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Nonverbal reasoning, mathematical, analytical, Puzzles, coding

Q.No: 1
Test Name : CAT Paper 2001

Directions for questions 121 to 127: Each question is followed by two statements, I and II.

Mark
(a) if the question can be answered by one of the statements alone and not by the other.
(b) if the question can be answered by using either statement alone.
(c) if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
(d) if the question cannot be answered even by using both statements together.

What are the values of m and n?
I. n is an even integer, m is an odd integer, and m is greater than n.
II. Product of m and n is 30.

A
a
B
b
C
c
D
d
Answer key/Solution
Solution:
From statement II, m, n could be (2, 15) (5, 6), (3, 10) and (1, 30) but from statement I, we get m, n as (2, 15).
Hence, the question can be answered by using both the statements together.
Q.No: 2
Test Name : CAT Paper 2001

Directions for questions 121 to 127: Each question is followed by two statements, I and II.

Mark
(a) if the question can be answered by one of the statements alone and not by the other.
(b) if the question can be answered by using either statement alone.
(c) if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
(d) if the question cannot be answered even by using both statements together.

What is the value of X?
I. X and Y are unequal even integers, less than 10, and X/Y is an odd integer.
II. X and Y are even integers, each less than 10, and product of X and Y is 12.

A
a
B
b
C
c
D
d
Answer key/Solution
Solution:
Q.No: 3
Test Name : CAT Paper 2001

Directions for questions 121 to 127: Each question is followed by two statements, I and II.

Mark
(a) if the question can be answered by one of the statements alone and not by the other.
(b) if the question can be answered by using either statement alone.
(c) if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
(d) if the question cannot be answered even by using both statements together.

On a given day a boat ferried 1,500 passengers across the river in 12 hr. How many round trips did it make?
I. The boat can carry 200 passengers at any time.
II. It takes 40 min each way and 20 min of waiting time at each terminal.

A
a
B
b
C
c
D
d
Answer key/Solution
Solution:
Statement I gives the capacity of boat and is of no help in finding out the number of round trips. From statement II round trips can be calculated since we know the total time taken is 12 hr.
Q.No: 4
Test Name : CAT Paper 2001

Directions for questions 121 to 127: Each question is followed by two statements, I and II.

Mark
(a) if the question can be answered by one of the statements alone and not by the other.
(b) if the question can be answered by using either statement alone.
(c) if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
(d) if the question cannot be answered even by using both statements together.

What will be the time for downloading software?
I. Transfer rate is 6 kilobytes per second.
II. The size of the software is 4.5 megabytes.

A
a
B
b
C
c
D
d
Answer key/Solution
Solution:
Statement I gives the rate and statement II gives the size. It is like statement I gives the speed and statement II the distance and we are to find out time. So both statements are needed.
Q.No: 5
Test Name : CAT Paper 2001

Directions for questions 121 to 127: Each question is followed by two statements, I and II.

Mark
(a) if the question can be answered by one of the statements alone and not by the other.
(b) if the question can be answered by using either statement alone.
(c) if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
(d) if the question cannot be answered even by using both statements together.

Two friends, Ram and Gopal, bought apples from a wholesale dealer. How many apples did they buy?
I. Ram bought one-half the number of apples that Gopal bought.
II. The wholesale dealer had a stock of 500 apples.

A
a
B
b
C
c
D
d
Answer key/Solution
Solution:
Statement I gives a general figure of Ram and Gopal. Statement II does not give any idea of how many apples Ram and Gopal purchased.
Both statements together also cannot give any result.
Q.No: 6
Test Name : CAT Paper 1990
Questions. 51 to 58 : Each of the following questions is followed by two statements. MARK,
(a), if the question can be answered with the help of statement I alone,
(b), if the question can be answered with the help of statement II alone,
(c), if both, statement I and statement II are needed to answer the question, and
(d), if the statement cannot be answered even with the help of both the statements.

A man distributed 43 chocolates to his children. How many of his children are more than five years old?
I. A child older than five years gets 5 chocolates.
II. A child 5 years or younger in age gets 6 chocolates.

