Your last marks
Mrs Auger gave an exam in a mathematics class of five students. She entered the scores in random order into a spreadsheet, which recalculated the class average after each score was entered. Mrs. auger noticed that after each score was entered, the average was always an integer. The scores (listed in ascending order) were 71,76,80,82, and 91. What was the last score Mrs.auger entered?
The answer is 80.
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Lets start evaluating reverse.
Total sum is 400 which is divisible by 5.
Since this is also divisible by 4, the last number should be divisible by 4 to get average of first four numbers as an integer.
So last number will be 76 or 80
If last number is 76, sum of first four numbers is 324 (which is divisible by 4 & also by 3)
Now next we have to subtract a number divisible by 3 so that sum of first 3 numbers is divisible by 3. But there is no number in the list divisible by 3.
Let's now assume last number is 80. So sum of first four numbers is 320 (3k+2 form)
From this we can subtract 71 (3k+2 form) to ger 249 which ia divisible by 3.
Now we subtract 91 to get 158=76+82
So we have 76,82,91,71,80 or 82,76,91,71,80
Last number is 80.