Question:
Tick (✓) the correct answer
If x7y5 is exactly divisible by 3, then the least value of (x + y) is
(a) 6
(b) 0
(c) 4
(d) 3
Solution:
(d) 3
When a number is divisible by 3, the sum of the digits must also be divisible by 3.
$x+7+y+5=(x+y)+12$
This sum is divisible by 3 if x+y+12 is 12 or 15.
For x+y+12 = 12:
x+y=0
But x+y cannot be 0 because then x and y both will have to be 0.
Since x is the first digit, it cannot be 0.
∴ x+y+12 = 15
or x+y = 15-12=3
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