## DILR – Logical Reasoning – Set

The following set contains four questions related to Logical Reasoning. Choose the best answer to each question.

A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands. When an employee first joins the lab, her fingers are scanned in an order of her choice, and then when she wants to re-enter the facility, she has to scan the five fingers in the same sequence.

The lab authorities are considering some relaxations of the scan order requirements, since it is observed that some employees often get locked-out because they forget the sequence.

## Questions

Q1) The lab has decided to allow a variation in the sequence of scans of the five fingers so that at most two scans (out of five) are out of place. For example, if the original sequence is Thumb (T), index finger (I), middle finger (M), ring finger (R) and little finger (L) then TLMRI is also allowed, but TMRLI is not.

How many different sequences of scans are allowed for any given person’s original scan?

Q2) The lab has decided to allow variations of the original sequence so that input of the scanned sequence of five fingers is allowed to vary from the original sequence by one place for any of the fingers. Thus, for example, if TIMRL is the original sequence, then ITRML is also allowed, but LIMRT is not.

How many different sequences are allowed for any given person’s original scan?
A) 7
B) 5
C) 8
D) 13

Q3) The lab has now decided to require six scans in the pass key sequence, where exactly one finger is scanned twice, and the other fingers are scanned exactly once, which can be done in any order. For example, a possible sequence is TIMTRL.

Suppose the lab allows a variation of the original sequence (of six inputs) where at most two scans (out of six) are out of place, as long as the finger originally scanned twice is scanned twice and other fingers are scanned once.

How many different sequences of scans are allowed for any given person’s original scan?

Q4) The lab has now decided to require six scans in the pass key sequence, where exactly one finger is scanned twice, and the other fingers are scanned exactly once, which can be done in any order. For example, a possible sequence is TIMTRL.

Suppose the lab allows a variation of the original sequence (of six inputs) so that input in the form of scanned sequence of six fingers is allowed to vary from the original sequence by one place for any of the fingers, as long as the finger originally scanned twice is scanned twice and other fingers are scanned once.

How many different sequences of scans are allowed if the original scan sequence is LRLTIM?
A) 8
B) 11
C) 13
D) 14

Q1: 11
Q2: Option (C)
Q3: 15
Q4: Option (C)

## Solutions

Q1
CAT 2017 – Logical Reasoning
Since the order of exactly one out of the five scans can’t be changed, either all the scans are in the correct order or one pair of scans can be varied, i.e. their positions can be interchanged.
Case (1): when all the scans are in the correct order = 1 way
Case (2): when exactly two are interchanged: We can choose any two of the five scans that can be interchanged in 5C2 ways = 10 ways
Case(1) + Case(2) = 10+1 = 11

Q2
CAT 2017 – Logical Reasoning
Let the original scan be: TIMRL
(1) All sequence as original = 1 way
(2) Interchange of TI = 1 way
(TI) + (RL) = 1 way
= 2 way
(3) Interchange of IM = 1 way
(IM) + (RL) = 1 way
= 2 way
(4) Interchange of MR = 1 way
(MR) + (TI) = 1 way
= 2 way
(5) Interchange of RL = 1 way
Total = 1 + 2 + 2 + 2 + 1 = 8 ways.
Option (C)

Q3
CAT 2017 – Logical Reasoning
Let us say original input: TIMTRL.
Case (1): None of them misplaced : 1.
Case (2): When exactly two are misplaced.
T can be misplaced in 4 ways.
I can be misplaced in 4 ways.
M can be misplaced in 3 ways.
T can be misplaced in 2 ways.
R can be misplaced in 1 way.
Total ways in case (2) = 4 + 4 + 3 + 2 + 1
= 14 ways.
Both case (1) and case (2) = 14 + 1 = 15 ways

Q4
CAT 2017 – Logical Reasoning
Given LRLTIM
The distinct possibilities are:
1. No shift = 1 way
2. (a) LR = 1 way
(b) LR + LT = 1 way
(c) LR + LT + IM = 1 way
(d) LR + IM = 1 way
(e) LR + IT = 1 way (Total 5 ways)
3. (a) RL = 1 way
(b) RL + TI = 1 way
(c) RL + IM = 1 way (Total 3 ways)
4. (a) LT = 1 way
(b) LT + IM = 1 way (Total 2 way)
5. TI = 1 way
6. IM = 1 way
Total ways = 1 + 5 + 3 +2 +1 + 1 = 13 ways.
Option (C)

## CAT 2017 Questions from Logical Reasoning

Logical Reasoning – Set 1: Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata
Logical Reasoning – Set 2: In an 8 X 8 chessboard a queen placed anywhere can attack another piece if the piece is present in the same row
Logical Reasoning – Set 3: A tea taster was assigned to rate teas from six different locations – Munnar, Wayanad, Ooty, Darjeeling, Assam and Himachal.
Logical Reasoning – Set 4: Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N).
Logical Reasoning – Set 5: A new airlines company is planning to start operations in a country.
Logical Reasoning – Set 6: In a square layout of size 5m × 5m, 25 equal sized square platforms of different heights are built.
Logical Reasoning – Set 7: There are 21 employees working in a division, out of whom 10 are special-skilled employees (SE) and the remaining are regular skilled employees (RE).
Logical Reasoning – Set 8: Healthy Bites is a fast food joint serving three items: burgers, fries and ice cream.

## Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video

## DILR – Logical Reasoning – Set

The following set contains four questions related to Logical Reasoning. Choose the best answer to each question.

Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata by a flight operated by Cheap Air. In the flight, sitting is arranged in 30 rows, numbered 1 to 30, each consisting of 6 seats, marked by letters A to F from left to right, respectively. Seats A to C are to the left of the aisle (the passage running from the front of the aircraft to the back), and seats D to F are to the right of the aisle. Seats A and F are by the windows and referred to as Window seats, C and D are by the aisle and are referred to as Aisle seats while B and E are referred to as Middle seats. Seats marked by consecutive letters are called consecutive seats (or seats next to each other). A seat number is a combination of the row number, followed by the letter indicating the position in the row; e.g., 1A is the left window seat in the first row, while 12E is the right middle seat in the 12th row.

Cheap Air charges Rs. 1000 extra for any seats in Rows 1, 12 and 13 as those have extra legroom. For Rows 2-10, it charges Rs. 300 extra for Window seats and Rs. 500 extra for Aisle seats. For Rows 11 and 14 to 20, it charges Rs. 200 extra for Window seats and Rs. 400 extra for Aisle seats. All other seats are available at no extra charge.

The following are known:
1. The eight friends were seated in six different rows.
2. They occupied 3 Window seats, 4 Aisle seats and 1 Middle seat.
3. Seven of them had to pay extra amounts, totaling to Rs. 4600, for their choices of seat. One of them did not pay any additional amount for his/her choice of seat.
4. Jayanta, Ajit and Byomkesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but all of them paid different amounts for their choices of seat. One of these amounts may be zero.
5. Gargi was sitting next to Kikira, and Manik was sitting next to Jayanta.
6. Prodosh and Tapesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but they paid different amounts for their choices of seat. One of these amounts may be zero.

## Questions

Q1) In which row was Manik sitting?
A) 10
B) 11
C) 12
D) 13

Q2) How much extra did Jayanta pay for his choice of seat?
A) Rs. 300
B) Rs. 400
C) Rs. 500
D) Rs. 1000

Q3) How much extra did Gargi pay for her choice of seat?
A) 0
B) Rs. 300
C) Rs. 500
D) Rs. 1000

Q4) Who among the following did not pay any extra amount for his/her choice of seat?
A) Kikira
B) Manik
C) Gargi
D) Tapesh

Q1: Option (A)
Q2: Option (C)
Q3: Option (D)
Q4: Option (D)

## Solutions

CAT 2017 – Logical Reasoning
Let’s take the initial letter of each friend. From the given data, we can observe that Row number 1 to 20 have extra charges except for middle seat. J, A, B must be in Aisle seats to get the sum as 4600; and we know that J, A, B paid different amount. Therefore,

G, K and K, G can be interchanged. Moreover they can be placed in row 1 to 0. So also the right window positions and aisle seats can be interchanged.

Q1
CAT 2017 – Logical Reasoning
Manik was sitting in Row number 10
Option (A)

Q2
CAT 2017 – Logical Reasoning
Jayanta paid Rs. 500 extra for his choice of seat
Option (C)

Q3
CAT 2017 – Logical Reasoning
Gargi paid Rs. 1000 extra for her choice of seat
Option (D)

Q4
CAT 2017 – Logical Reasoning
Tapesh did not pay any extra amount for his choice of seat
Option (D)

## CAT 2017 Questions from Logical Reasoning

Logical Reasoning – Set 1: A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands.
Logical Reasoning – Set 2: In an 8 X 8 chessboard a queen placed anywhere can attack another piece if the piece is present in the same row
Logical Reasoning – Set 3: A tea taster was assigned to rate teas from six different locations – Munnar, Wayanad, Ooty, Darjeeling, Assam and Himachal.
Logical Reasoning – Set 4: Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N).
Logical Reasoning – Set 5: A new airlines company is planning to start operations in a country.
Logical Reasoning – Set 6: In a square layout of size 5m × 5m, 25 equal sized square platforms of different heights are built.
Logical Reasoning – Set 7: There are 21 employees working in a division, out of whom 10 are special-skilled employees (SE) and the remaining are regular skilled employees (RE).
Logical Reasoning – Set 8: Healthy Bites is a fast food joint serving three items: burgers, fries and ice cream.

## Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video

## DILR – Logical Reasoning – Set

The following set contains four questions related to Logical Reasoning. Choose the best answer to each question.

In an 8 X 8 chessboard a queen placed anywhere can attack another piece if the piece is present in the same row, or in the same column or in any diagonal position in any possible 4 directions, provided there is no other piece in between in the path from the queen to that piece.

The columns are labelled a to h (left to right) and the rows are numbered 1 to 8 (bottom to top). The position of a piece is given by the combination of column and row labels. For example, position c5 means that the piece is in cth column and 5th row.

