Let x be the least number which when divided by 12, 16, 18, 20 and 25, the remainder in each case is 3, and x is divisible by 13. What is the sum of the digits of x?

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HPCL Engineer Electrical 01 Nov 2022 Official Paper

Answer 1

Given:

x is the least number which when divided by 12, 16, 18, 20 and 25, the remainder in each case is 3, and x is divisible by 13

Concept used:

LCM is the smallest common multiple of two or more numbers.

Calculation:

LCM (12, 16, 18, 20, 25) = 3600

So, X must be in the form of (3600n + 3) where n is any arbitrary integer.

Performing the hit and trial method,

taking n = 1, (3600 × 1 + 3) i.e. 3603 isn't divisible by 13.

taking n = 2, (3600 × 2 + 3) i.e. 7203 isn't divisible by 13.

taking n = 3, (3600 × 3 + 3) i.e. 10803 is divisible by 13.

So, x = 10803

Now, the sum of digits of x = 1 + 0 + 8 + 0 + 3

⇒ 12

∴ The sum of the digits of x is 12.