Multiple choice

Average of 13 numbers is 58, the average of Ist 7 numbers is 63 and the average of last 7 numbers is 70. Find the 7th number.

  1. $167$
  2. $77$
  3. $187$
  4. $177$
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D Correct answer
Explanation

The sum of first 7 numbers is 7 × 63 = 441. The sum of last 7 numbers is 7 × 70 = 490. The total sum of all 13 numbers is 13 × 58 = 754. The 7th number is counted in both groups, so: 441 + 490 - 7th number = 754. Therefore, 7th number = 441 + 490 - 754 = 177. This is a weighted average problem where the overlapping element must be subtracted.

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