Multiple choice softskills communication

The average between a two digit number and the number obtained by interchanging the digits is 9. What is the difference between the two digits of the number ?

  1. 8

  2. 2

  3. 5

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the number be 10x + y where x and y are digits. The interchange gives 10y + x. Their average is (11x + 11y)/2 = 9, so x + y = 18/11 which is not an integer. For a valid two-digit number, x + y must be an integer between 1 and 18. The conditions create an impossible scenario, so the difference cannot be uniquely determined from the given information.

AI explanation

To solve this problem, let's assume the two-digit number as "10a + b" where 'a' is the tens digit and 'b' is the units digit.

The number obtained by interchanging the digits is "10b + a".

According to the given information, the average between these two numbers is 9. We can express this mathematically as:

(10a + b + 10b + a) / 2 = 9

Simplifying the equation, we get:

11a + 11b = 18

Dividing both sides by 11, we get:

a + b = 18/11

Since 'a' and 'b' represent integers, the sum of two integers cannot be a non-integer value. Therefore, it is not possible to determine the difference between the two digits of the number.

Hence, the correct answer is D. Cannot be determined.

Keep practicing — related questions