Let abc be a three-digit number. Then abc - cba is not divisible by
(a) 9
(b) 11
(c) 18
(d) 33

Solution:

abc = a × 10² + b × 10¹ + c × 10⁰

cba = c × 10² + b × 10¹ + a × 10⁰

Therefore

abc - cba = (100 - 1)a - (1 - 100)c = 99a - 99c = 99(a - c)

Therefore abc - cba is not divisible by 18

The correct choice is (c ).

✦ Try This: Let ab be a two-digit number. Then ab - ba is divisible by (a) 9, (b) 11, (c) 18, (d) 33

ab = a × 10¹ + b × 10⁰ = 10a + b

ba = b × 10¹ + a × 10⁰ = 10b + a

ab - ba = 10a + b - 10b - a = 9a - 9b = 9(a - b)

Therefore we can state that ab - ba = 9(a-b) and

It is divisible by 9.

The correct choice is (a).

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 16

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NCERT Exemplar Class 8 Maths Chapter 13 Problem 4

Let abc be a three-digit number. Then abc - cba is not divisible by (a) 9, (b) 11, (c) 18, (d) 33

Summary:

Let abc be a three-digit number. Then abc - cba is not divisible by 18.

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