36. What is the least number which when divided by 8, 12, 15 and 20 leaves in

each case a remainder of 5 ?

A. 125 B. 117 C. 132 D. 112

**Answer : Option A**

Explanation :

LCM of 8, 12, 15 and 20 = 120

Required Number = 120 + 5 = 125

37. Three numbers which are co-prime to each other are such that the product of the first two is 119 and that of the last two is 391. What is the sum of the three numbers?

A. 47 B. 43 C. 53 D. 51

**Answer : Option A**

Explanation :

Since the numbers are co-prime, their HCF = 1

Product of first two numbers = 119

Product of last two numbers = 391

The middle number is common in both of these products.

Hence if we take HCF of 119 and 391, we get the common middle number

HCF of 119 and 391 = 17

=> Middle Number = 17

First Number = 119?17 = 7

Last Number = 391?17 = 23

Sum of the three numbers = 7+17+23 = 47

Sum of the three numbers = 7+17+23 = 47

38. What is the greatest number which divides 24, 28 and 34 and leaves the same remainder in each case?

A. 1 B. 2 C. 3 D. 4

**Answer : Option B**

Explanation :

If the remainder is same in each case and remainder is not given, HCF of the

differences of the numbers is the required greatest number

34 - 24 = 10

34 - 28 = 6

28 - 24 = 4

Hence, the greatest number which divides 24, 28 and 34 and gives the same remainder

= HCF of 10, 6, 4

= 2

39. Six bells start ringing together and ring at intervals of 4, 8, 10, 12, 15 and 20 seconds respectively. how many times will they ring together in 60 minutes ?

A. 31 B. 15 C. 16 D. 30

**Answer : Option A**

Explanation :

LCM of 4, 8, 10, 12, 15 and 20 = 120

120 seconds = 2 minutes

Hence all the six bells will ring together in every 2 minutes

Hence, number of times they will ring together in 60 minutes

=1+(60÷2)=31

40. The HCF of two numbers is 23 and the other two factors of their LCM are 13 and 14. What is the largest number?

A. 312 B. 282 C. 299 D. 322

**Answer : Option D**

Explanation :

The HCF of a group of numbers will be always a factor of their LCM

HCF is the product of all common prime factors using the least power of each

common prime factor.

LCM is the product of highest powers of all prime factors

HCF of the two numbers = 23

=> Highest Common Factor in the numbers = 23

Since HCF will be always a factor of LCM,

23 is a factor of the LCM.

Other two factors in the LCM are 13 and 14.

Hence factors of the LCM are 23, 13, 14

So, numbers can be taken as (23 × 13) and (23 × 14) = 299 and 322

Hence, largest number = 322

41. What is the smallest number which when diminished by 12, is divisible 8, 12, 22 and 24?

A. 276 B. 264 C. 272 D. 268

**Answer : Option A**

Explanation :

Required Number = (LCM of 8, 12, 22 and 24) + 12 = 264 + 12 = 276

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