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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
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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
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I did not quite understand the question. It is quite confusing that this question is labeled 'x10x', I thought it was trying to say 10x^2 was divisible by 36 and decided to skip it..
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I did not quite understand the question. It is quite confusing that this question is labeled 'x10x', I thought it was trying to say 10x^2 was divisible by 36 and decided to skip it..
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I did not quite understand the question. It is quite confusing that this question is labeled 'x10x', I thought it was trying to say 10x^2 was divisible by 36 and decided to skip it..

The question clearly states that x10x is a four-digit number and also explicitly asks for the value of digit x at the end. In addition, 10x^2 is never written as x10x.
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