Question
Download Solution PDFIf the number 3823P8 is divisible by 11, then what is the value of P?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Number = 3823P8
Divisible by 11
Formula used:
Rule of 11: (Sum of digits at odd positions) - (Sum of digits at even positions) ≡ 0 (mod 11)
Calculation:
Digits: 3, 8, 2, 3, P, 8
Odd positions (1st, 3rd, 5th): 3, 2, P → Sum = 3 + 2 + P = 5 + P
Even positions (2nd, 4th, 6th): 8, 3, 8 → Sum = 8 + 3 + 8 = 19
⇒ (5 + P) - 19 ≡ 0 (mod 11)
⇒ P - 14 ≡ 0 (mod 11)
⇒ P ≡ 14 (mod 11)
⇒ P = 14 - 11 = 3
∴ Value of P = 3
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