The average score in an examination of 10 students of a class is 60

Just to confuse those who do not read the question properly.

Can a be 55? Or can it start from 56 only? That's what I was not sure about


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Look at Bunuel 's explanation above. It has to be 55 to make e the max.

Hi,
Another method although logic is same as rhat used by Bunuel

If the value of all other except the largest is 55..
Largest will be 60*10-55*9=600-495=105..

However the top 5 are distinct and the smallest of these can be 55, so remaining THREE will be 1,2,&3 more so total combined value will be 1+2+3 or 6 more..
Therefore the largest will be 6 less than max possible..... 105-6=99
C

If the average of least 5 scores is 55, then is it allowed to have a score of 55 (a) in the top 5 set ?

May be to help the test takers by setting up the easiest answer choice to eliminate or for those who don't bother reading the question during time crunch.

Dear "Bunuel",

I have confusion on you solution.

The 5 smallest scores has an average of 55. For example: they could score 53,54,55,56,57 with total 275. In way of minimizing the the top 5 scores, you assumed that the lowest score is 55. However, in my example above, there at least 2 scores from the 5 smallest scores is larger that 2 scores in second group of top scores. Hence, I believe the smallest scores should not be 55, otherwise there are students in smallest group score higher than 2 students in top scores.

Where I go wrong?

Thanks

Since, we need to find the maximum possible score of the topper, we need to make sure that the 5th person from the top should have the least score. So, if the average of last 5 is 275 and if we take all of those scores as 55, we can have the minimum value of the 5th also as 55. Hence, We need to take all the last 6 students to have a score of 55 so that we can maximize the topper student score. I hope it is clear now.

What's happening here ?
54+56+57+58+100 = 325

Maximum marks scored could be D 100. ?

What am I or you missing ? Bunuel

With 54 as the score of 5th highest, the remaining 5 would be at the most 54 only.
That is 100, 58, 57, 56, 54, 54, 54, 54, 54, 54.
Total : 325+5*54=325+270=595, which 5 less than the actual total 600.

The 5th lowest 54 or 55 will have an effect on the remaining 5 scores.

Dear abhimahna chetan2u Bunuel, after reading all the explanations and clarifications posted by you on this thread, I still have a query. We are taking the lowest score among the top-5 students as 55. In light of this, the scores are 99, 58, 57, 56, 55, 55, 55, 55, 55, 55. Now reading the stem again: Now what is "top-5" in our case? Because the 5th position is tied among 6 people, we cannot pick one over the other, therefore, if the scores of top five students are not considered, there is nobody remaining in the set to meet the later half of the above quote. Am I missing something?

Hi IanStewart ScottTargetTestPrep JeffTargetTestPrep can you please help with this?

The average score of 10 students = 60.
Average score of bottom 5 students = 60 - 5 = 55
Thus, total score of bottom 5 students = 55*5 = 275
Total score of top 5 students = 600 - 275 = 325,
Thus, average of top 5 = 65

Since the maximum score of the topper is considered, the lowest score of the bottom 5 should be minimum. Thus, let us suppose all the bottom 5 scored 55.
Since all the top scorers scored distinct integral scores, to maximise the topper, let the score of other toppers be 55, 56, 57, 58 and 59.
Thus, the maximum score of topper = 65 + (10 + 9 + 8 + 7) = 65 + 44 = 99.

Thus, the correct option is C.

Yes, I see your point -- I'm not sure where this question is from, but the wording is awful, and the question is not well-constructed, so I'd just ignore this problem. There are enough official Stats questions that test maximization and minimization to practice from.

I am surprised that given the volume of visitors to this problem, nobody raised the concern that I highlighted. But thank you once again for your prompt response as always, IanStewart. You are incredibly helpful and make this platform a wonderful place for us students.

If the question were reworded to say "top 5 scores" rather than "top 5 students" it might eliminate the ambiguity.

Maximizing the top value suggests minimizing every other value, consistent with constraints.

The highest value of the bottom 5 places a floor on the minimum value for the top 5, so we would like to minimize that value.

Since we know that the average for the bottom 5 is 55, any departure below that average for any of the lower numbers will have to be made up in the higher numbers, increasing the highest value, not what we want.

So all of the bottom 5 have to be 55.

So now we have the floor on the top 5 and we can proceed to minimize them.

The least value of the top 5 can also be 55, no constraint there.

Since the other 3 to be minimized are to be distinct they can be 56 57 58.

So 55 56 57 and 58 are possible numbers to be subtracted from 325 to maximize the highest number as long as that doesn't make the highest number>100.

The subtraction yields 99, so this complies.

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