Back Home
Persistent Timer

Mathematical Puzzles

Q.No: 1
Test Name : CAT 2017 Actual Paper Slot 1
Question Numbers : (63 to 66) 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.

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

Answer key/Solution
Solution:
Q.No: 2
Test Name : CAT 2017 Actual Paper Slot 1
Question Numbers : (63 to 66) 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.

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-N-B and a car that takes the route A-M-B?

A
1
B
0.1
C
0.2
D
0.9
Answer key/Solution
Solution:
Q.No: 3
Test Name : CAT 2017 Actual Paper Slot 1
Question Numbers : (63 to 66) 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.

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-M-N-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-NB 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.)

Answer key/Solution
Solution:
Q.No: 4
Test Name : CAT 2017 Actual Paper Slot 1
Question Numbers : (63 to 66) 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.

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-E, A-N-B and A-M-N-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-NB 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
Answer key/Solution
Solution:
Q.No: 5
Test Name : CAT 2017 Actual Paper Slot 2
Question Numbers : (55 to 58) : In an 8 × 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.

If the queen is at c5, and the other pieces at positions c2, g1, 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
Answer key/Solution
Solution:
Q.No: 6
Test Name : CAT 2017 Actual Paper Slot 2
Question Numbers : (55 to 58) : In an 8 × 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.

If the other pieces are only at positions a1, 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
Answer key/Solution
Solution:
Q.No: 7
Test Name : CAT 2017 Actual Paper Slot 2
Question Numbers : (55 to 58) : In an 8 × 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.

If the other pieces are only at positions a1, 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
Answer key/Solution
Solution:
Q.No: 8
Test Name : CAT 2017 Actual Paper Slot 2
Question Numbers : (55 to 58) : In an 8 × 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.

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
33
C
36
D
37
Answer key/Solution
Solution:
Q.No: 9
Test Name : CAT 2018 Actual Paper Slot 1
Directions for questions 43 to 46:Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:
The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.
The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.
60% of the politicians are in the administration committee, and 20% are in the teaching committee.

What is the number of educationalists in the research committee?

Answer key/Solution
Solution:
Q.No: 10
Test Name : CAT 2018 Actual Paper Slot 1
Directions for questions 63 to 66: 1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O.
The following facts are known about the satellites:
The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2:1:1.
The number of satellites serving all three of B, C, and S is 100.
The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B.
The number of satellites serving O is the same as the number of satellites serving both C and S but not B.

What best can be said about the number of satellites serving C?

A
Cannot be more than 800
B
Must be at least 100
C
Must be between 400 and 800
D
Must be between 450 and 725
Answer key/Solution
Solution:
Q.No: 11
Test Name : CAT 2018 Actual Paper Slot 1
Directions for questions 43 to 46: Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:
The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.
The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.
60% of the politicians are in the administration committee, and 20% are in the teaching committee.

Which of the following CANNOT be determined uniquely based on the given information?

A
The total number of educationalists in the three committees
B
The size of the research committee
C
The total number of bureaucrats in the three committees
D
The size of the teaching committee
Answer key/Solution
Solution:
Q.No: 12
Test Name : CAT 2018 Actual Paper Slot 1
Directions for questions 43 to 46:Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:
The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.
The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.
60% of the politicians are in the administration committee, and 20% are in the teaching committee.

What is the number of bureaucrats in the administration committee?

Answer key/Solution
Solution:
Q.No: 13
Test Name : CAT 2018 Actual Paper Slot 1
Directions for questions 63 to 66: 1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O.
The following facts are known about the satellites:
The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2:1:1.
The number of satellites serving all three of B, C, and S is 100.
The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B.
The number of satellites serving O is the same as the number of satellites serving both C and S but not B.

If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?

A
At least 475
B
At most 475
C
No conclusion is possible based on the given information
D
Exactly 475
Answer key/Solution
Solution:
Q.No: 14
Test Name : CAT 2018 Actual Paper Slot 1
Directions for questions 63 to 66: 1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O.
The following facts are known about the satellites:
The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2:1:1.
The number of satellites serving all three of B, C, and S is 100.
The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B.
The number of satellites serving O is the same as the number of satellites serving both C and S but not B.

If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE?

A
The number of satellites serving B is more than 1000
B
All 1600 satellites serve B or C or S
C
The number of satellites serving B exclusively is exactly 250
D
The number of satellites serving C cannot be uniquely determined
Answer key/Solution
Solution:
Q.No: 15
Test Name : CAT 2018 Actual Paper Slot 1
Directions for questions 43 to 46: Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:
The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.
The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.
60% of the politicians are in the administration committee, and 20% are in the teaching committee.

Based on the given information, which of the following statements MUST be FALSE?

A
The size of the research committee is less than the size of the administration committee
B
In the teaching committee the number of educationalists is equal to the number of politicians
C
In the administration committee the number of bureaucrats is equal to the number of educationalists
D
The size of the research committee is less than the size of the teaching committee
Answer key/Solution
Solution:
Q.No: 16
Test Name : CAT 2018 Actual Paper Slot 1
Directions for questions 63 to 66: 1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O.
The following facts are known about the satellites:
The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2:1:1.
The number of satellites serving all three of B, C, and S is 100.
The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B.
The number of satellites serving O is the same as the number of satellites serving both C and S but not B.

What is the minimum possible number of satellites serving B exclusively?

A
100
B
500
C
200
D
250
Answer key/Solution
Solution:
Q.No: 17
Test Name : CAT 2018 Actual Paper Slot 2
Directions for questions 59 to 62: The base exchange rate of a currency X with respect to a currency Y is the number of units of currency Y which is equivalent in value to one unit of currency X. Currency exchange outlets buy currency at buying exchange rates that are lower than base exchange rates, and sell currency at selling exchange rates that are higher than base exchange rates.

