Multiple choice

The difference between two 2-digit numbers is equal to their HCF. If first number is obtained by reversing the digits of second number, find the sum of the digits of the any number.

  1. 6

  2. 7

  3. 8

  4. 9
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the number be 10x + y. The reversed number is 10y + x. The difference is |9x - 9y| = 9|x - y|. This must be the HCF. Since the difference is a multiple of 9, the HCF must be 9. Thus, 9|x - y| = 9, so |x - y| = 1. The sum of digits x + y can vary, but in many such problems, the sum is constant. Checking options, 9 is the only digit sum that fits common constraints.

AI explanation

Let the numbers be 10a plus b and 10b plus a, where the digits are a and b. The difference between the numbers is 9a minus 9b, which factors to 9(a minus b), meaning the difference must be a multiple of 9. Since the difference equals their HCF, the HCF must be 9, making the digits differ by 1 and sum to 9. The sum of the digits of the number is 9.

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