Question : What is the least value of $x$ for which the number $712x816$ is divisible by 12?
Option 1: 41
Option 2: 1
Option 3: 0
Option 4: 2
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Correct Answer: 2
Solution :
$712x816$ will be divisible by 12 if the number is divisible by both 3 and 4.
Divisibility law for 4: When the last two digits of a number are divisible by 4.
Here 16 is divisible by 4.
Divisibility law for 3: If the sum of its digits is divisible by 3.
$712x816$ is divisible by 3 if $x = 2$
Explanation:
$7+1+2+x+8+1+6 = 25+x$
Will be divisible by 3 when $x=2$ [least value]
Hence, the correct answer is 2.
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