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A test is scored out of 100 and the scores are divided into

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A test is scored out of 100 and the scores are divided into [#permalink] New post 16 Jun 2017, 01:18
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A test is scored out of 100 and the scores are divided into five quintile groups. Students are not told their scores, but only their quintile group.


Quantity A
Quantity B
The scores of two students in the bottom quintile group,
chosen at random and added together
The score of a student in the top quintile group,
chosen at random


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

Last edited by Carcass on 16 Jun 2017, 06:32, edited 1 time in total.
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Re: A test is scored out of 100 and the scores are divided into [#permalink] New post 16 Jun 2017, 06:33
Expert's post
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Re: A test is scored out of 100 and the scores are divided into [#permalink] New post 16 Jun 2017, 17:04
Expert's post
Explanation

Let us assume there are 10 students (one for each quantile)

So let the scores be:
1, 1, 2, 2, 3, 3, 4, 4, 5, 5

In this case, adding up two lowest quintile students would be 1 + 1 = 2, which is less than 5, the score of a top quintile student.


So let the scores be:
10, 10, 11, 11, 12, 12, 13, 13, 14, 14

In this case, adding up two lowest quintile students would be 10 + 10 = 20, which is greater than 14, the score of a top quintile student.

Thus, you cannot determine which quantity is larger.
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Re: A test is scored out of 100 and the scores are divided into   [#permalink] 16 Jun 2017, 17:04
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