# AILET (All India Law Entrance Test) 2019 MCQs Questions with Solutions and Explanations at Doorsteptutor. Com Part 22

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## Elementary Mathematics

Question 141

If , where x is the product of four consecutive positive integers, then which of the following is true?

I. n is an even number

II. n is a prime number

III. n is a perfect square

IV. n is an odd number

A. I, III

B. I, II

C. I, IV

D. III, IV

Question 142

Three wheels can complete 40,24 and 16 revolutions per minutes respectively. There is a green spot on each wheel that touches the ground at time zero. After how much time, all these spots will simultaneously touch the ground again?

A. 7 and seconds

B. 7 seconds

C. 7 and minutes

D. 7 minutes

Question 143

In a group of students in a class, 20 are in the debating club, 24 in the drama club and 27 in the recitation club. If 12 like drama and debate, 10 like recitation and debate, 14 like drama and recitation and 7 like all the three activities, then the total number of students in the class is

A. 40

B. 42

C. 50

D. 52

Question 144

Class XII of XYZ international school has three sections – K, L and M. In Mathematics examination, the average marks obtained by these sections are 72,60 and 50 respectively. The average marks of sections K and L taken together is 69. If the ratio of the number of students in sections L and M is 6: 7, what is the average score of all the three sections put together?

A. 65

B. 64

C. 63.4

D. 64.7

Question 145

Sheena՚s test had 75 questions i.e.. , 10 on English, 30 on Reasoning and 35 on Legal aptitude. Although she answered 70 % of the English, 40 % of the Reasoning and 60 % of the Legal Aptitude questions correctly, she did not pass the test because she got less than 60 % of the questions right. How many questions she would have needed to answer correctly to earn a 60 % passing grade?

A. 7

B. 6

C. 5

D. 4

Question 146

Amrit wants to sell cars at 25 % above the cost price. Due to a slump in the market, his cost reduces by 5 % . He thus offers a discount of 8 % due to which the sales go up by 25 % . Compute the change in Amrit՚s profit.

A. unchanged

B. 5 %

C. 4 %

D. 3 %

Question 147

A water tank has eight pipes fitted into it. Pipes are of two types: Green Pipe and Red Pipe. Green Pipes are used to fill the tank and the Red pipes are used to empty the tank. Every Green pipe can fill the tank in 12 hours and every Red pipe can empty it in 36 hours. On opening all the pipes an empty tank is filled in 3 hours. The number of Red pipes is

A. 5

B. 3

C. 4

D. 2

Question 148

Anju is waiting on the railway station for the arrival of her train. Two trains running in opposite directions cross Anju on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speed is

A. 2: 3

B. 1: 2

C. 3: 2

D. 2: 1

Question 149

Neeraj is going to Agra on his bike from Delhi. He overtakes a bus travelling from Delhi to Agra at 4.30 pm. Neeraj reaches Agra at 6 pm. After stopping there for an hour, he starts back towards Delhi and meets the same bus at 7.30 pm which was moving towards Agra at the time. If both the bus and the bike were travelling with uniform speeds on the same route, at what time would the bus reach Agra?

A. 9.45 pm

B. 9.30 pm

C. 9.15 pm

D. 9 pm

Question 150

Sonam has a rectangular garden. If the length of the garden is reduced by 5 m and breadth is increased by 3 m, then the area of the garden gets reduced by 9 . However, if we increase the length by 3 m and breadth by 2 m, the area is increased by 67 . What is the length of the garden?

A. 16 m

B. 17 m

C. 16.5 m

D. 17.5 m

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