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Find the digit x.

 

 Jul 8, 2020
 #1
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Divisible by 42 means all of below: 

1) divisible by 2

2) divisible by 3

3) divisible by 7

 

So, by 1), we know that x is an even digit.

 

By 2), the digit sum must be divisible by 3 because of the divisibility trick.

The digit sum is \(x + 3 + 5 + 7 + 9 + x = 2x + 24\)

We know that 24 is divisible by 3. That means if 2x is divisible by 3, then the entire number is divisible by 3.

 

We don't even need 3) to work out the answer.

 

Out of all even digits(0,2,4,6,8), there is only one digit satisfying the conditions, which is 6.

 Jul 8, 2020

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