Average
- The average of the first 100 positive integers is
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As we know that ,
1 + 2 + 3 +.........+ n = n(n + 1) 2 Average of these numbers = (n + 1) 2
Here , n = 100
Correct Option: C
As we know that ,
1 + 2 + 3 +.........+ n = n(n + 1) 2 Average of these numbers = (n + 1) 2
Here , n = 100∴ Required average = 100 + 1 = 50.5 2
- The average of 7 consecutive numbers is 20. The largest of these numbers is :
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Average of 7 consecutive numbers is 20.
Since the numbers are consecutive, they form an arithmetic series with common difference 1.
Since, 7 is odd, 20 must be the middle number.
We can write the series as below,
17, 18, 19, 20, 21, 22, 23Correct Option: B
Average of 7 consecutive numbers is 20.
Since the numbers are consecutive, they form an arithmetic series with common difference 1.
Since, 7 is odd, 20 must be the middle number.
We can write the series as below,
17, 18, 19, 20, 21, 22, 23
∴ The largest of these numbers is 23.
- The average of 15 numbers is 7. If the average of the first 8 numbers is 6.5 and the average of the last 8 numbers is 8.5, then the middle number is :
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Given that , The average of 15 numbers = 7
The average of the first 8 numbers = 6.5
and the average of the last 8 numbers = 8.5
Middle i.e. eighth number = 8 × 6.5 + 8 × 8.5 – 15 × 7Correct Option: D
Given that , The average of 15 numbers = 7
The average of the first 8 numbers = 6.5
and the average of the last 8 numbers = 8.5
Middle i.e. eighth number = 8 × 6.5 + 8 × 8.5 – 15 × 7
Middle i.e. eighth number = 52 + 68 – 105
Middle i.e. eighth number = 120 – 105 = 15
- The average of 8 numbers is 21. If each of the numbers is mulitiplied by 8, the average of the new set of numbers is :
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Here , The average of 8 numbers = 21
When each number is multiplied by 8, the new average gets multiplied by 8.Correct Option: D
Here , The average of 8 numbers = 21
When each number is multiplied by 8, the new average gets multiplied by 8.
So , New average = 21 × 8 = 168
- The average of 11 numbers is 63. If the average of first six numbers is 60 and the last six numbers is 65, then the 6th number is
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Given , Sum of 11 numbers = 63 × 11 = 693
Sum of the first 6 numbers = 60 × 6 = 360
and Sum of the last 6 numbers = 65 × 6 = 390
∴ Sixth number = Sum of the first 6 numbers + Sum of the last 6 numbers – Sum of 11 numbersCorrect Option: A
Given , Sum of 11 numbers = 63 × 11 = 693
Sum of the first 6 numbers = 60 × 6 = 360
and Sum of the last 6 numbers = 65 × 6 = 390
∴ Sixth number = Sum of the first 6 numbers + Sum of the last 6 numbers – Sum of 11 numbers
Sixth number = 360 + 390 – 693 = 57