CAT > CAT Quant Mock Test - 2

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CAT Quant Mock Test - 2 - Question 1

DIRECTIONS for question: Select the correct alternative from the given choices.

Find the ratio in which the line joining the points (-3, 3) and (2, 6) is divided by they-axis.

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CAT Quant Mock Test - 2 - Question 2

DIRECTIONS for questions: Select the correct alternative from the given choices.

There are 50 students divided into two groups, P and Q, with 20 and 30 students respectively. One student from group P shifts to group Q. If as a result of this, the average weight of group P decreases, while the average weight of group Q increases, which of the following holds true?

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CAT Quant Mock Test - 2 - Question 3

DIRECTIONS for questions: Select the correct alternative from the given choices.

What is the least distance from the point (4, 0) to the curvex^{2} + y^{2} − 6y − 12x + 28 = 0?

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CAT Quant Mock Test - 2 - Question 4

DIRECTIONS for questions: Select the correct alternative from the given choices.

During the placements in an MBA college, students were placed in four different sectors -Marketing (M), Finance (F), Operations (O) and IT (I). The averages of the annual CTCs of the students placed in M, F, O together and F, O, I together are Rs.13 lakh and Rs.14 lakh respectively, while the averages of the annual CTCs of the students placed in M, O, I together and M, F, I together are Rs.12 lakh and Rs.15 lakh respectively. Which of the following (in Rs. lakhs) could possibly be the average annual CTC of all the students placed?

I. 12.5

II. 13.6

III. 14

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CAT Quant Mock Test - 2 - Question 5

DIRECTIONS for questions: Select the correct alternative from the given choices.

A function f(x) is defined for a non-zero variable x, such that the value of f(y), where y = x + 1 / x, equals x^{2} + 1 / x^{2}equals . The function f(x) can be

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CAT Quant Mock Test - 2 - Question 6

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Five identical tennis balls are kept in a cylindrical container whose length is such that the five balls just fit into it in a single column. Find the ratio of the volume of the unoccupied portion of the container to that of the occupied portion, given that each ball is of the maximum possible size that can fit inside the container.

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CAT Quant Mock Test - 2 - Question 7

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The arithmetic mean of a set of numbers was calculated as 24. However, the frequency of one of the numbers was erroneously taken as 6, instead of 9. As a result, the arithmetic mean calculated was 5 less than the actual mean. If all the numbers in the set are integers, then which of the following could be the sum of all frequencies?

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CAT Quant Mock Test - 2 - Question 8

DIRECTIONS for questions : Select the correct alternative from the given choices.

Find the sum of the first n terms of the series:

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CAT Quant Mock Test - 2 - Question 9

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WIMCO employs a total of 75 units to make coir products for export. The total monthly revenue from all the units is Rs.10,00,000. The total manufacturing cost and the total overheads (both of which vary with the number of units working) for all the units are Rs.1,50,000 and 1,00,000 every month respectively. If, in one month, the total profit reduced by Rs.35,000, how many units, on an average, were not working everyday during that month?

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CAT Quant Mock Test - 2 - Question 10

DIRECTIONS for questions: Select the correct alternative from the given choices.

The breadth of a rectangle is decreased by 25%, as a result of which the perimeter of the rectangle decreased by 10%. By what percentage should the length of the rectangle now be increased, such that the perimeter of the rectangle will be the same as the initial one (i.e., before the breadth was decreased)?

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CAT Quant Mock Test - 2 - Question 11

DIRECTIONS for questions: Select the correct alternative from the given choices.

What is the radius (in cm) of the largest possible circle that can be cut out from a quadrant of a circle of radius 6 cm?

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CAT Quant Mock Test - 2 - Question 12

DIRECTIONS for questions: Select the correct alternative from the given choices.

Find the positive square root of 13 + √48 + √72 + √96.

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CAT Quant Mock Test - 2 - Question 13

DIRECTIONS for question: The question is followed by two statements, I and II. You have to decide whether the information provided in the statements is sufficient for answering the question and select the correct answer option.