## Questions

Q1) If the queen is at c5, and the other pieces at positions c2, gl, g3, g5 and a3, how many are under attack by the queen? There are no other pieces on the board.
A) 2 ‘
B) 3
C) 4
D) 5

Q2) If the other pieces are only at positions al, a3, b4, d7, h7 and h8, then which of the following positions of the queen results in the maximum number of pieces being under attack?
A) f8
B) a7
C) c1
D) d3

Q3) If the other pieces are only at positions al, a3, b4, d7, h7 and h8, then from how many positions the queen cannot attack any of the pieces?
A) 0
B) 3
C) 4
D) 6

Q4) Suppose the queen is the only piece on the board and it is at position d5.
In how many positions can another piece be placed on the board such that it is safe from attack from the queen?

A) 32
B) 35
C) 36
D) 37

Q1: Option (C)
Q2: Option (D)
Q3: Option (C)
Q4: Option (C)

## Solutions

Q1
CAT 2017 – Logical Reasoning

P1 is in the same column as Queen
P2 is in the same diagonal as Queen
P3 is not in the same diagonal, column or row of the queen
P4 is in the same row as queen
P5 is diagonal to queen
So, acc to the question, queen can attack P1, P2, P4 and P5

Q2
CAT 2017 – Logical Reasoning
When Queen is at f8

The Queen can attack P6 (same row), P3 (Same diagonal). So, 2

When Queen is at a7

The Queen can attack P2 (Same column), P4 (Same row). So, 2

When Queen is at c1

The Queen can attack P1 (Same row), P2 (Same Diagonal). So, 2

When Queen is at d3

Here, the queen can attack P2 (Same row), P4 (Same Column), P5 (Same Diagonal). So, 3

Option (D) is the right answer.

Q3
CAT 2017 – Logical Reasoning
Queen cannot be placed in Columns A, B, D, and H. From the remaining columns, it has to be assessed. For e.g.
COLUMN C:-> If Queen is placed in c2, it will attack h7. Further, other positions in the column c can be ruled out. Similarly, analyzing other squares, the result is as follows:
Queen can be placed in e2, f2, g2, g5 (such that the pieces on board are NOT under attack). So, there are a total of 4 such squares for the Queen.

Q4
CAT 2017 – Logical Reasoning
Given that Queen is at d5. The squares which will be under attack are as indicated below. These squares are either lying in the diagonal, or in the row or in the column. The remaining squares that are safe have been kept empty. A total of 36 such squares are safe (by counting).

Option (C)

## CAT 2017 Questions from Logical Reasoning

Logical Reasoning – Set 1: A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands.
Logical Reasoning – Set 2: Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata by a flight operated by Cheap Air.
Logical Reasoning – Set 3: A tea taster was assigned to rate teas from six different locations – Munnar, Wayanad, Ooty, Darjeeling, Assam and Himachal.
Logical Reasoning – Set 4: Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N).
Logical Reasoning – Set 5: A new airlines company is planning to start operations in a country.
Logical Reasoning – Set 6: In a square layout of size 5m × 5m, 25 equal sized square platforms of different heights are built.
Logical Reasoning – Set 7: There are 21 employees working in a division, out of whom 10 are special-skilled employees (SE) and the remaining are regular skilled employees (RE).
Logical Reasoning – Set 8: Healthy Bites is a fast food joint serving three items: burgers, fries and ice cream.

## Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video

## DILR – Logical Reasoning – Set

The following set contains four questions related to Logical Reasoning. Choose the best answer to each question.

A tea taster was assigned to rate teas from six different locations – Munnar, Wayanad, Ooty, Darjeeling, Assam and Himachal. These teas were placed in six cups, numbered 1 to 6, not necessarily in the same order. The tea taster was asked to rate these teas on the strength of their flavour on a scale of 1 to 10. He gave a unique integer rating to each tea. Some other information is given below:

1. Cup 6 contained tea from Himachal.
2. Tea from Ooty got the highest rating, but it was not in Cup 3.
3. The rating of tea in Cup 3 was double the rating of the tea in Cup 5.
4. Only two cups got ratings in even numbers.
5. Cup 2 got the minimum rating and this rating was an even number.
6. Tea in Cup 3 got a higher rating than that in Cup 1. 7. The rating of tea from Wayanad was more than the rating of tea from Munnar, but less than that from Assam.

## Questions

Q1) What was the second highest rating given?

Q2) What was the number of the cup that contained tea from Ooty?

Q3) If the tea from Munnar did not get the minimum rating, what was the rating of the tea from Wayanad?
A) 3
B) 5
C) 1
D) 6

Q4) If cups containing teas from Wayanad and Ooty had consecutive numbers, which of the following statements may be true?
A) Cup 5 contains tea from Assam
B) Cup 1 contains tea from Darjeeling
C) Tea from Wayanad has got a rating of 6
D) Tea from Darjeeling got the minimum rating

Q1: 7
Q2: 4
Q3: Option (B)
Q4: Option (B)

## Solutions

CAT 2017 – Logical Reasoning
There can be only two even numbers in rating.

Assam > Wayanand > Munnar (Ratings)

Q1
CAT 2017 – Logical Reasoning
As per the table, we can see that the second highest rating is 7 (Himachal, Cup number 6)

Q2
CAT 2017 – Logical Reasoning
As per the table, the cup from Ooty has number 4.

