The sum of all 3-digit numbers less than or equal to 500, that are formed without using the digit "1" and they all are multiple of 11, is _____________.
Answer (integer)
7744
Solution
209, 220, 231, ..........., 495<br><br>Sum = ${{27} \over 2}$(209 + 495) = 9504<br><br>Number containing 1 at unit place $$\matrix{
{\underline 2 } & {\underline 3 } & {\underline 1 } \cr
{\underline 3 } & {\underline 4 } & {\underline 1 } \cr
{\underline 4 } & {\underline 5 } & {\underline 1 } \cr
} $$<br><br>Number containing 1 at 10<sup>th</sup> place $$\matrix{
{\underline 3 } & {\underline 1 } & {\underline 9 } \cr
{\underline 4 } & {\underline 1 } & {\underline 8 } \cr
} $$<br><br>Required = 9504 $-$ (231 + 341 + 451 + 319 + 418)<br><br>= 7744
About this question
Subject: Mathematics · Chapter: Sequences and Series · Topic: Arithmetic Progression
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