Gayatri spent less than Rs.180 to buy three kg of each of rice, wheat and jowar. Which of the three cereals she bought was the cheapest?

I. 4 kg rice and 2 kg wheat cost less than 2 kg rice and 4 kg wheat.

II. 2 kg wheat and 4 kg jowar cost the same as 4 kg rice and 2 kg jowar.

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CAT Quant Mock Test - 2 - Question 14

DIRECTIONS for questions: Select the correct alternative from the given choices. Robert bought an equal number of each of three kinds of articles, whose cost prices were Rs.8, Rs.25 and Rs.38 per article respectively. If, on the whole, he spent Rs.2,769, what is the total number of articles that he bought?

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CAT Quant Mock Test - 2 - Question 15

DIRECTIONS for questions: Select the correct alternative from the given choices.

The range of cos^{6}x + sin^{6}x is

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CAT Quant Mock Test - 2 - Question 16

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A milkman has two containers, containing mixtures of milk and water. The first container has 110 litres of a mixture of milk and water in the ratio of 5 : 6. The second container has a mixture of milk and water in the ratio of 7 : 3. How much mixture should be taken from the second container and added to the first so that the ratio of the milk and water in the first container will become 6 : 5?

Detailed Solution for CAT Quant Mock Test - 2 - Question 16

CAT Quant Mock Test - 2 - Question 17

DIRECTIONS for questions: Select the correct alternative from the given choices.

A man has a special rechargeable electric vehicle, which can maintain a speed ofx km/hr for (100 − x) minutes, after which it has to be recharged. What is the maximum distance (in km) that the man can cover on the vehicle without recharging in between?

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CAT Quant Mock Test - 2 - Question 18

DIRECTIONS for question: Select the correct alternative from the given choices.

Ashok told his son, “x years ago, my age was twice your age and 5x years ago, my age was thrice your age.” If the difference of their present ages is 24 years, find the sum of their present ages (in years).

Detailed Solution for CAT Quant Mock Test - 2 - Question 18

CAT Quant Mock Test - 2 - Question 19

At a parking lot, there are total of 50 two-wheelers and four-wheelers. The total number of wheels of these vehicles is 160. Find the number of two-wheelers at the parking lot.

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CAT Quant Mock Test - 2 - Question 20

Find the length (in m) of the platform which a 600 m long train, travelling at 72 kmph, can cross in 50 seconds.

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CAT Quant Mock Test - 2 - Question 21

A merchant purchased a pack of 15 bottles of soft drink, at a cost price of Rs.15 per bottle, and sold the pack at a profit of 20%. What is the additional profit (in Rs.) he would have made, if he had sold the pack at 15% more than what he sold it for?

[Enter your answer as a decimal value, rounded off to two decimal places.]

Detailed Solution for CAT Quant Mock Test - 2 - Question 21

CAT Quant Mock Test - 2 - Question 22

A work can be done by P in 48 days, whereas Q and R together can do the same work in 20 days. If Q is thrice as efficient as R, then P and R can do the work in

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CAT Quant Mock Test - 2 - Question 23

This year, during the months of January and February, each day Ramu went to a fruit shop and bought exactly three varieties of fruits, such that for any two days, he bought at least one variety of fruit on one of the days that was different from what he bought on the other day. What is the minimum number of different varieties of fruits that he could have bought during that period?

Detailed Solution for CAT Quant Mock Test - 2 - Question 23

CAT Quant Mock Test - 2 - Question 24

The following graph plots the time of travel (in seconds) and the speed of travel (in meters per second) of a particle. What is the total distance (in m) travelled by the particle from t = 0 to t = 4 seconds?

Detailed Solution for CAT Quant Mock Test - 2 - Question 24

CAT Quant Mock Test - 2 - Question 25

If the area enclosed by the lines 3x − 2y + 6 = 0, 3x + 5y − 15 = 0 and the x-axis is A sq. units, find the value of 4A.

Detailed Solution for CAT Quant Mock Test - 2 - Question 25

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