The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of last 7 is 61. Find the 7th number?
- 32
- 46
- 68
- 51
Explanation
Let's denote the sum of all 13 numbers as S.S = 13 * 60 = 780
Sum of the first 7 numbers = 7 * 57 = 399
Sum of the last 7 numbers = 7 * 61 = 427
Now, let's find the sum of all 13 numbers using the sum of first 7 and last 7 numbers. Notice that the 7th number is counted twice in this calculation:
Sum of first 7 + Sum of last 7 - 7th number = Sum of all 13 numbers
399 + 427 - 7th number = 780
826 - 7th number = 780
7th number = 826 - 780
7th number = 46
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