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## #1 2016-10-08 08:05:51

بِسمِ اللَّهِ الرَّحمٰنِ الرَّحيمِ
From: Sahiwal Division
Registered: 2012-03-22
Posts: 22,197
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# Mathematics QuizzesMathematics

Question:
The three-digit number ABC has the following properties:
The middle digit is the sum of the first and last digits.
None of the digits repeat.
ABC is divisible by 5.
Which of the following could equal B?

Option A):
5
Option B):
2
Option C):
3
Option D):
6
Option E):
4

6

Explanation:
Start with the last fact given in the question, that the three-digit number ABC is divisible by 5. Every number that's divisible by 5 ends in either 0 or 5, so C must be one of those numbers. The first and second facts make it impossible for C to be zero, because, if C were zero, A and B would be equal to each other, which is illegal. Therefore, C must be 5. Because B = A + C, and A must be at least 1, B must be at least 6.

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