Q3
CAT 2017 – Logical Reasoning
If tea from Munnar did not get the minimum rating, then tea from Darjeeling got the minimum rating (2)
The remaining ratings are 5, 6, 3
The only possibility is
Assam (6, Cup 3) > Wayanand (5, Cup 1) > Munnar (3, Cup 5)
So, the rating of tea from Wayanand is 5.
Option (B)

Q4
CAT 2017 – Logical Reasoning
The choices are Cup 3 (Rating – 6) and Cup 5 (Rating – 3), Assam can’t be Cup 5 because it has a higher rating than Wayanand. So, Wayanad will be Cup 5. Munnar has a rating lesser than Wayanand. So, the only choice for Munnar is Cup 2 (Rating – 2). Assam can be Cup 1 or 3 and Darjeeling can also be Cup 1 or 3.
Option (B) seems fit.

## CAT 2017 Questions from Logical Reasoning

Logical Reasoning – Set 1: A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands.
Logical Reasoning – Set 2: Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata by a flight operated by Cheap Air.
Logical Reasoning – Set 3: In an 8 X 8 chessboard a queen placed anywhere can attack another piece if the piece is present in the same row, or in the same column or in any diagonal position in any possible 4 directions, provided there is no other piece in between in the path from the queen to that piece.
Logical Reasoning – Set 4: Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N).
Logical Reasoning – Set 5: A new airlines company is planning to start operations in a country.
Logical Reasoning – Set 6: In a square layout of size 5m × 5m, 25 equal sized square platforms of different heights are built.
Logical Reasoning – Set 7: There are 21 employees working in a division, out of whom 10 are special-skilled employees (SE) and the remaining are regular skilled employees (RE).
Logical Reasoning – Set 8: Healthy Bites is a fast food joint serving three items: burgers, fries and ice cream.

## Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video

## DILR – Logical Reasoning – Set

The following set contains four questions related to Logical Reasoning. Choose the best answer to each question.

Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N). The roads from A to M, and from N to B, are both short and narrow. In each case, one car takes 6 minutes to cover the distance, and each additional car increases the travel time per car by 3 minutes because of congestion. (For example, if only two cars drive from A to M, each car takes 9 minutes.) On the road from A to N, one car takes 20 minutes, and each additional car increases the travel time per car by 1 minute. On the road from M to B, one car takes 20 minutes, and each additional car increases the travel time per car by 0.9 minute.

The police department orders each car to take a particular route in such a manner that it is not possible for any car to reduce its travel time by not following the order, while the other cars are following the order.

## Questions

Q1) How many cars would be asked to take the route A-N-B, that is Akala-Nanur-Bakala route, by the police department?

Q2) If all the cars follow the police order, what is the difference in travel time (in minutes) between a car which takes the route A-NB and a car that takes the route A-M-B?
A) 1
B) 0.1
C) 0.2
D) 0.9

Q3) A new one-way road is built from M to N. Each car now has three possible routes to travel from A to B: A-M-B, A-N-B and A-MN-B. On the road from M to N, one car takes 7 minutes and each additional car increases the travel time per car by 1 minute. Assume that any car taking the A-M-N-B route travels the A-M portion at the same time as other cars taking the A-M-B route, and the N-B portion at the same time as other cars taking the A-N-B route.

How many cars would the police department order to take the A-M-N-B route so that it is not possible for any car to reduce its travel time by not following the order while the other cars follow the order? (Assume that the police department would never order all the cars to take the same route.)

Q4) A new one-way road is built from M to N. Each car now has three possible routes to travel from A to B: A-M-B, A-N-B and A-MN-B. On the road from M to N, one car takes 7 minutes and each additional car increases the travel time per car by 1 minute. Assume that any car taking the A-M-N-B route travels the A-M portion at the same time as other cars taking the A-M-B route, and the N-B portion at the same time as other cars taking the – A-N-B route.

If all the cars follow the police order, what is the minimum travel time (in minutes) from A to B? (Assume that the police department would never order all the cars to take the same route.)
A) 26
B) 32
C) 29.9
D) 30

Q1: 2
Q2: Option (B)
Q3: 2
Q4: Option (B)

## Solutions

Q1
From CAT 2017 – Logical Reasoning – Set, we can infer that,

When two cars go from the route A – N – B

Total time taken = 30 minutes
When two cars go from the route A – M – B

Total time taken = 29.9 minutes
So, the number of cars that can go from the route A-N-B are 2

Q2
From CAT 2017 – Logical Reasoning – Set, we can infer that,

As we can see from the above question, the difference in time will be 30-29.9 = 0.1 minutes
Option (B)

Q3
From CAT 2017 – Logical Reasoning – Set, we can infer that,

When only one care takes the route A – N –B

Total time = 26 minutes
When only one car takes the route A – M – B

Total time = 26 minutes
So, police department will ask 2 cars to take the route A – M – N – B

Q4
From CAT 2017 – Logical Reasoning – Set, we can infer that,

When all cars follow the police order the time taken would be A-M-B (1 car) = 12 + 20 = 32 minutes.
A-M-N-B (2cars) = 12 + 8 + 12 = 32 minutes. A-N-B (1 car) = 20 + 12 =32 minutes.
Option (B)

