Let abc be a three digit number. Then abc + bca + cab is not divisible by
(a) a + b + c
(b) 3
(c) 37
(d) 9

Solution:

abc = a × 10² + b × 10¹ + c × 10⁰

bca = b × 10² + c × 10¹ + a × 10⁰

cab = c × 10² + a × 10¹ + b × 10⁰

Adding the three numbers we have:

abc + bca + cab = 111a + 111b + 111c = 111(a + b + c)

Hence the sum of three numbers is divisible by (a + b + c), 3 and 37. The only number given above by which the sum of three numbers is not divisible is 9.

✦ Try This: Let abc be a three digit number. Then abc - bca - cab is divisible by (a) a + b + c, (b) 3, (c) 37, (d) 89

abc = a × 10² + b × 10¹ + c × 10⁰

bca = b × 10² + c × 10¹ + a × 10⁰

cab = c × 10² + a × 10¹ + b × 10⁰

abc - bca - cab is calculated as:

abc - bca + cab = (100a - 10a - a) + (100b - 10b - b) + (100 - 10c - c) = 89(a - b - c)

Hence abc - bca - cab is divisible by a - b - c and 89.

Hence the correct choice of answer is (d).

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

NCERT Exemplar Class 8 Maths Chapter 13 Problem 7

Let abc be a three digit number. Then abc + bca + cab is not divisible by (a) a + b + c, (b) 3, (c) 37, (d) 9

Summary:

If abc be a three digit number. Then abc + bca + cab is not divisible by 9.

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