Question
For what number of values of 'z' is the number 1269zq
divisible by 15?Solution
ATQ,
Divisible by 15 ⇒ divisible by 5 and 3
Divisible by 5 ⇒ q = 0 or 5
Divisible by 3 ⇒ sum divisible by 3
Case 1: q = 0
Sum = 1 + 2 + 6 + 9 + z + 0 = z + 18
Divisible by 3 ⇒ z = 0, 3, 6, 9
Case 2: q = 5
Sum = 1 + 2 + 6 + 9 + z + 5 = z + 23
Divisible by 3 ⇒ z = 1, 4, 7
Total values of z: 4 + 3 = 7
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