Question 4 of 22intermediate💡 UnderstandShort Answer2 marks

What sums can we get when we add a 2-digit number with its reverse?

Correct Answer

Pattern: When adding a 2-digit number to its reverse, the sum equals 11 times the sum of the digits. ∴ All sums are multiples of 11.

Possible sums: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198.

Smallest sum: 11 (from 10 + 01 = 11)

Largest sum: 198 (from 99 + 99 = 198)

Reasoning: The digit sum ranges from 1 (for 10) to 18 (for 99). ∴ Sums range from 11×111 \times 1 = 11 to 11×1811 \times 18 = 198.

Exercise: Reverse and Add | Q: b | (Page Page 3)
For More Understanding

Explanation

The chapter explores the pattern when adding a 2-digit number to its reverse. Since the sum equals 11 times the sum of the digits, all results are multiples of 11. The range depends on the digit sum, which can be from 1 (for 10) to 18 (for 99).

Solution Steps

  1. Identify the pattern: the sum equals 11 times the sum of the digits.

  2. Recognize that all results are multiples of 11.

  3. Determine the range: digit sum goes from 1 (for 10) to 18 (for 99).

  4. Calculate the smallest sum: 11×111 \times 1 = 11.

  5. Calculate the largest sum: 11×1811 \times 18 = 198.

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