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50 students of a certain class took a test. How many of them got a sco

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Bunuel
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50 students of a certain class took a test. How many of them got a sco [#permalink] New post   19 May 2021, 07:00
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50 students of a certain class took a test. How many of them got a score less than 82?

(1) The average score is 82.

(2) The median score is 82.
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E
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50 students of a certain class took a test. How many of them got a sco [#permalink] New post   22 May 2021, 06:51
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Bunuel wrote:
50 students of a certain class took a test. How many of them got a score less than 82?

(1) The average score is 82.

(2) The median score is 82.


1) Average score of 50 students = 82
Total score of 50 students = 410
Doesn't help - Insufficient!

2)Median = 82
Which means \(\frac{25th student's score + 26th student's score}{2} = 82\)
25th student's score + 26th student's score= 164
Case1:
25th student's score = 26th student's score = 82. In this case, number of students who got a score of less than 82 = 24
Case2:
25th student's score = 81, 26th's score = 83. In this case, number of students who got a score of less than 82 = 25
Insufficient!
Even after combining, it is insufficient. Hence, (E)
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Re: 50 students of a certain class took a test. How many of them got a sco [#permalink] New post   21 Jul 2021, 05:05
Why isn't this one's answer C? When we combine both the statements, we learn that mean = median. And we know that mean and median are equal only when all the values in the set are equal. So if we combine statements 1 and 2, we get our answer, that nobody scored less than 82 since all of them scored exactly 82. So answer should be C.
Am I wrong somewhere? Bunuel, would greatly appreciate your insights. Thanks in advance!
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Re: 50 students of a certain class took a test. How many of them got a sco [#permalink] New post   21 Jul 2021, 07:34
RiyaJain69 wrote:
Why isn't this one's answer C? When we combine both the statements, we learn that mean = median. And we know that mean and median are equal only when all the values in the set are equal. So if we combine statements 1 and 2, we get our answer, that nobody scored less than 82 since all of them scored exactly 82. So answer should be C.
Am I wrong somewhere? Bunuel, would greatly appreciate your insights. Thanks in advance!


Hi RiyaJain69, though the question is not directed at me. Let me still try to answer this.

If mean = median, it means that the distribution is symmetric. The set could have:
1)Consecutive numbers
2)Same numbers
Hence, the answer is (E)!
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Re: 50 students of a certain class took a test. How many of them got a sco [#permalink] New post   21 Jul 2021, 07:44
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Showmeyaa wrote:
If mean = median, it means that the distribution is symmetric.


That's actually not quite right. It's true (and useful to know) that if a distribution is symmetric, then the mean and median are always equal. So for example, in any equally spaced set (1, 3, 5, 7, 9, say) the mean and median are equal, and in any other symmetric list (1, 1, 2, 8, 9, 9, say, or when every element is the same) the mean and median will also be equal. But the mean and median can be equal in all kinds of other situations as well. So in this set, which is not symmetric:

0, 2, 10, 11, 27

the mean and median are both 10.
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Re: 50 students of a certain class took a test. How many of them [#permalink] New post   31 Mar 2022, 03:46
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Re: 50 students of a certain class took a test. How many of them [#permalink]
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