# Logic question

Peter Pan
This question is making me angry. I think I know the answer but I have some co-workers that disagree.

Q. Sally is the 50th best student in her class and the 50th worst. How many students are in her class?

A. 101, 100, 99, 50

I believe the anwser is 99

Staff Emeritus
Gold Member
i think the answer is 50

Peter Pan
I think 50 is the answer

Tell my how you came up with that. This is why I believe the answer is 99.

If sally is the 50th best student in her class, that means there are 49 student who are better. Also, if Sally is the 50th worst student, that means there are 49 that are worse than her

49 better + 49 worse + sally = 99

quartodeciman
Let's try something shorter. If Sally were 3rd best and also 3rd worst, the rankings would look like this:

best rank/worst rank/name

1st /5th /Cheryl
2nd /4th /Laura
3rd /3rd /Sally <---
4th /2nd /Anne
5th /1st /Betty

Note that 1st best simply means "the best" and 1st worst simply means "the worst".

There are 5, or 2(3)-1 class members. I don't think it makes any significant difference for 50th best and 50th worst. So, the number of members ought to be 2(50)-1 = 99, and you, Peter, are correct.

Of course, if some class members have equal rank, then more members are required.

Homework Helper
Well, you also need to make sure there are no ties for 50th

Peter Pan
Assume to ties

photon
1st /5th /Cheryl
2nd /4th /Laura
3rd /3rd /Sally <---
4th /2nd /Anne
5th /1st /Betty
Seems like the answer has to be 99. There are no ties, and Sally is 3rd best and 3rd worst out of five. There are not 6 people in the group, but five because a number has to be odd to have a middle integer. 3 is Sally's rank. 3x2-1=5. So, for Peter Pans's question: 50 is Sally's rank. 50x2-1=99
EDIT: When I subtract 1, I am subtracting Sally.

Staff Emeritus
Gold Member
well the way i worked it out is 50th best would mean 49 people in front of her were better, and 49 people in front of her were worse...so that's how i came up with a total of 50...but 99 also makes sense...

Mentat
Originally posted by Kerrie
well the way i worked it out is 50th best would mean 49 people in front of her were better, and 49 people in front of her were worse...so that's how i came up with a total of 50...but 99 also makes sense...

Yes, 49 people in front of her were better, but 50 plus 49 is 99.

stevenson
Simple

If she's the 50th best that would mean she's number 50 from the top.
If she's the 50th worst that would also mean she's the 50th from the
top. Both are saying the same exact thing but they are worded different, really simple. Thanks

Peter Pan
"If she's the 50th best that would mean she's number 50 from the top.
If she's the 50th worst that would also mean she's the 50th from the
top. Both are saying the same exact thing but they are worded different, really simple."

diverz
Theres no additional information to determine the number of students in Sally's class.

The statement you gave merely states that Sally is in the 50th position.

Peter Pan
Theres no additional information to determine the number of students in Sally's class.

I disagree. The question states that sally is both the 50th best and worst student in her class.

50th best implies that 49 students have done better.
50th worst implies that 49 students have done worst.

fffbone
The statement simply implies that there are 49 students better than sally and 49 students worse, so the minimum number of students in her class in 99. As there can be infinite many students having the same grade as her, there can be infinte many students in tie for the 50th place. Thus the number of students in her class can be any of the natural numbers that is greater than or equal to 99.