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97 students take part in a test and the median score is 85.

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97 students take part in a test and the median score is 85. [#permalink] New post 10 Oct 2012, 18:00
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36% (02:14) correct 64% (01:15) wrong based on 61 sessions
97 students take part in a test and the median score is 85. Which of the following descriptions must be correct?

I. At least 49 students’ score are equal to or more than 85.
II. At least 49 students’ score are less than 85.
III. At most 49 students’ score are equal to or more than 85.

A. I
B. II
C. III
D. I & II
E. I & III

Need help since I don't agree with the answ.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 29 Dec 2013, 03:38, edited 1 time in total.
Edited the OA.
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Re: 97 students take part in a test and the median score is 85. [#permalink] New post 11 Oct 2012, 02:13
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aeros232 wrote:
97 students take part in a test and the median score is 85. Which of the following descriptions must be correct?

I. At least 49 students’ score are equal to or more than 85.
II. At least 49 students’ score are less than 85.
III. At most 49 students’ score are equal to or more than 85.

A. I
B. II
C. III
D. I & II
E. I & III

Need help since I don't agree with the answ.


You are right, the correct answer is not E.
If we order the scores increasingly, then on the 49th place we have the score of 85. There must be 48 scores (those on the right of the 85 score) greater or equal to 85. So, I is necessarily correct.
The scores on the left of the 49th place, all have to be equal or less than 85. Since we can have the extreme case of all the scores 85, neither II, nor III is correct. The question asks for descriptions that "must be correct".

Answer A.
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Re: 97 students take part in a test and the median score is 85. [#permalink] New post 29 Dec 2013, 00:52
I agree with the OA. We have exactly 49 students’ score are equal to or more than 85 and I & III must be true. With I, we cannot have 48 students’ score are equal to or more than 85 and with III, we cannot have 50 students’ score are equal to or more than 85. I & III must be true in this case.
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Re: 97 students take part in a test and the median score is 85. [#permalink] New post 29 Dec 2013, 01:29
AnChu wrote:
I agree with the OA. We have exactly 49 students’ score are equal to or more than 85 and I & III must be true. With I, we cannot have 48 students’ score are equal to or more than 85 and with III, we cannot have 50 students’ score are equal to or more than 85. I & III must be true in this case.


Hello An

Evajager is correct, A is the answer. OA can't be E.
Let see an example:
Student 1: 50
Student 2: 51
Student 3: 51
...
...
Student 47: 84
Student 48: 85
Student 49: 85
Student 50: 85

Student 51: 86
....
....
Student 97: 90

Median is still 85
Clearly, we have 50 students who have test score higher than 85 --> We can't say "At most 49 students’ score are equal to or more than 85". Thus, E is not a "must be true" answer. Only A is correct.

Hope it helps.
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Re: 97 students take part in a test and the median score is 85.   [#permalink] 29 Dec 2013, 01:29
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