pareekbharat86 wrote:A test is taken by 100 people and possible scores are the integers between 0 and 50, inclusive. Would the avg. score be greater than 30? (Answer Yes, No or Uncertain)
Condition- No more than 2 test takers scored any given score.
Ans: NO
Alternate approach:
Step 1: Plug in the THRESHOLD.
Here, the threshold = an average of 30.
If the average of the 100 scores = 30, then the SUM of the 100 scores = (number)(average) = 100*30 = 3000.
Step 2: Determine the MAXIMUM POSSIBLE SUM
Since each score can be included at most 2 times, the maximum possible sum will be yielded if the 100 scores are as follows:
50, 50, 49, 49, 48, 48....3, 3, 2, 2, 1, 1.
In the list above, each integer between 1 and 50, inclusive, appears TWICE.
Implication:
The maximum possible sum is equal to 2 times the sum of the integers between 1 and 50, inclusive.
Sum of consecutive integers = (number of integers)(average of biggest and smallest).
Thus, the maximum possible sum = 2 * (number of integers)(average of biggest and smallest) = 2 * 50 * (50+1)/2 = 2550.
Result:
Since the maximum possible sum is LESS than 3000, the average of the 100 scores must be LESS than 30.
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