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Find the sum of all values of the digit $X$ such that $39504X2$ is divisible by 4.

 May 19, 2019
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The divisibility rule for 4 says that for a number to be divisible by four, the last two digits must make a multiple of four, so the only digits you care about are X2. If this number is divisible by four the whole number will be.

The possible values for the number X2 are:

02

12

22

32

42

52

62

72

82

92

 

12, 32, 52, 72 and 92 are divisible by four so the sum of the possible values of x is \(1+3+5+7+9= \boxed{25}\)

.
 May 19, 2019

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