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If an 8-digit number 1862383A is divisible by 22, find the value of A.
- a)6
- b)4
- c)2
- d)More than one of the above
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If an 8-digit number 1862383Ais divisible by 22, find the value of A.a...
Given:
The eight-digit number is 1862383A.
Concept used:
Divisibility rule for 2: The last digit of any digit number is an even number.
Divisibility rule for 11: The difference for the sum of the digits in the odd and even places of the given number is 0 or divisible by 11.
Divisibility rule for 22: The required number is divisible by 2 and 11 then the number is divisible by 22.
Calculation:
Prime factorization of 22 = 2 × 11
As we know, If the required number 1862383A is divisible by 2 and 11 then the number is divisible by 22.
As per the divisibility rule for 2, the value of A must be an even number.
The possible value of A: 2, 4, 6, 8, 0
As per the divisibility rule for 11,
⇒ (8 + 2 + 8 + A) - (1 + 6 + 3 + 3) = 0 or multiple of 11
⇒ 18 + A - 13 = 0 or multiple of 11
⇒ 5 + A = 0 or multiple of 11
For 5 + A to be a multiple of 11, the value of A must be 6.
∴ The required value of A is 6.
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Community Answer
If an 8-digit number 1862383Ais divisible by 22, find the value of A.a...
Explanation:
There are two conditions for a number to be divisible by 22:
1. The number must be divisible by 2
2. The sum of the digits at odd places minus the sum of the digits at even places must be divisible by 11.
Given number: 1862383A
Step 1: Check divisibility by 2
Since the number ends with A, we don't know if A is an even digit or not. However, the divisibility by 2 only depends on the last digit, so the number is divisible by 2 regardless of the value of A.
Step 2: Check divisibility by 11
Sum of digits at odd places: 1 + 6 + 3 + 3 = 13
Sum of digits at even places: 8 + 2 + 8 = 18
Difference: 18 - 13 = 5
Since 5 is not divisible by 11, the number is not divisible by 22.
Therefore, the correct answer is Option A) 6 because the given number is not divisible by 22 when A is replaced by 6.
There are two conditions for a number to be divisible by 22:
1. The number must be divisible by 2
2. The sum of the digits at odd places minus the sum of the digits at even places must be divisible by 11.
Given number: 1862383A
Step 1: Check divisibility by 2
Since the number ends with A, we don't know if A is an even digit or not. However, the divisibility by 2 only depends on the last digit, so the number is divisible by 2 regardless of the value of A.
Step 2: Check divisibility by 11
Sum of digits at odd places: 1 + 6 + 3 + 3 = 13
Sum of digits at even places: 8 + 2 + 8 = 18
Difference: 18 - 13 = 5
Since 5 is not divisible by 11, the number is not divisible by 22.
Therefore, the correct answer is Option A) 6 because the given number is not divisible by 22 when A is replaced by 6.
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