Interview Q&A / Aptitude

1. Four bells toll at intervals of 6, 8, 12 and 18 minutes. If they toll together at 8:00 AM, when do they next toll together, and how many times in 12 hours?

   LCM(6, 8, 12, 18) = 72 minutes, so they next ring together at 9:12 AM. In 12 hours (720 minutes) they ring together 720 / 72 = 10 more times, or 11 times counting the 8:00 AM ring.

   BeginnerQuick answer1 min read
2. The HCF of two numbers is 12 and their LCM is 336. If one number is 48, what is the other?

   The other number is 84. For any two numbers, HCF x LCM = product of the numbers, so the other number is 12 x 336 / 48 = 84.

   BeginnerQuick answer1 min read
3. What is the least number which, when divided by 12, 15, 20 and 54, leaves a remainder of 8 in each case?

   548. The number minus 8 must be a multiple of all four divisors. LCM(12, 15, 20, 54) = 540, so the least such number is 540 + 8 = 548.

   BeginnerQuick answer1 min read
4. Find the greatest number that divides 43, 91 and 183 leaving the same remainder in each case.

   The answer is 4. If a number leaves the same remainder for all three, it divides their differences exactly: 48, 92 and 140. HCF(48, 92, 140) = 4, and indeed each number leaves remainder 3 when divided by 4.

   IntermediateQuick answer1 min read
5. What is the largest square tile that can pave a floor 15 m 17 cm long and 9 m 2 cm wide, and how many such tiles are needed?

   Convert to centimetres: 1517 and 902. HCF(1517, 902) = 41, so the largest tile is 41 cm by 41 cm. Tiles needed = (1517/41) x (902/41) = 37 x 22 = 814.

   IntermediateQuick answer1 min read
6. How do you find the HCF and LCM of fractions such as 2/3, 8/9 and 16/81?

   HCF of fractions = HCF of numerators / LCM of denominators; LCM of fractions = LCM of numerators / HCF of denominators. For 2/3, 8/9, 16/81 the HCF is 2/81 and the LCM is 16/3.

   AdvancedQuick answer1 min read