Competency Based Questions

Three bulbs red, green and yellow flash at intervals of 80 seconds, 90 seconds and 110 seconds. All three flash together at 8:00 am. At what time will the three bulbs flash altogether again?

• 9:00 am

• 9:12 am

• 10:00 am

• 10:12 am

Which of the following is an irrational number?

Rahul has 40 cm long red and 84 cm long blue ribbon. He cuts each ribbon into pieces such that all pieces are of equal length. What is the length of each piece?

• 4 cm as it is the LCM of 40 and 84

• 4 cm as it is the HCF of 40 and 84

• 8 cm as it is the LCM of 40 and 84

• 8 cm as it is the HCF of 40 and 84

Which of the following is rational?

If ‘p’ is multiple of ‘q’, then HCF and LCM of ‘p’ and ‘q’ is:

• HCF = p, LCM = q

• HCF = q, LCM = p

• HCF = p x q = LCM

• None of these

The prime factorization for 1729 is:

Assertion (A): LCM of 26 and 91 is 182. Reason (R): The prime factorization of 26 = 2×13 and 91=7×13, hence LCM=13× 13 × 2×7.

• Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

• Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

• Assertion (A) is true but reason (R) is false.

• Assertions (A) is false but reason (R) is true.

Assertion (A): LCM of and is Reason (R): LCM is always a multiple of HCF.

• Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

• Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

• Assertion (A) is true but reason (R) is false.

• Assertion (A) is false but reason (R) is true.

A merchant has 120 soap cubes of 1st kind in box I, 180 soap cubes of 2nd kind in box II and 240 soap cubes of 3rd kind in box III. He wants to sell the soap cubes by filling three kinds of soap cubes in small packets of equal capacity. On the basis of above information, answer the following: What would be the largest capacity of such packets?

• 30

• 50

• 60

• 120

Which of the following concept is used to find the largest capacity?

• HCF only

• LCM only

• HCF and LCM both

• None of these