A group of students visit a book fair and each purchased

Question

A group of students visit a book fair and each purchased some books. What is the median number of books that the students purchased at the book fair?

(1) 35% of the students purchased at least 10 books
(2) 25% of the students purchased no more than 8 books

Fistail · Answer

C. seems i saw this question earlier. median = 9.

Syu · Answer

This is how I solved it. I hope it's right and hope there is an easier way to solve it.

(1) Not sufficient - Does not tell us how many books the remaining 40% has.

(2) Not sufficient - Does not tell us how many books the remaining 40% has.
 
(1) & (2) combined - Sufficient.

Say there are 20 students in total. Then,

35% 7 students 10 books (at least 10 books)
25% 5 students 8 books (8 or less books)
40% 8 students 9 books (9 books because 9 is between 10 and 8)
---------------------------------
100% 20 students
===================

If we list the above in an order:

 # of books
1 - 8
2 - 8
3 - 8
4 - 8
5 - 8

6 - 9
7 - 9
8 - 9
9 - 9
10 - 9
11 - 9
12 - 9 
13 - 9

14 - 10 
15 - 10
16- 10
17- 10
18- 10
19- 10
20- 10

So, from the above list, the mdian is:
(10th + 11th) / 2 = (9+9)/2 = 9

gowani · Answer

Syu: why do you assume that when it says 35% of students pick atleast 10 books that it is 10? Can they not pick 50, 100, or more books?

Syu · Answer

Hi gowani,

For the 35%, you can assume any number greater than 9. If you use any number greater than 9 but other than 10 (say 50, 100 whatever number), it does not change the fact that 9 is still the median (mid point in a series of numbers). For example,

# of books 
1 - 8 
2 - 8 
3 - 8 
4 - 8 
5 - 8 

6 - 9 
7 - 9 
8 - 9 
9 - 9 
10 - 9 
11 - 9 
12 - 9 
13 - 9 

14 - 50 
15 - 51 
16- 72
17- 78 
18- 88 
19- 99 
20- 10000

Also, the same logic applies for 8 books for the 25%.

Path · Answer

E?

We need # for 50%.
1. only 35% that too lower boundry is given. INSUFF

2. # of only 25% students is given INSUFF

Good question and nice explanaiton by Sue

gowani · Answer

don't know why my post didn't go through but thanks for the clarification Syu. I was confusing 'mean' with 'median'

A group of students visit a book fair and each purchased

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