[Download PDF] MAT 2004 Paper with Solutions

Instructions

Each item is followed by two statements A and B. Answer each question using the following Options :

Question 1

A rectangular floor that is 4 metres wide is to be completely covered with square tiles, each with the side of length 0.25 metre. What is the least number of such tiles required?
A. The length of the floor is three times the width.
B. The area of the floor is 48 square metres.

Video Solution

Solution

Width of floor = 4 m and side of square tile = 0.25 m. Now, to find the number of tiles required we need to divide the area of floor by area of tile.

A) : Length = 12 m, thus area of floor = 48 sq. mt

Hence, this statement is sufficient.

B) : Area of floor = 48 sq. mt

Hence, this statement is also sufficient.

=> Ans - (B)

Question 2

Each student in a class of 40 students voted for exactly one of the three candidates A, B or C for the post of class representative. Did candidate A receive the maximum votes from the 40 votes cast?
A. Candidate A received 11 of the votes
B. Candidate C received 14 of the votes

Video Solution

Solution

Total number of student in class = 40

A) : Candidate A received 11 of the votes

Since, A received less than half the number of votes, then A did not receive the maximum number of votes.

Thus, statement A alone is sufficient.

B) : Candidate C received 14 of the votes

Now, A could have received more than 20 votes or even less than 14, since it cannot be determined, hence this statement alone is not sufficient.

=> Ans - (A)

Question 3

$$I_1, I_2 and I_3$$ are lines in a plane. Is $$I_1$$ perpendicular to $$I_3$$?
A. $$I_1$$ is perpendicular to $$I_2$$
B. $$I_2$$ is perpendicular to $$I_3$$

Video Solution

Solution

Clearly, each statement alone is insufficient, as there is information about only two lines in each statement.

By combining, both statements, we get that if $$I_1$$ is perpendicular to $$I_2$$ and $$I_2$$ is perpendicular to $$I_3$$ , then $$I_1$$ is parallel to $$I_3$$

Thus, the answer to the question is : No, $$I_1$$ is not perpendicular to $$I_3$$, which is feasible by combining both statements.

=> Ans - (C)

Question 4

Was 70 the average grade on a class test?
A. On the test, half of the class had grades below 70 and half of the class had grades above 70.
B. The lowest grade on the test was 45 and the highest grade on the test was 95.

Video Solution

Solution

A) : Let us assume there are two students in the class, scores of each are 68 and 73 respectively. (Since, half scored less than 70 and half more than 70)

Now, average is not equal to 70, but if each scored 68 and 72, then the average will be 70.

Since, marks are not given, hence this statement alone is not sufficient.

B) : Similarly this statement alone is also not sufficient, as marks of rest of the students are not given.

Even by combining both statements, we wont be able to find the average.

=> Ans - (D)

Question 5

If $$x$$ is an integer, then what is the value of $$x^2$$ ?

A. $$\left(\frac{1}{5}\right) < \left(\frac{1}{(x + 1)}\right) < \left(\frac{1}{2}\right)$$

B. $$(x - 3) (x- 4) = 0$$

Video Solution

Solution

A) : $$\left(\frac{1}{5}\right) < \left(\frac{1}{(x + 1)}\right) < \left(\frac{1}{2}\right)$$

=> $$2<(x+1)<5$$

=> $$1<x<4$$

Thus, possible values of $$x$$ are : 2, 3 and since there is not a unique value, hence this statement alone is insufficient.

B) : $$(x - 3) (x- 4) = 0$$

=> $$x=3,4$$

Similarly, this statement alone is also not sufficient. But by combining both statements, we get : $$x=3$$ and $$x^2=9$$

=> Ans - (C)

Instructions

Refer to the given line graph and the pie charts to answer these questions:

Question 6

How many hectares of FSI has been distributed between 1994-2002?

Video Solution

Question 7

How many years witnessed a decline in FNI and an increase in FSI?

Video Solution

Question 8

During 1994-2002, the greatest proportion of FNI was put to commercial use in

Video Solution

Instructions

Study the information given below to answer these questions:

Investing in real estate would be a profitable venture at this time. A survey in House magazine revealed that 85% of the magazine's readers are planning to buy a second home over the next few years. A study of the real estate industry, however, revealed that the current supply or homes could only provide for 65%of that demand each year.

Question 9

Which of the following, if true, reveals a weakness in the evidence cited above?

