Question

The average of 13 result is 60. if the average of the first 7 result is 59 and that of the last 7 is 61, then what will be the 7th result?

• A. 60
• B. 70
• C. 80
• D. 96

Answer 1

Answer:

A. 60

• Total Sum of 13 Results: Given that the average of 13 results is 60.

  • Sum = Number of Results × Average = 13 × 60 = 780.

• Sum of the First 7 Results: Given that the average of the first 7 results is 59.

  • Sum = Number of Results × Average = 7 × 59 = 413.

• Sum of the Last 7 Results: Given that the average of the last 7 results is 61.

  • Sum = Number of Results × Average = 7 × 61 = 427.

Identifying the Overlap

• The problem involves two overlapping sets of results: the 'first 7 results' (1st, 2nd, 3rd, 4th, 5th, 6th, 7th) and the 'last 7 results' (7th, 8th, 9th, 10th, 11th, 12th, 13th).

• Notice that the 7th result is common to both of these groups.

• Therefore, when you add the sum of the 'first 7 results' and the sum of the 'last 7 results', the 7th result is inadvertently included or counted twice.

Finding the 7th Result

• To find the value of the 7th result, we utilize the fact that its value is counted twice in the combined sum of the first 7 and last 7 results, but only once in the total sum of all 13 results.

• The formula to find the overlapping term (the 7th result in this case) is:

• 7th Result = (Sum of First 7 Results) + (Sum of Last 7 Results) - (Total Sum of 13 Results)

• Substitute the calculated values into the formula:

• 7th Result = 413 + 427 - 780

• 7th Result = 840 - 780

• 7th Result = 60.