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24 Mar 2021, 01:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
63% (01:07) correct
37%
(01:14)
wrong
based on 148
sessions
History
Date
Time
Result
Not Attempted Yet
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.
(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.
25 Mar 2021, 01:15
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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. 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:
Discussed here: https://gmatclub.com/forum/what-is-the- ... 31892.html
Similar question to practice: https://gmatclub.com/forum/what-is-the- ... 54875.html
Hope this helps.
General Discussion
24 Mar 2021, 01:59
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(1) Exactly 35% of the students in the class purchased two or fewer books.
This gives us information about lower values range.
If 100 students are there..,35 of them have 2 or 1 or 0 books.
Insufficient
(2) Exactly 25% of the students in the class purchased four or more books.
This gives information regarding higher range of values.
Considering 100 students again, 35 students have >=4 books..
Insufficient
Combining both,
0------25------65-----100
65-25 = 40 students have 3 books,
51st student has 3 books, which is the median.
IMO C
Posted from my mobile device
This gives us information about lower values range.
If 100 students are there..,35 of them have 2 or 1 or 0 books.
Insufficient
(2) Exactly 25% of the students in the class purchased four or more books.
This gives information regarding higher range of values.
Considering 100 students again, 35 students have >=4 books..
Insufficient
Combining both,
0------25------65-----100
65-25 = 40 students have 3 books,
51st student has 3 books, which is the median.
IMO C
Posted from my mobile device