## CAT 2017 Questions from Logical Reasoning

Logical Reasoning – Set 1: A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands.
Logical Reasoning – Set 2: Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata by a flight operated by Cheap Air.
Logical Reasoning – Set 3: In an 8 X 8 chessboard a queen placed anywhere can attack another piece if the piece is present in the same row, or in the same column or in any diagonal position in any possible 4 directions, provided there is no other piece in between in the path from the queen to that piece.
Logical Reasoning – Set 4: A tea taster was assigned to rate teas from six different locations – Munnar, Wayanad, Ooty, Darjeeling, Assam and Himachal.
Logical Reasoning – Set 5: A new airlines company is planning to start operations in a country.
Logical Reasoning – Set 6: In a square layout of size 5m × 5m, 25 equal sized square platforms of different heights are built.
Logical Reasoning – Set 7: There are 21 employees working in a division, out of whom 10 are special-skilled employees (SE) and the remaining are regular skilled employees (RE).
Logical Reasoning – Set 8: Healthy Bites is a fast food joint serving three items: burgers, fries and ice cream.

## Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video

## DILR – Logical Reasoning – Set

The following set contains four questions related to Logical Reasoning. Choose the best answer to each question.

A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with. The flight duration between any pair of cities will be less than one hour. To start operations, the company has to decide on a daily schedule.

The underlying principle that they are working on is the following:

Any person staying in any of these 10 cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day.

## Questions

Q1) If the underlying principle is to be satisfied in such a way that the journey between any two cities can be performed using only direct (non-stop) flights, then the minimum number of direct flights to be scheduled is:
A) 45
B) 90
C) 180
D) 135

Q2) Suppose three of the ten cities are to be developed as hubs. A hub is a city which is connected with every other city by direct flights each way, both in the morning as well as in the evening. The only direct flights which will be scheduled are originating and/or terminating in one of the hubs. Then the minimum number of direct flights that need to be scheduled so that the underlying principle of the airline to serve all the ten cities is met without visiting more than one hub during one trip is:
A) 54
B) 120
C) 96
D) 60

Q3) Suppose the 10 cities are divided into 4 distinct groups 01,02,03,04 having 3, 3, 2 and 2 cities respectively and that G1 consists of cities named A, B and C. Further, suppose that direct flights are allowed only between two cities satisfying one of the following:
1. Both cities are in G1
2. Between A and any city in G2
3. Between B and any city in G3
4. Between C and any city in G4

Then the minimum number of direct flights that satisfies the underlying principle of the airline is:

Q4) Suppose the 10 cities are divided into 4 distinct groups G1, G2, G3, G4 having 3, 3, 2 and 2 cities respectively and that G1 consists of cities named A, B and C. Further, suppose that direct flights are allowed only between two cities satisfying one of the following:
1. Both cities are in G1
2. Between A and any city in G2
3. Between B and any city in G3
4. Between C and any city in G4

However, due to operational difficulties at A, it was later decided that the only flights that would operate at A would be those to and from B. Cities in G2 would have to be assigned to G3 or to G4.

What would be the maximum reduction in the number of direct flights as compared to the situation before the operational difficulties arose?

Q1: Option (C)
Q2: Option (C)
Q3: 40
Q4: 4

## Solutions

Q1
As per CAT 2017 – Logical Reasoning – Set
For any pair of cities, say A and B, to satisfy the underlying principle, there must be a morning flight from A to B, an evening flight from B to A and a morning flight from B to A and an evening flight from A to B.
Only then can a person from A or B travel to B or A and return the same day. Hence, there must be four flights between any pair of cities.
Number of ways of selecting two cities from ten cities
= 10C2
= (10*9)/2 = 45
Hence, the minimum number of flights that must be scheduled = 45 ×4 = 180.
Option (C)

Q2
As per CAT 2017 – Logical Reasoning – Set
Let the ten cities be represented by A – J. Among these ten cities, consider A, B and C to be hubs and the other seven cities to be non-hub cities. It is given that any direct flight should originate or terminate at a hub.

Consider city D, which is not a hub. D is connected to each of A, B and C. Between D and each of A, B and C, theremust be four flights (see the above solution). Hence, from D, there must be 4 × 3 = 12 flights to the three hubs, A, B and C. Similarly, for each of the other six non-hub cities, there must be 12 flights connecting each non-hub city with the three hubs. Hence, a total of 12 ×7 = 84 flights will connect a non-hub city with a hub. In addition to this, the three hubs must be connected amongst themselves. Since there must be four flights between any pair of cities, there will be a total of 4 × 3 = 12 flights connecting any pair of hubs.

So, the total minimum number of flights that should be scheduled = 84 + 12 = 96.
Option (C)

Q3
As per CAT 2017 – Logical Reasoning – Set
Given that G1 has the cities A, B and C. G2, G3 and G4 have 3, 2 and 2 cities respectively.

As per the given conditions, we can see that a city in G2 cannot be connected by a direct flight to a city in G3 or G4. Hence, for a person to travel from a city in G2 to a city in G3 or G4, all the cities in G2 must be connected to A and from A, he can travel to B or C to travel to a city G3 or G4 respectively.

Hence, the 3 cities in G2 must be connected to A. Between each pair of cities there must be four flights. Hence, there must be 4 × 3 = 12 flights between cities in G2 and A.

