A60
B70
C80
D96
Answer:
A. 60
Read Explanation:
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.