Hi, I used a similar idea but instead said for a number to be divisible by 36 it must be divisible by 6
For a number to be divisible by 6 it needs to be divisible by both 2 and 3
We know it has to be an even number to be divisible by 2 (this doesn't help much as all our answer choices are even)
Then to be divisible by 3 the sum of the digits need to be divisible by 3.
With this in mind, I chose 4 as I noticed 4+1+0+4=9 and none of the other answer choices would add to a multiple of 3.
Is this train of thought correct?
Bunuel
Official Solution:
If \(x10x\) represents a four-digit integer divisible by 36, what is the value of digit \(x\)?
A. 0
B. 2
C. 4
D. 6
E. 8
For a number to be divisible by 36, it must be divisible by both 4 and 9.
For divisibility by 4: the last two digits must be divisible by 4. Therefore, the only possibilities for \(x\) are 4 and 8.
For divisibility by 9: the sum of the digits must be divisible by 9. From the two possible values of 4 and 8, only 4 satisfies this condition: \(4 + 1 + 0 + 4 = 9\).
Thus, \(x = 4\).
Answer: C