Question
Download Solution PDFFind the value of (9K − 5) for which the number 35K84 is divisible by 11.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The number 35K84 is divisible by 11.
Formula used:
A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is divisible by 11.
Calculation:
The digits of the number are 3, 5, K, 8, and 4.
Sum of digits in odd positions = 3 + K + 4 = (3 + 4 + K) = (7 + K)
Sum of digits in even positions = 5 + 8 = 13
For divisibility by 11:
⇒ (Sum of odd-position digits) - (Sum of even-position digits) = Multiple of 11
⇒ (7 + K) - 13 = Multiple of 11 or 0
⇒ K - 6 = Multiple of 11 or 0
The valid values of K are those that satisfy the above equation.
Here, K = 6 is valid.
So, (9K - 5) = (9 × 6 - 5) = 54 - 5 = 49
∴ The correct answer is option (4).
Last updated on Jul 16, 2025
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