Bunuel
What is the median number of books purchased per student in a certain class?
(1) Exactly 35% of the students in the class purchased two or fewer books.
(2) Exactly 25% of the students in the class purchased four or more books.
Project DS Butler Data Sufficiency (DS3)
For DS butler Questions Click Here What is the median number of books purchased per student in a certain class?(1) Exactly 35% of the students in the class purchased two
or fewer books. Not sufficient on its own.
(2) Exactly 25% of the students in the class purchased four
or more books. Not sufficient on its own.
(1)+(2) Since 35% of of the students purchased 2
or fewer (\(\leq{2}\)) books and 25% of the students purchased 4
or more (\(\geq{4}\)) books, then 100%-(25%+35%)=40% of the students purchased
exactly 3 books. So, the median number of books purchased per student is 3. Sufficient.
Answer: C.
To elaborate more: consider there are 100 students: \(\{s_1, \ s_2, \ ... , \ s_{100}\}\). The values of \(s_1\) to \(s_{35}\) will be 0, 1, or 2; the values of \(s_{36}\) to \(s_{75}\) will be exactly 3; the values of \(s_{76}\) to \(s_{100}\) will be 4 or more. \(Median=\frac{s_{50}+s_{51}}{2}=\frac{3+3}{2}=3\).
For example list can be:
\(\{2, \ 2, \ 2, \ ..., \ (s_{35}=2), \ (s_{36}=3), \ 3, \ ..., \ (s_{75}=3), \ (s_{76}=4), \ 4, \ ..., \ (s_{100}=4)\}\);
OR:
\(\{0, \ 0, \ 1, \ 1, \ 1, \ 2, \ 2, \ ..., \ (s_{35}=2), \ (s_{36}=3), \ 3, \ ..., \ (s_{75}=3), \ (s_{76}=4), \ 5, \ 7, \ 27, \ ..., \ (s_{100}=10000)\}\) (of course there are a lot of other breakdowns).
In any case median=3.
The above question is almost exact copy of the following question from
OG:
Quote:
What is the median number of employees assigned per project for the projects at Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project.
(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project
Discussed here:
https://gmatclub.com/forum/what-is-the- ... 31892.htmlSimilar question to practice:
https://gmatclub.com/forum/what-is-the- ... 54875.htmlHope this helps.