Questions for Practice on Number System and HCF LCM for CLAT

Questions for Practice on Number System and HCF LCM for CLAT

Directions for Question 1-3:​​ Aman and Raman met at Noida city Centre after a long time. Aman resides at Vaishali while Raman lives in Saket.​​ They decided to take bus for their homes from the bus stop, but when they reached the bus stop their buses had just left​​ for respective destinations.​​ Both of them don’t want to leave the other one alone at the bus stop hence they decided to board the buses to their respective destinations simultaneously. If the frequency of buses from Noida City Centre Bus stop to Vaishali is in every 11 minutes and from the same bus stop to Saket is every 13 minutes, Answer the following questions.

  • How long they would need to wait at the bus stop?

  • How many buses Aman would not board till he gets a simultaneous bus as Saket?

  • How many buses Raman would not board till he gets a simultaneous bus as Vaishali?

Directions for Question 4-6:​​ The number of students who opted for Industry training A B and C are 108, 192 and 84 respectively. Post training Test is to be conducted for the students such that only the students with same training are allowed to sit in one room. Also the number of students in each room must be same. Answer the questions based on this information.

  • How many students can be seated in one room as per given conditions of the question?

  • How many rooms are required for students of training A?

  • How many rooms are required for students of training B and C together?

Question 7-8:​​ Joe multiplied two numbers and he mistakenly assumed one number to be 43 instead of 34. Because of this mistake the product went up by​​ 450. .​​ 

  • What is the wrong product that he calculated?

  • In the previous question what was the original product?​​ 

Question 9-10:​​ In an examination, a student was asked to find 7/18 of a number, by mistake he calculated 11/30 of the given number, which turned out to be 40 less than what it should have been.

  • What was the given number?

  • What should have been the original product?

Answers and Solutions

  • Ans:​​ 143 minutes​​ 

Sol:​​ As bus for Vaishali leaves in every 11 min while bus for Saket leaves every 13 min, and both the numbers are co-prime, the earliest they can leave is the LCM of these two numbers i.e., 11*13 minutes = 143 minutes.

  • Ans:​​ 12 buses

Sol:​​ Total number of buses that would leave Noida bus stop for Vaishali in 143 minutes

= 143/11 = 13,

  ​​ ​​ ​​ ​​ ​​​​  Hence Aman would board 13th​​ bus, i.e., he will leave 12 buses on purpose.

  • Ans:​​ 10 buses

Sol:​​ Total number of buses that would leave Noida bus stop for Vaishali in 143 minutes

= 143/13 = 11,

  ​​ ​​ ​​ ​​ ​​​​  Hence Raman would board 11th​​ bus, i.e., he will leave 10 buses on purpose.

  • Ans:​​ 12

Sol:​​ There are 2 criteria’s given in question, first is equal number of students in each room and second is only same training student in one room. For the first condition, we will need to find HCF of 108, 192 and 84, i.e., 12.

  • Ans: 9

Sol:​​ Rooms Required for Training A student = 108/12 = 9​​ 

  • Ans:​​ 25

Sol:​​ Rooms required for Training B students = 192/12 = 17

 ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ Rooms required for Training C students = 84/12 = 8

Together training B and C student will require 17+8 rooms, i.e., 25

  • Ans:​​ 450​​ 

Sol:​​ Let the number​​ that was originally multiplied with wrong number 43 be N.

Hence wrong product = N*43

Correct Product = N*34

Given, Wrong Product – Correct Product = 450

N(43-34) = 450

N = 450/9 = 50

Wrong Product = 50*43 = 2150

  • Ans:​​ 1700

Sol:​​ Original Product =50*34 = 1700

  • Ans: 1800

Sol:​​ Let the given number be N. As the new product is 40 less than original product, we can make the equation as follows,

New product +40 = Original product​​ 

(N*11/30)​​ + 40 = N*7/18

N = 40/[7/18 – 11/30]

N = 40/ [(70-66)/180] = 1800

  • Ans: 700

Sol:​​ As the given number is 1800, the original product would be 7/18th​​ of 1800 i.e., 7*1800/18 = 7*100 = 700

​​ 

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