JEE MAIN - Mathematics (2021 - 26th August Evening Shift - No. 17)
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
7744
Explanation
209, 220, 231, ..........., 495
Sum = $${{27} \over 2}$$(209 + 495) = 9504
Number containing 1 at unit place $$\matrix{ {\underline 2 } & {\underline 3 } & {\underline 1 } \cr {\underline 3 } & {\underline 4 } & {\underline 1 } \cr {\underline 4 } & {\underline 5 } & {\underline 1 } \cr } $$
Number containing 1 at 10th place $$\matrix{ {\underline 3 } & {\underline 1 } & {\underline 9 } \cr {\underline 4 } & {\underline 1 } & {\underline 8 } \cr } $$
Required = 9504 $$-$$ (231 + 341 + 451 + 319 + 418)
= 7744
Sum = $${{27} \over 2}$$(209 + 495) = 9504
Number containing 1 at unit place $$\matrix{ {\underline 2 } & {\underline 3 } & {\underline 1 } \cr {\underline 3 } & {\underline 4 } & {\underline 1 } \cr {\underline 4 } & {\underline 5 } & {\underline 1 } \cr } $$
Number containing 1 at 10th place $$\matrix{ {\underline 3 } & {\underline 1 } & {\underline 9 } \cr {\underline 4 } & {\underline 1 } & {\underline 8 } \cr } $$
Required = 9504 $$-$$ (231 + 341 + 451 + 319 + 418)
= 7744
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