Since there are 2 cities in G3, there must be 2 × 4 = 8 flights between cities in G3 and B. Since there are 2 cities in G4, there must be 2 × 4 = 8 flights between cities in G4 and C. Also, the cities in G1, i.e., A, B and C must be connected to each other. Hence, there must be an additional 4 × 3 = 12 flights between these three cities. Therefore, the total minimum number of direct flights that must be scheduled = 12 + 8 + 8 + 12 = 40

Q4
As per CAT 2017 – Logical Reasoning – Set, it is given that the cities in G2 will be assigned to G3 or G4. However, this, by itself, will not result in any reduction in the number of flights because the cities in G2 will still have to be connected to either B or C. However, it is also given that there are now no flights between A and C. Hence, the 4 flights that would have been scheduled in the previous case, will now not be scheduled.

Hence, the reduction in the number of flights can be a maximum of 4.

## CAT 2017 Questions from Logical Reasoning

Logical Reasoning – Set 1: A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands.
Logical Reasoning – Set 2: Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata by a flight operated by Cheap Air.
Logical Reasoning – Set 3: In an 8 X 8 chessboard a queen placed anywhere can attack another piece if the piece is present in the same row, or in the same column or in any diagonal position in any possible 4 directions, provided there is no other piece in between in the path from the queen to that piece.
Logical Reasoning – Set 4: A tea taster was assigned to rate teas from six different locations – Munnar, Wayanad, Ooty, Darjeeling, Assam and Himachal.
Logical Reasoning – Set 5: Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N). The roads from A to M, and from N to B
Logical Reasoning – Set 6: In a square layout of size 5m × 5m, 25 equal sized square platforms of different heights are built.
Logical Reasoning – Set 7: There are 21 employees working in a division, out of whom 10 are special-skilled employees (SE) and the remaining are regular skilled employees (RE).
Logical Reasoning – Set 8: Healthy Bites is a fast food joint serving three items: burgers, fries and ice cream.

## Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video

## DILR – Logical Reasoning – Set

The following set contains four questions related to Logical Reasoning. Choose the best answer to each question.

In a square layout of size 5m × 5m, 25 equal sized square platforms of different heights are built. The heights (in metres) of individual platforms are as shown below:

Individuals (all of same height) are seated on these platforms. We say an individual A can reach art individual B if all the three following conditions are met:

(i) A and B are In the same row or column

(ii) A is at a lower height than B

(iii) If there is/are any individuals (s) between A and B, such individual(s) must be at a height tower than that of A.

Thus in the table given above, consider the Individual seated at height 8 on 3rd row and 2nd column. He can be reached by four individuals. He can be reached by the individual on his left at height 7, by the two individuals on his right at heights of 4 and 6 and by the individual above at height 5.

Rows in the layout are numbered from top to bottom and columns are numbered from left to right.

## Questions

Q1) How many individuals in this layout can be reached by just one individual?
A) 3
B) 5
C) 7
D) 8

Q2) Which of the following is true for any individual at a platform of height 1 m in this layout?
A) They can be reached by all the individuals in their own row and column
B) They can be reached by at least 4 individuals
C) They can be reached by at least one individual
D) They cannot be reached by anyone

Q3) We can find two individuals who cannot be reached by anyone in
A) the last row
B) the fourth row
C) the fourth column
D) the middle column

A) Each row has an individual who can be reached by 5 or more individuals
B) Each row has an individual who cannot be reached by anyone
C) Each row has at least two individuals who can be reached by an equal number of individuals
D) All individuals at the height of 9 m can be reached by at least 5 individuals

Q1: Option (C)
Q2: Option (D)
Q3: Option (C)
Q4: Option (C)

## Solutions

Q1
CAT 2017 – Logical Reasoning – Set
As per the table, we can see that 7 individuals can be reached by 7 people.
Option (C)

Q2
CAT 2017 – Logical Reasoning – Set
As per the table, we can see that individuals of height 1mm cannot be reached by anyone.
Option (D)

Q3
CAT 2017 – Logical Reasoning – Set
This can be observed from the table.
Option (3)

Q4
CAT 2017 – Logical Reasoning – Set
This can be observed from the table.
Option (C)

## CAT 2017 Questions from Logical Reasoning

Logical Reasoning – Set 1: A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands.
Logical Reasoning – Set 2: Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata by a flight operated by Cheap Air.
Logical Reasoning – Set 3: In an 8 X 8 chessboard a queen placed anywhere can attack another piece if the piece is present in the same row, or in the same column or in any diagonal position in any possible 4 directions, provided there is no other piece in between in the path from the queen to that piece.
Logical Reasoning – Set 4: A tea taster was assigned to rate teas from six different locations – Munnar, Wayanad, Ooty, Darjeeling, Assam and Himachal.
Logical Reasoning – Set 5: Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N). The roads from A to M, and from N to B
Logical Reasoning – Set 6: A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with.
Logical Reasoning – Set 7: There are 21 employees working in a division, out of whom 10 are special-skilled employees (SE) and the remaining are regular skilled employees (RE).
Logical Reasoning – Set 8: Healthy Bites is a fast food joint serving three items: burgers, fries and ice cream.

## Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video

## DILR – Logical Reasoning – Set

The following set contains four questions related to Logical Reasoning. Choose the best answer to each question.

There are 21 employees working in a division, out of whom 10 are special-skilled employees (SE) and the remaining are regular skilled employees (RE). During the next five months, the division has to complete five projects every month. Out of the 25 projects, 5 projects are “challenging”, while the remaining ones are “standard”. Each of the challenging projects has to be completed in different months. Every month, five teams – T1, T2, T3, T4 and T5, work on one project each. T1, T2, T3, T4 and T5 are allotted the challenging project in the first, second, third, fourth and fifth month, respectively. The team assigned the challenging project has one more employee than the rest.

In the first month, T1 has one more SE than T2, T2 has one more SE than T3, T3 has one more SE than T4, and T4 has one more SE than T5. Between two successive months, the composition of the teams changes as follows:

a. The team allotted the challenging project, gets two SE from the team which was allotted the challenging project in the previous month. In exchange, one RE is shifted from the former team to the latter team.

b. After the above exchange, if T1 has any SE and T5 has any RE, then one SE is shifted from T1 to T5, and one RE is shifted from T 5 to T1. Also, if T2 has any SE and T4 has any RE, then one SE is shifted from T2 to T4, and one RE is shifted from T4 to T2.

Each standard project has a total of 100 credit points, while each challenging project has 200 credit points. The credit points are equally shared between the employees included in that team.

## Questions

Q1) The number of times in which the composition of team T 2 and the number of times in which composition of team T 4 remained unchanged in two successive months are:
A) (2, 1)
B) (1, 0)
C) (0, 0)
D) (1, 1)

Q2)The number of SE in T1 and T5 for the projects in the third month are, respectively:
A) (0, 2)
B) (0, 3)
C) (1, 2)
D) (1, 3)

Q3) Which of the following CANNOT be the total credit points earned by any employee from the projects?
A) 140
B) 150
C) 170
D) 200

Q4) One of the employees named Aneek scored 185 points. Which of the following CANNOT be true?
A) Aneek worked only in teams T1, T2, T3, and T4
B) Aneek worked only in teams T1, T2, T4, and T5
C) Aneek worked only in teams T2, T3, T4, and T5
D) Aneek worked only in teams T1, T3, T4, and T5

Q1: Option (B)
Q2: Option (A)
Q3: Option (B)
Q4: Option (D)

## Solutions

From CAT 2017 – Logical Reasoning – Set, we can infer that,
Number of Special Skilled Employees (SE) = 10
Number of Regular Skilled Employees (RE) = 11

Q1
From CAT 2017 – Logical Reasoning – Set, we can infer that,
The composition of T2 remains unchanged in T2 in 3rd and 4th months. The composition for T4 changes constantly.
Option (B)

Q2
From CAT 2017 – Logical Reasoning – Set, we can infer that,
Number of SE in T1 in third month = 0
Number of SE in T5 in third month = 2
Option (A)

Q3
From CAT 2017 – Logical Reasoning – Set, we can infer that,
Money one person earns in a Challenging Project = 200/5 = 40
Money one person earns in a Standard Project = 100/4 = 25
An employee can earn 140 when they work in one Challenging project and 4 Standard Projects = 40 + 25*4 = 140
An employee can earn 170 when they work in 3 Challenging Projects and 2 Standard Projects = 3*40 + 2*25 = 170
An employee can earn 200 when they work in 5 Challenging Projects = 5*40 = 200
So, option (B) does not seem possible

Q4
From CAT 2017 – Logical Reasoning – Set, we can infer that,
Since Aneek secured 185 credits, he has worked in four challenging projects and one standard project.
Option A: Aneek could have worked in T1 in 1st month (in challenging project), T2 in 2nd month (in challenging project), T3 in 3rd month (in challenging project), T4 in 4th month (in challenging project) and 5th month (in standard project). Hence, this is possible.
Option B: Aneek could have worked in T1 in 1st month (in challenging project), T2 in 2nd month (in challenging project), T4 in 3rd month (in standard project), T4 in 4th month (in challenging project) and T5 in 5th month (in challenging project). Hence, this is possible.
Option C: Aneek could have worked in T2 in 1st month (in standard project), T2 in 2nd month (in challenging project), T3 in 3rd month (in challenging project), T4 in 4th month (in challenging project) and T5 in 5th month (in challenging project). Hence, this is possible.
Option D: Aneek could have worked in T1 in 1st month (in challenging project). He can work in T1 or T5 in the 2nd month. In either case, he cannot work in T3 without working in T2 first. If we assume, he worked in T3 in the 1st month, he could not have worked in four teams in the five months. Similarly, we can rule out the other possibilities. Hence, this is the answer.
Option (D) is the right answer.

