If the 5-digit number 284xy is divisible by 3 and 77, then the value of (8x - y) is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 5.
A number is divisible by 3 if the sum of its digits is divisible by 3.
Sum of digits = 2 + 8 + 4 + x + y = 14 + x + y
14 + x + y ≡ must be a multiple of 3
i.e., (x + y) ≡ -14 ≡ 1 (mod 3)
77 = 7 × 11
28413 → Not divisible by 3 (sum = 2 + 8 + 4 + 1 + 3 = 18), try 77 → 28413 ÷ 77 = 369.0
So 28413 is divisible by 3 and 77 both.
Now check:
x = 1, y = 3
Then 8x - y = 8 × 1 - 3 = 5