Video Solution

Question 10

Which of the following, if true, would undermine the validity of the investment advice in the paragraph above?

Video Solution

CAT Content

MAT 2004

A rectangular floor that is 4 metres wide is to be completely covered with square tiles, each with the side of length 0.25 metre. What is the least number of such tiles required?
A. The length of the floor is three times the width.
B. The area of the floor is 48 square metres.

Each student in a class of 40 students voted for exactly one of the three candidates A, B or C for the post of class representative. Did candidate A receive the maximum votes from the 40 votes cast?
A. Candidate A received 11 of the votes
B. Candidate C received 14 of the votes

$$I_1, I_2 and I_3$$ are lines in a plane. Is $$I_1$$ perpendicular to $$I_3$$?
A. $$I_1$$ is perpendicular to $$I_2$$
B. $$I_2$$ is perpendicular to $$I_3$$

Was 70 the average grade on a class test?
A. On the test, half of the class had grades below 70 and half of the class had grades above 70.
B. The lowest grade on the test was 45 and the highest grade on the test was 95.

If $$x$$ is an integer, then what is the value of $$x^2$$ ?

A. $$\left(\frac{1}{5}\right) < \left(\frac{1}{(x + 1)}\right) < \left(\frac{1}{2}\right)$$

B. $$(x - 3) (x- 4) = 0$$

How many hectares of FSI has been distributed between 1994-2002?

How many years witnessed a decline in FNI and an increase in FSI?

During 1994-2002, the greatest proportion of FNI was put to commercial use in

Which of the following, if true, reveals a weakness in the evidence cited above?

Which of the following, if true, would undermine the validity of the investment advice in the paragraph above?

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CAT Content

MAT 2004

A rectangular floor that is 4 metres wide is to be completely covered with square tiles, each with the side of length 0.25 metre. What is the least number of such tiles required?A. The length of the floor is three times the width.B. The area of the floor is 48 square metres.

Each student in a class of 40 students voted for exactly one of the three candidates A, B or C for the post of class representative. Did candidate A receive the maximum votes from the 40 votes cast?A. Candidate A received 11 of the votesB. Candidate C received 14 of the votes

$$I_1, I_2 and I_3$$ are lines in a plane. Is $$I_1$$ perpendicular to $$I_3$$?A. $$I_1$$ is perpendicular to $$I_2$$B. $$I_2$$ is perpendicular to $$I_3$$

Was 70 the average grade on a class test?A. On the test, half of the class had grades below 70 and half of the class had grades above 70.B. The lowest grade on the test was 45 and the highest grade on the test was 95.

If $$x$$ is an integer, then what is the value of $$x^2$$ ? A. $$\left(\frac{1}{5}\right) < \left(\frac{1}{(x + 1)}\right) < \left(\frac{1}{2}\right)$$ B. $$(x - 3) (x- 4) = 0$$

How many hectares of FSI has been distributed between 1994-2002?

How many years witnessed a decline in FNI and an increase in FSI?

During 1994-2002, the greatest proportion of FNI was put to commercial use in

Which of the following, if true, reveals a weakness in the evidence cited above?

Which of the following, if true, would undermine the validity of the investment advice in the paragraph above?

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A rectangular floor that is 4 metres wide is to be completely covered with square tiles, each with the side of length 0.25 metre. What is the least number of such tiles required?
A. The length of the floor is three times the width.
B. The area of the floor is 48 square metres.

Each student in a class of 40 students voted for exactly one of the three candidates A, B or C for the post of class representative. Did candidate A receive the maximum votes from the 40 votes cast?
A. Candidate A received 11 of the votes
B. Candidate C received 14 of the votes

$$I_1, I_2 and I_3$$ are lines in a plane. Is $$I_1$$ perpendicular to $$I_3$$?
A. $$I_1$$ is perpendicular to $$I_2$$
B. $$I_2$$ is perpendicular to $$I_3$$

Was 70 the average grade on a class test?
A. On the test, half of the class had grades below 70 and half of the class had grades above 70.
B. The lowest grade on the test was 45 and the highest grade on the test was 95.

If $$x$$ is an integer, then what is the value of $$x^2$$ ?

A. $$\left(\frac{1}{5}\right) < \left(\frac{1}{(x + 1)}\right) < \left(\frac{1}{2}\right)$$

B. $$(x - 3) (x- 4) = 0$$