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The average of five different positive numbers is 25.
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11 Apr 2019, 16:24
11 Apr 2019, 16:24
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31% (01:55) correct
68% (01:31) wrong based on 116 sessions
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The average of five different positive numbers is 25. \(\triangle\)is the decrease in the average when the smallest number among them is replaced by 0.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(\triangle\) |
5 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Re: The average of five different positive numbers is 25.
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13 Apr 2019, 02:54
13 Apr 2019, 02:54
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If the average of five different positive numbers is 25, then their sum is 5*25 = 125.
To decrease the average the most, we need to decrease the sum the most. The more we decrease the sum, the more we decrease the average.
To maximize this decrease, we need to maximize the smallest number. Thus, when it's changed to 0, we will decrease the sum by the greatest amount possible.
The smallest number can't be greater than 23. If it is 24, then our smallest sum would be 24 + 25 + 26 + 27 + 28 = 130, which is too much.
So if the smallest number is 23, then our 5 numbers are 23, 24, 25, 26, and 27.
When we change 23 to 0, we get a sum of 0 + 24 + 25 + 26 + 27 = 102, and an average of \(\frac{102}{5} = 20.4\). So the average only decreased by 4.6. And that's the most we could possibly decrease the average. Thus, the decrease in average will always be less than 5, and Quantity B will always be greater.
To decrease the average the most, we need to decrease the sum the most. The more we decrease the sum, the more we decrease the average.
To maximize this decrease, we need to maximize the smallest number. Thus, when it's changed to 0, we will decrease the sum by the greatest amount possible.
The smallest number can't be greater than 23. If it is 24, then our smallest sum would be 24 + 25 + 26 + 27 + 28 = 130, which is too much.
So if the smallest number is 23, then our 5 numbers are 23, 24, 25, 26, and 27.
When we change 23 to 0, we get a sum of 0 + 24 + 25 + 26 + 27 = 102, and an average of \(\frac{102}{5} = 20.4\). So the average only decreased by 4.6. And that's the most we could possibly decrease the average. Thus, the decrease in average will always be less than 5, and Quantity B will always be greater.
General Discussion
Re: The average of five different positive numbers is 25.
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13 Apr 2019, 02:58
13 Apr 2019, 02:58
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For more advanced students:
To decrease the average of n items by x, then we need to decrease the sum by nx.
So to decrease the average of 5 items by 5, we would need to decrease the sum by 25.
This means that to decrease the average by 5, our smallest number would have to be 25. But this is impossible, as this would make the sum greater than 125. Our smallest number has to be smaller than 25, and hence our decrease to the sum will be less than 25, and our decrease to the average less than 5.
To decrease the average of n items by x, then we need to decrease the sum by nx.
So to decrease the average of 5 items by 5, we would need to decrease the sum by 25.
This means that to decrease the average by 5, our smallest number would have to be 25. But this is impossible, as this would make the sum greater than 125. Our smallest number has to be smaller than 25, and hence our decrease to the sum will be less than 25, and our decrease to the average less than 5.
