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The average of the two-digit numbers, which remain the same when the digits interchange their positions, is__________?

Correct answer: C. 55

  • A. 33
  • B. 44
  • C. 55
  • D. 66

Explanation

Two-digit numbers unchanged by reversing their digits are 11, 22, 33, 44, 55, 66, 77, 88 and 99. These form an arithmetic sequence, so their average is the middle value, 55, or equivalently (11 + 99) / 2 = 55. A student may choose 44 by omitting one of the valid palindromic two-digit numbers.

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About Averages

An average represents the total of a set of values divided by the number of values, and a weighted average gives different importance to different groups. Problems involve missing values, combined averages, replacement of observations, and changes in the average, so the total and count must be tracked separately.

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