Let n be an odd integer and the number is divisible by but is not equal to it. Then the half of sum of the digits of smallest value of is (where denotes )

JEE MainMathematicsModerateBinomial Theorem

Let n be an odd integer and the number $(n\ 151\ )$ is divisible
by $(n\ 150\ )$ but is not equal to it. Then the half of sum of the
digits of smallest value of is (where $(n\ r\ )\$ denotes
$\ ^{n}C_{r}$ )

Show answer and solution

Let [IMAGE] where

q \neq 1

[IMAGE] or n = 150q + 150
Smallest n will be when q = 3 (n should be odd)
n = 453 + 150
n = 603

\Rightarrow

sum of the digit = 9

Source: Grass-G / M-08 Mathematics Paper 23 October.docx

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