﻿ If an eight-digit number 1634562A is divisible by 22, then A is equal to

#### Multiple Choice Question (MCQ)

If an eight-digit number 1634562A is divisible by 22, then A is equal to

1. ×

2

2. ×

4

3. 6

4. ×

8

Collected in the board: Number Theory

Steven Zheng posted 9 hours ago

1. \because 22 = 2\times 11

Therefore

The number is divisible by 22 if and only if it is divisible by both 11 and 1.

divisibility rule for 2 - the last digit of the number is an even number

divisibility rule for 11 - the difference of the sum of all digits on even places of the number and the sum of all digits on odd places is zero or divisible by 11

Given number: 1634562A

Sum of digits on odd places of given number

A+6+4+6 = 16+A

Sum of digits on even places of given number

2+5+3+1 = 11

difference

16+A-11 = 5+A

When A = 6, the difference is divisible by 11. Since the number is also an even number, it is divisible by 22

Therefore, C is the right option.

Steven Zheng posted 9 hours ago

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