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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]

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New post 10 Oct 2012, 19:00
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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, 04:38, 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]

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New post 11 Oct 2012, 03:13
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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]

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New post 29 Dec 2013, 01:52
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]

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New post 29 Dec 2013, 02:29
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]

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Re: 97 students take part in a test and the median score is 85. [#permalink]

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New post 24 Aug 2015, 15:28
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.


My solution process:

Step 1. Rephrase the question: The question is testing a simple concept, but the GMAC muddied the waters with convoluted statements and large #s. Therefore, I changed 'n' to 7 (see graphic below).

Step 2. Analyze the type of question: 'Must be true' ... Subsequently, I need to test the validity of the statements.
Attachments

Stats and Sets Prob.png
Stats and Sets Prob.png [ 19.67 KiB | Viewed 566 times ]

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Re: 97 students take part in a test and the median score is 85. [#permalink]

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New post 24 Aug 2015, 22:25
Expert's post
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.


Takeaway: Whenever you are given the median of a set and you need to consider cases of what the other numbers could be, never forget to take the case where all numbers are equal to the median.
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Re: 97 students take part in a test and the median score is 85. [#permalink]

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New post 23 Mar 2016, 19:08
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.


median is 85. it means 48 scored up to 85, INCLUSIVE. the 49th scored 85, and 48 scored at least 85 and more.

1. YES, at least 49 scored at least 85 or more. this one we know for SURE, since the 49th person in the middle scored 85, and there are 48 more people with either 85 or MORE. so I is true. we can eliminate B and C.
2. NO, even if everyone got a different score, there are 48 people who scored below 85. since the middle person, 49th one scored 49, and the rest 48 scored 85 or more, this case is never true. D eliminated.
3. at most 49 students got 85. this is a tempting one but NO. suppose all 97 students got 85. the median is still 85, but the statement is not true. E is eliminated, and only A stands.
Re: 97 students take part in a test and the median score is 85.   [#permalink] 23 Mar 2016, 19:08
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97 students take part in a test and the median score is 85.

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