If the 7-digit number 612x97y is divisible by 72, and the 6-digit number 34z178 is divisible by 11, then the value of (x - 2y + 3z) is:
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Correct answer: C
Explanation
The correct answer is option 3 i.e. 2.
Divisibility of 612x97y by 72 (8 × 9):
97y is divisible by 8
If y = 6 then 97y = 976 (Divisible by 8)
Sum of digits = 6 + 1 + 2 + x + 9 + 7 + 6 = 31 + x
If x = 5 then 31 + x = 36 (Divisible by 9)
Divisibility of 34z178 by 11:
Alternating sum = (3 + z + 7) - (4 + 1 + 8) = (10 + z) - 13 = z - 3
If z = 3, then z - 3 = 0
(x - 2y + 3z) = 5 - 2(6) + 3(3) = 5 - 12 + 9 = 2