(c) 3
(d) 5

2. Which two leaders, among the given pairs, cannot sit adjacent to each other?
(a) Mukul and Kamal
(b) Azad and Ambika
(c) Kamal and Kapil
(d) Ajeet and Mukul

• 12 shirts
i) B got all primes so B have 2,3,5,7,11
ii) A got 2 Even so (4,6) (4,8) (4,10) (4,12) (6,8),(6,10),(6,12) ,(8,10),(8.12)(10,12) are possibilities
iii) The sum of the numbers on two shirts of C is the same as the sum of numbers on all the shirts of A.

Now Sum of two shirts of A = 10/12/14/16/18/20/22
now Check 10=4+6 , this is not possible for C
Check 12= this is not possible for C
only two cases are possible 14 & 18
when A=14 (4+10) and when A=18 (8+10)
case1- when A=4,10 then C=1,6,8,12 , D=9 and B=2,3,5,7,11
Case2- When A=8,10 then C=1,6,12 , D=9 and B=2,3,4,5,7,11
So OA = B,C,A,D

• Q5) A group has to be selected from seven persons containing two women (Rehana and Kavya) and five men (Rohit, Rahul, Kamal, Nusarat and John). Rohit would not like to be in the group if Rahul is selected. Rahul and John want to be selected together in the group. Kavya would like to be in the group only if Kamal is also there. Kamal, if selected, would not like Nusarat in the group. Rohit would like to be in the group only if Nusarat is also there. Kamal insists that Rehana must be selected in case he is there in the group.

1. Which of the following is an acceptable combination of a group of three?
a) Rohit, John, Kavya
b) Rahul, Kamal, Nusarat
c) Rohit, Nusarat, Rahul
d) Rohit, Nusarat, Rehana

2. Which of the following is an acceptable combination of a group of four?
a) Rohit, Nusarat, Rehana, John
b) Rahul, John, Kavya, Kamal
c) Rahul, John, Rehana, Kamal
d) Rehana, Kamal, Rohit, Nusarat

3. Which of the following statements is true?
a) Kavya and Rohit both can be selected in a group of four.
b) A group of four can have both the women.
c) A group of four can have four men.
d) None of the above

4. If a group of five members has to be selected, then in how many ways is it possible such that Kamal is definitely a member of the group?
a) 1
b) 0
c) 2
d) 3

• Q6) From ISBT, buses ply on 6 different routes viz. 414, 413, 427, 966, 893 and 181 at an interval of 10 min, 10 min, 12 min, 15 min, 20 min and 30 min, not necessarily in that order, to four different destinations viz. Mehrauli, Badarpur, Uttam Nagar and Azadpur. There is at least one bus for each destination.

Further information is also known:
i. Two buses to the same destination cannot start at the same time.
ii. If the timings of two buses plying different routes but heading towards the same destination clash, then the bus of the route number having the shorter time interval will skip this journey.
iii. Buses on two different routes ply between ISBT and Mehrauli.
iv. The difference between the time intervals of a route to Mehrauli and Uttam Nagar is equal to the difference between the time intervals of the two routes to Uttam Nagar.
v. Buses on a route to Mehrauli leaves after every 10 min.
vi. 414 leaves for Badarpur after every 30 min.
vii. Time intervals between two different routes heading towards the same destination cannot be equal.
viii. Buses on one of the routes to Uttam Nagar leave after every 15 min.
ix. Buses to any destination can leave from ISBT with an interval of at least one minute or an integral multiple of one minute.

1 - If 427 leaves to Mehrauli after every 10 min, then in a given hour a minimum of how many buses can ply on route 427?
a) 3
b) 4
c) 6
d) 2

2 - On a festival day, if frequency of all buses was increased by decreasing the time interval of all the routes by 5 min, then what can be the minimum time difference between any two buses plying to Mehrauli?
a) 2 min
b) 5 min
c) 1 min
d) None of these

3 - Which of the following statements is necessarily TRUE?
a) A maximum of 3 buses can depart at a given time.
b) Maximum of 11 buses can depart for Mehrauli in 1 hour.
c) Maximum difference between the intervals of the buses plying to Uttam Nagar and Badarpur is 10 min.
d)The difference between the time intervals of buses plying to Uttam Nagar is an integral multiple of 5 min.

4 - If condition (iii) is not there, then what can be the minimum difference between the time intervals between the buses plying to Uttam Nagar?
a 2 min
b 3 min
c 4 min
d 5 min

• OA: B, C

• OA : D, C, D, A

• Q7) In the village of Kpetewoma, there are two marriage groups Molango and Tsuande. No marriage is permitted within a group. On marriage,a male becomes a part of his wife’s group, while women remain in their own group. Children belong to the same group as their parents.Widowers and divorced males revert to the group of their birth. Marriage to more than one person at the same time and marriage to a direct descendent are forbidden.

