Let x be the smallest 5 digit number such that when it is divided by 5 6 7 and 21 it leaves the same...........

Quantitative Aptitude (MTS) Number System

Let x be the smallest 5-digit number such that when it is divided by 5, 6, 7 and 21, it leaves the same remainder 4. What is the

sum of the digits of x ?

This questions was previously asked in

SSC MTS 27th October 2021 Shift-2

To solve the problem, follow these steps:

- Find the common remainder: We need x = 4 (mod 5), x = 4 (mod 6), x = 4 (mod 7), and x = 4 (mod 21).

- Identify the least common multiple (LCM): Since the number leaves the same remainder, focus on the LCM of 5, 6, 7, and 21, which is 210.

- Establish the equation: x = 210k + 4.

- Find the smallest 5-digit number: Start from 10000 and solve for k:

- 10000 = 210k + 4

- 9996 = 210k

- k = 48

- Calculate the number: Plug k = 48:

- x = 210 * 48 + 4 = 10084.

- Sum the digits of 10084: 1 + 0 + 0 + 8 + 4 = 13.

- The answer is Option 2: 13.

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