CAT 2018 Question Paper Slot 2

Instructions

Seven candidates, Akil, Balaram, Chitra, Divya, Erina, Fatima, and Ganeshan, were invited to interview for a position. Candidates were required to reach the venue before 8 am. Immediately upon arrival, they were sent to one of three interview rooms: 101, 102, and 103. The following venue log shows the arrival times for these candidates. Some of the names have not been recorded in the log and have been marked as ‘?’.


Additionally here are some statements from the candidates:

Balaram: I was the third person to enter Room 101.
Chitra: I was the last person to enter the room I was allotted to.
Erina: I was the only person in the room I was allotted to.
Fatima: Three people including Akhil were already in the room that I was allotted to when I entered it.
Ganeshan : I was one among the two candidates allotted to Room 102.

Question 61

When did Erina reach the venue?

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Question 62

If Ganeshan entered the venue before Divya, when did Balaram enter the venue?

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Instructions

There are only four brands of entry level smartphones called Azra, Bysi, Cxqi, and Dipq in a country.
Details about their market share, unit selling price, and profitability (defined as the profit as a percentage of the revenue) for the year 2016 are given in the table below:

In 2017, sales volume of entry level smartphones grew by 40% as compared to that in 2016. Cxqi offered a 40% discount on its unit selling price in 2017, which resulted in a 15% increase in its market share. Each of the other three brands lost 5% market share. However, the profitability of Cxqi came down to half of its value in 2016. The unit selling prices of the other three brands and their profitability values remained the same in 2017 as they were in 2016.

Question 63

The brand that had the highest revenue in 2016 is:

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Question 64

The brand that had the highest profit in 2016 is:

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Question 65

The brand that had the highest profit in 2017 is:

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Question 66

The complete list of brands whose profits went up in 2017 from 2016 is:

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Instructions

For the following questions answer them individually

Question 67

A water tank has inlets of two types A and B. All inlets of type A when open, bring in water at the same rate. All inlets of type B, when open, bring in water at the same rate. The empty tank is completely filled in 30 minutes if 10 inlets of type A and 45 inlets of type B are open, and in 1 hour if 8 inlets of type A and 18 inlets of type B are open. In how many minutes will the empty tank get completely filled if 7 inlets of type A and 27 inlets of type B are open?

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Question 68

Let f(x)= $$\max(5x, 52-2x^2)$$, where x is any positive real number. Then the minimum possible value of f(x) 

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Question 69

Points A, P, Q and B lie on the same line such that P, Q and B are, respectively, 100 km, 200 km and 300 km away from A. Cars 1 and 2 leave A at the same time and move towards B. Simultaneously, car 3 leaves B and moves towards A. Car 3 meets car 1 at Q, and car 2 at P. If each car is moving in uniform speed then the ratio of the speed of car 2 to that of car 1 is

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Question 70

The smallest integer $$n$$ such that $$n^3-11n^2+32n-28>0$$ is

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