## CAT 2017 Questions from Logical Reasoning

Logical Reasoning – Set 1: A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands.
Logical Reasoning – Set 2: Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata by a flight operated by Cheap Air.
Logical Reasoning – Set 3: In an 8 X 8 chessboard a queen placed anywhere can attack another piece if the piece is present in the same row, or in the same column or in any diagonal position in any possible 4 directions, provided there is no other piece in between in the path from the queen to that piece.
Logical Reasoning – Set 4: A tea taster was assigned to rate teas from six different locations – Munnar, Wayanad, Ooty, Darjeeling, Assam and Himachal.
Logical Reasoning – Set 5: Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N). The roads from A to M, and from N to B
Logical Reasoning – Set 6: A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with.
Logical Reasoning – Set 7: In a square layout of size 5m × 5m, 25 equal sized square platforms of different heights are built.
Logical Reasoning – Set 8: Healthy Bites is a fast food joint serving three items: burgers, fries and ice cream.

## Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video

## DILR – Logical Reasoning – Set

The following set contains four questions related to Logical Reasoning. Choose the best answer to each question.

Healthy Bites is a fast food joint serving three items: burgers, fries and ice cream. It has two employees Anish and Bani who prepare the items ordered by the clients. Preparation time is 10 minutes for a burger and 2 minutes for an order of ice cream. An employee can prepare only one of these items at a time. The fries are prepared in an automatic fryer which can prepare up to 3 portions of fires at a time, and takes 5 minutes irrespective of the number of portions. The fryer does not need an employee to constantly attend to it, and we can ignore the time taken by an employee to start and stop the fryer; thus, an employee can be engaged in preparing other items while the frying is on. However fries cannot be prepared in anticipation of future orders.

Healthy Bites wishes to serve the orders as early as possible. The individual items in any order are served as and when ready; however, the order is considered to be completely served only when all the items of that order are served.

The table below gives the orders of three clients and the times at which they placed their orders;

## Questions

Q1) Assume that only one client’s order can be processed at any given point of time. So, Anish or Bani cannot start preparing a new order while a previous order is being prepared.
At what time is the order placed by Client 1 completely served?

A) 10:17
B) 10:10
C) 10:15
D) 10:20

Q2) Assume that only one client’s order can be processed at any given point of time. So, Anish or Bani cannot start preparing a new order while a previous order is being prepared.
At what time is the order placed by Client 3 completely served?

A) 10:35
B) 10:22
C) 10:25
D) 10:17

Q3)Suppose the employees are allowed to process multiple orders at a time, but the preference would be to finish orders of clients who placed their orders earlier.
At what time is the order placed by Client 2 completely served?

A) 10:10
B) 10:12
C) 10:15
D) 10:17

Q4) Suppose the employees are allowed to process multiple orders at a time, but the preference would be to finish orders of clients who placed their orders earlier.
Also assume that the fourth client came in only at 10:35. Between 10:00 and 10:30, for how many minutes is exactly one of the employees idle?

A) 7
B) 10
C) 15
D) 23

Q1: Option (B)
Q2: Option (C)
Q3: Option (A)
Q4: Option (B)

## Solutions

Q1
After going through CAT 2017 – Logical Reasoning – Set, we can see that, the order of Client 1 has 1 burger, 3 portions of fries and one ice cream
Start the fries (They will take 5 mins). While the fries are in progress, one of them can make Ice Cream (2 mins) and another can start on Burger. After 5 mins are over, Burger still needs 5 minutes more. So, the order will be prepared in 5 + 5 = 10 mins in total. So, the order will be served at 10:10.

Q2
After going through CAT 2017 – Logical Reasoning – Set, we can see that, the order for client 1 got completed at 10:10.
The order for client will start at 10:10. Fries will take 5 mins and while the fries are getting prepared, Ice cream can be prepared by one of them. So, in total it will take 5 mins to process the order for Client 2.
We will start the order for Client 3 at 10:15. We will start with the fries first, while the fries are being prepared, one of them can start with Burger. Burger takes 10 mins, so after the fries are prepared, it will take additional 5 mins for the burger to get prepared. So, in total in total it will take 10 mins for the processing of the order of Client 3.
By 10:25, order of Client 3 will be prepared.

Q3
This timeline from CAT 2017 – Logical Reasoning – Set will help you understand

The order for Client 2 will be served by 10:10. Even, Client 1 will get its order by 10:10 (because of burger)

Q4
After going through CAT 2017 – Logical Reasoning – Set, we can see that,

As per the timeline, one person will be idle during 2-5, 10-15 and 15-17.
So, 3+5+2 = 10 minutes.
Exactly one person will be idle for 10 minutes.

## CAT 2017 Questions from Logical Reasoning

Logical Reasoning – Set 1: A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands.
Logical Reasoning – Set 2: Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata by a flight operated by Cheap Air.
Logical Reasoning – Set 3: In an 8 X 8 chessboard a queen placed anywhere can attack another piece if the piece is present in the same row, or in the same column or in any diagonal position in any possible 4 directions, provided there is no other piece in between in the path from the queen to that piece.
Logical Reasoning – Set 4: A tea taster was assigned to rate teas from six different locations – Munnar, Wayanad, Ooty, Darjeeling, Assam and Himachal.
Logical Reasoning – Set 5: Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N). The roads from A to M, and from N to B
Logical Reasoning – Set 6: A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with.
Logical Reasoning – Set 7: In a square layout of size 5m × 5m, 25 equal sized square platforms of different heights are built.
Logical Reasoning – Set 8: There are 21 employees working in a division, out of whom 10 are special-skilled employees (SE) and the remaining are regular skilled employees (RE).

## Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video