1 - A Tsuande female could have:
I. A grandfather born as a Molango.
II. A grandmother born as a Molango.
III.Both the grandfathers born as a Tsuande.
a) I only
b) III only
c) I and II only
d) II and III only

2 - Which of the following is not permitted under the rules?
a) A Tsuande male marrying his father’s sister.
b) A Molango female marrying her mother’s unmarried brother.
c) A man born as a Molango and now a widower, marrying his brother’s widow.
d) A widower marrying his wife’s sister.

3 - If widowers and divorced males retained the group they went into upon marrying, which of the following would be permissible?
a) A woman marrying her dead sister’s husband.
b) A woman marrying her divorced daughter’s ex-husband.
c) A widower marrying his brother’s daughter.
d) A woman marrying her mother’s brother who is a widower

• Q8) The following Table gives the number of students across six different classes of Pune Modern School in the years 2010 and 2011.

It is known:
i. New students join the school only in class V.
ii. No student leaves the school before passing out class X.
iii. The students who fail in a class in a year will study in the same class next year.

1. What was the maximum possible number of students who joined the school in 2011?
a) 100
b) 76
c) 75
d) None of these

2. In 2010, which of the following was not a possible pass percentage of class VI?
a) 60%
b) 16%
c) 58.66%
d) More than one of these

• Q9) A company has five directors – Parjit, Manjit, Charjit, Daljit and Jasjit. Two of the directors are females. All the directors have different ages. Their annual incomes (in Rs. Lakhs) are 40, 45, 50, 60 and 75, in no
particular order. It is also known that:

(i) The director with the least annual income is not the oldest. The director with the highest annual
income is older than one of the two female directors and younger than the other.
(ii) The absolute difference between the annual incomes of Manjit and Daljit is Rs. 15 lakhs.
(iii) The annual income of Charjit is not the highest among the five directors.
(iv) The annual income of the older female director is more than that of the younger female director.
(v) Manjit is the youngest among the male directors and Jasjit is the older of the two female directors.
Parjit was older than both Manjit and Jasjit.
(vi) The annual income of one among Parjit, Daljit and Jasjit is the average of the annual incomes of the
other two.

1. What is the annual income (in Rs. Lakhs) of Parjit?
(a) 40
(b) 45
(c) 50
(d) Cannot be determined

2. What is the annual income (in Rs. Lakhs) of the oldest among the five directors?
(a) 45
(b) 50
(c) 60
(d) 75

3. What is the absolute difference (in Rs. Lakhs) between the annual incomes of the younger female
director and the youngest male director?
(a) 10
(b) 30
(c) 15
(d) None of these

• Question should be rechecked.
(to satisfy the condition: the arithmetic average of the numbers in each row and in each column is the same integer.)
look in second row and in third column. First number in second row and first number in third column must be same where in the given list of numbers no two numbers are same.

• @hemant_malhotra
ans: 1. d) none of these(78)
2. c)58.66%

• Ans 1- A Tsuande female has her mother born as a Tsuande and her father born as a Molango. Thus, one of her grandmothers is born as a Molango, while the other is born as a Tsuande. Also, her maternal grandfather is born as a Molango and her paternal grandfather is born as a Tsuande. Hence, only statements I and II are true. Hence 3

Answer2- A Molango female’s mother’s unmarried brother is a Molango. Hence, according to the rules they cannot get married. Hence 2

Answer3- A woman’s mother’s brother is born in the same group as she is born in. But as he is a widower, he will be in the other group and hence, they can marry. Hence 4

• Q10) In a Blind Dating event, the participants comprise 'm' guys and 'n' girls (m > n). Each of the m guys gets to spend exactly 4 minutes with each of the n girls (any excess unpaired guys during any round await their turn). At the end of the event, each female has to submit a list of the males that she would like to meet again (which could even be all of the males, or none of them).

1. How much time would the event occupy, if organized efficiently (i.e. each guy moves immediately on to the next girl when the time is up)?
a) 4m minutes
b) 4n minutes
c) 4mn minutes
d) 4(m + n) minutes

2. In how many different ways could the final lists be made by the girls?
a) mn
b) nm+1
c) 2^m *n
d) (m + 1)n

1. Each boy has to meet n girls and will require at least 4n minutes.
Similarly each girl has to meet m guys and will take a minimum of 4m minutes.
But m > n and hence 4m > 4n;
thus the time needed for the event would be 4m minutes. so OA=1

2. Each of the n girls has 2m ways of writing her list
Now every girl has 2 options for a guy either he will choose them or reject them .. Same for other guy & same for .. so 2 * 2 * 2 * 2....m =2^m
so n * 2^m

42

45

47

62

58

31

200

164