If x and y are two digits of the number 653xy such that this number is divisible by 80, then x + y = ?
Explanation:
Co-prime factors of 80 are 5 and 16. If the number is divisible by both 5 and 16, we can say that the given number is divisible by 80.
Since the number is divisible by 16, it has to be an even number which is also divisible by 5. This is possible only when last digit is 0. Hence, y = 0
The number is 653x0.
This number is divisible by 5. To check if it is divisible by 16, we have to consider the last four digits of the number.
Option (a): Let x = 2 Last four digits = 5320 (not divisible by 16).
Option (b): Let x = 4 Last four digits = 5340 (not divisible by 16).
Option (b): Let x = 5 Last four digits = 5350 (not divisible by 16).
Option (b): Let x = 6 Last four digits = 5360 (divisible by 16). ∴ x + y = 6 + 0 = 6
Hence option (d).
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