Question
The six-digit number '83219y' is divisible by 6, but not by
5. What is the value of (2y + 5)?Solution
ATQ,
For divisibility by 6, the number must be divisible by both 2 and 3.
Sum of digits = 8 + 3 + 2 + 1 + 9 + y = 23 + y
For divisibility by 3, (23 + y) must be divisible by 3.
Also, y should be even (for divisibility by 2) and y ≠0 or 5 (to avoid divisibility by 5).
Even digits: 0, 2, 4, 6, 8
Trying values:
23 + 4 = 27 → divisible by 3 ✅ and 4 is even ✅ → y = 4
So, (2y + 5) = 2Ă—4 + 5 = 13
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