Passage Based Questions: HCF and LCM | Quantitative Techniques for CLAT PDF Download

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.
Q1: How long they would need to wait at the bus stop?
Ans: 143 minutes
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.

Q2: How many buses Aman would not board till he gets a simultaneous bus as Saket?
Ans: 12 buses
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.

Q3: How many buses Raman would not board till he gets a simultaneous bus as Vaishali?
Ans: 10 buses
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.

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.
Q4: How many students can be seated in one room as per given conditions of the question?
Ans: 12
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.

Q5: How many rooms are required for students of training A?
Ans: 9
Rooms Required for Training A student = 108/12 = 9

Q6: How many rooms are required for students of training B and C together?
Ans: 25
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

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.
Q7: What is the wrong product that he calculated?
Ans: 450
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

Q8: In the previous question what was the original product?
Ans: 1700
Original Product =50*34 = 1700

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.
Q9: What was the given number?
Ans: 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

Q10: What should have been the original product?
Ans: As the given number is 1800, the original product would be 7/18th of 1800 i.e., 7*1800/18 = 7*100 = 700.