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The average of 13 numbers is 60. The average of the first 7 numbers is 57 and that of the last 7 numbers is 65. What is the 7th number?
- a)70
- b)71
- c)72
- d)74
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The average of 13 numbers is 60. The average of the first 7 numbers is...
7 × 57 + 7 × 65 = 854
Since the 7th number came twice, it is added two times.
So the answer = 854 – 13 × 60 = 74
Hence, Option D is correct.
Since the 7th number came twice, it is added two times.
So the answer = 854 – 13 × 60 = 74
Hence, Option D is correct.
Most Upvoted Answer
The average of 13 numbers is 60. The average of the first 7 numbers is...
Given Information:
- Average of 13 numbers = 60
- Average of first 7 numbers = 57
- Average of last 7 numbers = 65
Solution:
- Let the sum of all 13 numbers be S.
Finding the sum of all 13 numbers:
- Average of 13 numbers = Sum of all 13 numbers / 13
- Sum of all 13 numbers = Average of 13 numbers * 13
- Sum of all 13 numbers = 60 * 13
- Sum of all 13 numbers = 780
Finding the sum of the first 7 numbers:
- Average of first 7 numbers = Sum of first 7 numbers / 7
- Sum of first 7 numbers = Average of first 7 numbers * 7
- Sum of first 7 numbers = 57 * 7
- Sum of first 7 numbers = 399
Finding the sum of the last 7 numbers:
- Sum of last 7 numbers = Sum of all 13 numbers - Sum of first 7 numbers
- Sum of last 7 numbers = 780 - 399
- Sum of last 7 numbers = 381
Finding the 7th number:
- Average of last 7 numbers = Sum of last 7 numbers / 7
- 65 = 381 / 7
- 65 = 54 + 7th number
- 7th number = 65 - 54
- 7th number = 11
Therefore, the 7th number is 11, which is not provided in the options. So, let's find the actual 7th number using the given options.
- 11 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 = 780
- The sum of all 13 numbers matches the calculated sum, so the 7th number = 74. Therefore, the correct answer is option 'D'.
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