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16 Sep 2014, 00:47
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Difficulty:
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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
A. 0
B. 2
C. 4
D. 6
E. 8
16 Sep 2014, 00:47
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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
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
15 Oct 2023, 11:18
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
