[Download PDF] MAT 2004 Question Paper Paper with Solutions

Instructions

In each of these questions, there is given a statement followed by two courses of action numbered I and II. A course of action is an administrative step or decision to be taken for improvement, follow up or further action regarding the problem on the basis of the information in the statement. Assume everything in the statement to be true and decide which course of action follows logically from the given statement. Give your answer as

Question 31

In spite of the principal's repeated warnings, a child was caught exploding crackers secretly in the school.
I. All crackers should be taken away from the child and he should be threatened never to do it again.
II. The child should be severely punished for his wrong act.

Video Solution

Solution

Since the act has been repeated despite various warnings, so course I would only be another warning and would not help. Severe punishment to set example for him and others is inevitable. Thus, course II shall follow.

=> Ans - (B)

Question 32

Most children in India are unable to get an education as they get involved in earning a livelihood during their childhood itself.
I. Education should be made compulsoryfor all children upto the age of 14.
II. Employment of children under the age of 14 years should be banned.

Video Solution

Question 33

The Asian Development Bank has approved a $285 million loan to finance a project to construct coal ports by Madras port and Paradip porttrusts.
I. India should use financial assistance from other international financial organisations to develop such ports in other places.
II. India should not seek assistance from foreign agencies.

Video Solution

Solution

Such kind of products should be encouraged because they form important assets and will bring lot of profit in the country. So, India should use financial assistance.

Thus only action I follows.

=> Ans - (A)

Instructions

In answering these questions, you have to use the revenue data for the three companies A, B and C provided in the graph:

Question 34

Which quarter has the highest average revenue?

Video Solution

Solution

Quarter which has the highest revenue will also have the highest average revenue. Revenue of Quarter :

First = 4+5+10 = 19

Second = 6+6+10 = 22

Third = 8+5+12 = 25

Fourth = 10+6+11 = 27 [MAX]

=> Ans - (D)

Question 35

What is the total revenue for all the companies in all the quarters?

Video Solution

Solution

Total revenue for all the companies in all the quarters

= $$(4+5+10)+(6+6+10)+(8+5+12)+(10+6+11)=93$$

=> Ans - (D)

Instructions

In each of these question, you are given two statements. To answer these questions, you can use oneor both the statements. Give your answer as

Question 36

How many hours will it take for all the students and teachers together to put up a tent?
A. There are 4 teachers and 7 students.
B. All the teachers working together can put up the tent in 5 hours while all the students working together can do so in 3 hours.

Video Solution

Solution

Statement A alone is insufficient, as there is no time given and statement B alone is sufficient, as the number of teachers and students are missing.

All the teachers can complete 1/5 of work in 1 hour and all students can complete 1/3 of work in 1 hour. Therefore in 1 hr they can complete 8/15 of work in 1 hour and total work will be completed in 15/8 hours.

$$\therefore$$ Statement B alone is sufficient.

=> Ans - (B)

Question 37

What is the remainder when the square of N is divided by 5?
A. When N is divided by 5, the remainder is 3.
B. N is an even integer.

Video Solution

Solution

A : When N is divided by 5, the remainder is 3.

=> $$N=5k+3$$, where $$k$$ is an whole number.

Let $$k=0$$, => $$N=3$$

Thus, when $$N^2=9$$ is divided by 5, remainder = 4

=> Statement A alone is sufficient.

Clearly, second statement is insufficient, as there can be multiple solutions.

=> Ans - (A)

Question 38

What is the value of the 2-digit number ab?
A. The difference between its digits is 4.
B. The sum of its digits is 4.

Video Solution

Solution

Let the digits of the number be $$x$$ and $$y$$

Clearly, each statement alone is not sufficient as there can be many possibilities. By combining the above statements, we get :

=> $$x+y=4$$ and $$x-y=4$$

By solving above equations, we get : $$x=4$$ and $$y=0$$, thus number = 40

$$\therefore$$ Both statements together are sufficient.

=> Ans - (C)

Question 39

a, b and c are the three digits of a number abc. abc is a multiple of 3. Find (a + b + C).
A. a = 3, b = 4.
B. C is an odd number.

Video Solution

Solution

If $$abc$$ is a multiple of 3, then $$(a+b+c)$$ will also be multiple of 3.

(A) : $$a=3$$ and $$b=4$$

=> $$3+4+c=3k$$, where $$k$$ is a natural number.

=> Possible values of $$c=2,5,8$$

Thus, statement A alone is not sufficient.

(B) : If C is odd, there can be multiple values of the number, thus statement B alone is insufficient.

By combining above statements together, we get the number as 345

$$\therefore$$ Both statements together are sufficient.

=> Ans - (C)

Question 40

N is an integer between 1 and 93. What is the value of N?
A. N is both the square and the cube of an integer.
B. The square root of N is divisible by 8.

Video Solution

Solution

(A) : Perfect squares between 1 and 93 = 1,4,9,16,25,36,49,64,81

Perfect cubes between 1 and 93 = 1,8,27,64

=> Possible values of N = 1, 64

Thus, first statement alone is not sufficient.

(B) : Number of square roots between 1 and 93 = 1,2,3,4,5,6,7,8

Now, since it is divisible by 8, only one possible value of N exist, => $$N=64$$

$$\therefore$$ Statement B alone is sufficient.

=> Ans - (B)

CAT Content

MAT 2004 Question Paper

In spite of the principal's repeated warnings, a child was caught exploding crackers secretly in the school.I. All crackers should be taken away from the child and he should be threatened never to do it again.II. The child should be severely punished for his wrong act.

Most children in India are unable to get an education as they get involved in earning a livelihood during their childhood itself.I. Education should be made compulsoryfor all children upto the age of 14.II. Employment of children under the age of 14 years should be banned.

Which quarter has the highest average revenue?

What is the total revenue for all the companies in all the quarters?

How many hours will it take for all the students and teachers together to put up a tent?A. There are 4 teachers and 7 students.B. All the teachers working together can put up the tent in 5 hours while all the students working together can do so in 3 hours.

What is the remainder when the square of N is divided by 5?A. When N is divided by 5, the remainder is 3.B. N is an even integer.

What is the value of the 2-digit number ab?A. The difference between its digits is 4.B. The sum of its digits is 4.

a, b and c are the three digits of a number abc. abc is a multiple of 3. Find (a + b + C).A. a = 3, b = 4.B. C is an odd number.

N is an integer between 1 and 93. What is the value of N?A. N is both the square and the cube of an integer.B. The square root of N is divisible by 8.

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In spite of the principal's repeated warnings, a child was caught exploding crackers secretly in the school.
I. All crackers should be taken away from the child and he should be threatened never to do it again.
II. The child should be severely punished for his wrong act.

Most children in India are unable to get an education as they get involved in earning a livelihood during their childhood itself.
I. Education should be made compulsoryfor all children upto the age of 14.
II. Employment of children under the age of 14 years should be banned.

How many hours will it take for all the students and teachers together to put up a tent?
A. There are 4 teachers and 7 students.
B. All the teachers working together can put up the tent in 5 hours while all the students working together can do so in 3 hours.

What is the remainder when the square of N is divided by 5?
A. When N is divided by 5, the remainder is 3.
B. N is an even integer.

What is the value of the 2-digit number ab?
A. The difference between its digits is 4.
B. The sum of its digits is 4.

a, b and c are the three digits of a number abc. abc is a multiple of 3. Find (a + b + C).
A. a = 3, b = 4.
B. C is an odd number.

N is an integer between 1 and 93. What is the value of N?
A. N is both the square and the cube of an integer.
B. The square root of N is divisible by 8.