A
B
C
D
Answer key/Solution
Solution:
Q.No: 7
Test Name : CAT Paper 1990
Questions. 51 to 58 : Each of the following questions is followed by two statements. MARK,
(a), if the question can be answered with the help of statement I alone,
(b), if the question can be answered with the help of statement II alone,
(c), if both, statement I and statement II are needed to answer the question, and
(d), if the statement cannot be answered even with the help of both the statements.

X is older than Y, Z is younger than W and V is older than Y. Is Z younger than X?
I. W may not be older than V.
II. W is not older than V.

A
B
C
D
Answer key/Solution
Solution:
Q.No: 8
Test Name : CAT Paper 1990
Questions. 59 and 60: In a game played by two people there were initially N match sticks kept on the table. A move in the game consists of a player removing either one or two matchsticks from the table. The one who takes the last matchstick loses. Players make moves alternately. The player who will make the first move is A. The other player is B.

The smallest value of N (greater than 5) that ensures a win for B is

A
7
B
6
C
10
D
8
Answer key/Solution
Solution:
Students please note that the best way to answer this question is by finding generally what would ensure a win for B. If B has to win, A has to pickup the last matchstick. This can be forced upon A if there are 2 or 3 matchsticks left on the table when it is B’s turn. As then, B could pick-up 1 or 2 match sticks and force upon A to pick-up the last one. For this to happen the number of match sticks initially must be of form 3k + 1.

The smallest number greater than 5 of the form 3k + 1 is 7.
Q.No: 9
Test Name : CAT Paper 1990
Questions. 59 and 60: In a game played by two people there were initially N match sticks kept on the table. A move in the game consists of a player removing either one or two matchsticks from the table. The one who takes the last matchstick loses. Players make moves alternately. The player who will make the first move is A. The other player is B.

The largest value of N (less than 50) that ensures a win for B is

A
46
B
47
C
48
D
49
Answer key/Solution
Solution:
Students please note that the best way to answer this question is by finding generally what would ensure a win for B. If B has to win, A has to pickup the last matchstick. This can be forced upon A if there are 2 or 3 matchsticks left on the table when it is B’s turn. As then, B could pick-up 1 or 2 match sticks and force upon A to pick-up the last one. For this to happen the number of match sticks initially must be of form 3k + 1.

The largest number less than 50 of the form 3k + 1 is 49.
Solution:
From statement II, m, n could be (2, 15) (5, 6), (3, 10) and (1, 30) but from statement I, we get m, n as (2, 15).
Hence, the question can be answered by using both the statements together.

Solution:

Solution:
Statement I gives the capacity of boat and is of no help in finding out the number of round trips. From statement II round trips can be calculated since we know the total time taken is 12 hr.

Solution:
Statement I gives the rate and statement II gives the size. It is like statement I gives the speed and statement II the distance and we are to find out time. So both statements are needed.

Solution:
Statement I gives a general figure of Ram and Gopal. Statement II does not give any idea of how many apples Ram and Gopal purchased.
Both statements together also cannot give any result.

Solution:

Solution:

Solution:
Students please note that the best way to answer this question is by finding generally what would ensure a win for B. If B has to win, A has to pickup the last matchstick. This can be forced upon A if there are 2 or 3 matchsticks left on the table when it is B’s turn. As then, B could pick-up 1 or 2 match sticks and force upon A to pick-up the last one. For this to happen the number of match sticks initially must be of form 3k + 1.

The smallest number greater than 5 of the form 3k + 1 is 7.

Solution:
Students please note that the best way to answer this question is by finding generally what would ensure a win for B. If B has to win, A has to pickup the last matchstick. This can be forced upon A if there are 2 or 3 matchsticks left on the table when it is B’s turn. As then, B could pick-up 1 or 2 match sticks and force upon A to pick-up the last one. For this to happen the number of match sticks initially must be of form 3k + 1.

The largest number less than 50 of the form 3k + 1 is 49.

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