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Playing with Numbers — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSPlaying with Numbers1 Mark
MCQ
Let $abc$ be a three-digit number. Then $abc – cba$ is not divisible by
  • A
    $9$
  • B
    $11$
  • ✓
    $18$
  • D
    $33$
✓

Answer

Correct option: C.
$18$
Given, abc is a three-digit number. Then,
$abc = 100a + 10b + c and$
$cba = 100c + 10b + a$
$abc − eba = (100a + 10b + c) − (100c + 10b + a)$
$= 100a - a + 10b - 10b + c - 100$
$= 99a - 99c = 99 (a - c)$
$= abc - cba$ is divisible by $99$
$abc - cba$ is divisible by $9, 11, 33,$ but it is not divisible by $18.$

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