Multiple choice

A girl finds the average of 6 positive integers, each integers containing two digits. By mistake she interchanges the digit of one number say xy for yx. Due to this the average becomes 1.5 less than the previous one. What was the difference between two digits x and y.

  1. 1

  2. 2

  3. 3

  4. 4

  5. None
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A Correct answer
Explanation

Let the number be 10x + y. Interchanging gives 10y + x. The difference in the number is 9(x-y). The average change is 1.5, so the total sum change is 1.5 * 6 = 9. Thus, 9(x-y) = 9, meaning x-y = 1.

AI explanation

When the digits of a number xy are reversed to yx, the value of the number changes by 9 times the difference of the digits. The total decrease in the sum of the 6 numbers is the average decrease multiplied by the count of numbers, which is 1.5 multiplied by 6, giving a total decrease of 9. Therefore, 9 times the difference between the two digits equals 9, making the difference between x and y equal to 1.

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