A currency exchange outlet uses the local currency L to buy and sell three international currencies A, B, and C, but does not exchange one international currency directly with another. The base exchange rates of A, B and C with respect to L are in the ratio 100:120:1. The buying exchange rates of each of A, B, and C with respect to L are 5% below the corresponding base exchange rates, and their selling exchange rates are 10% above their corresponding base exchange rates.

The following facts are known about the outlet on a particular day:

1. The amount of L used by the outlet to buy C equals the amount of L it received by selling C.
2. The amounts of L used by the outlet to buy A and B are in the ratio 5:3.
3. The amounts of L the outlet received from the sales of A and B are in the ratio 5:9.
4. The outlet received 88000 units of L by selling A during the day.
5. The outlet started the day with some amount of L, 2500 units of A, 4800 units of B, and 48000 units of C.
6. The outlet ended the day with some amount of L, 3300 units of A, 4800 units of B, and 51000 units of C.

How many units of currency A did the outlet buy on that day?

Answer key/Solution
Solution:
Q.No: 18
Test Name : CAT 2018 Actual Paper Slot 2
Directions for questions 59 to 62: The base exchange rate of a currency X with respect to a currency Y is the number of units of currency Y which is equivalent in value to one unit of currency X. Currency exchange outlets buy currency at buying exchange rates that are lower than base exchange rates, and sell currency at selling exchange rates that are higher than base exchange rates.

A currency exchange outlet uses the local currency L to buy and sell three international currencies A, B, and C, but does not exchange one international currency directly with another. The base exchange rates of A, B and C with respect to L are in the ratio 100:120:1. The buying exchange rates of each of A, B, and C with respect to L are 5% below the corresponding base exchange rates, and their selling exchange rates are 10% above their corresponding base exchange rates.

The following facts are known about the outlet on a particular day:

1. The amount of L used by the outlet to buy C equals the amount of L it received by selling C.
2. The amounts of L used by the outlet to buy A and B are in the ratio 5:3.
3. The amounts of L the outlet received from the sales of A and B are in the ratio 5:9.
4. The outlet received 88000 units of L by selling A during the day.
5. The outlet started the day with some amount of L, 2500 units of A, 4800 units of B, and 48000 units of C.
6. The outlet ended the day with some amount of L, 3300 units of A, 4800 units of B, and 51000 units of C.

How many units of currency C did the outlet sell on that day?

A
6000
B
22000
C
3000
D
19000
Answer key/Solution
Solution:
Q.No: 19
Test Name : CAT 2018 Actual Paper Slot 2
Directions for questions 59 to 62: The base exchange rate of a currency X with respect to a currency Y is the number of units of currency Y which is equivalent in value to one unit of currency X. Currency exchange outlets buy currency at buying exchange rates that are lower than base exchange rates, and sell currency at selling exchange rates that are higher than base exchange rates.

A currency exchange outlet uses the local currency L to buy and sell three international currencies A, B, and C, but does not exchange one international currency directly with another. The base exchange rates of A, B and C with respect to L are in the ratio 100:120:1. The buying exchange rates of each of A, B, and C with respect to L are 5% below the corresponding base exchange rates, and their selling exchange rates are 10% above their corresponding base exchange rates.

The following facts are known about the outlet on a particular day:

1. The amount of L used by the outlet to buy C equals the amount of L it received by selling C.
2. The amounts of L used by the outlet to buy A and B are in the ratio 5:3.
3. The amounts of L the outlet received from the sales of A and B are in the ratio 5:9.
4. The outlet received 88000 units of L by selling A during the day.
5. The outlet started the day with some amount of L, 2500 units of A, 4800 units of B, and 48000 units of C.
6. The outlet ended the day with some amount of L, 3300 units of A, 4800 units of B, and 51000 units of C.

What was the base exchange rate of currency B with respect to currency L on that day?

Answer key/Solution
Solution:
Q.No: 20
Test Name : CAT 2018 Actual Paper Slot 2
Directions for questions 59 to 62: The base exchange rate of a currency X with respect to a currency Y is the number of units of currency Y which is equivalent in value to one unit of currency X. Currency exchange outlets buy currency at buying exchange rates that are lower than base exchange rates, and sell currency at selling exchange rates that are higher than base exchange rates.

A currency exchange outlet uses the local currency L to buy and sell three international currencies A, B, and C, but does not exchange one international currency directly with another. The base exchange rates of A, B and C with respect to L are in the ratio 100:120:1. The buying exchange rates of each of A, B, and C with respect to L are 5% below the corresponding base exchange rates, and their selling exchange rates are 10% above their corresponding base exchange rates.

The following facts are known about the outlet on a particular day:

1. The amount of L used by the outlet to buy C equals the amount of L it received by selling C.
2. The amounts of L used by the outlet to buy A and B are in the ratio 5:3.
3. The amounts of L the outlet received from the sales of A and B are in the ratio 5:9.
4. The outlet received 88000 units of L by selling A during the day.
5. The outlet started the day with some amount of L, 2500 units of A, 4800 units of B, and 48000 units of C.
6. The outlet ended the day with some amount of L, 3300 units of A, 4800 units of B, and 51000 units of C.

What was the buying exchange rate of currency C with respect to currency L on that day?

A
1.90
B
0.95
C
1.10
D
2.20
Answer key/Solution
Solution:
Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

logo

© 2025 CL Educate Ltd. All rights reserved.