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Re: Three people each took 5 tests. If the ranges of their score [#permalink]

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22 Aug 2016, 10:55

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Re: Three people each took 5 tests. If the ranges of their score [#permalink]

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07 May 2017, 07:13

VeritasPrepKarishma wrote:

shankar245 wrote:

Hi Bunuel/Karihsma,

Can you please may be explain in a bit more detail the minimum part. I'm stuck with question of possibilities, I mean what if the first set had this value or that value.

thanks

The minimum range of the entire group will be the maximum range of individuals. Say there are 3 people: Anna - 30, 38, 45, 46, 47 - Range 17 Beth - 20, 29, 36, 39, 48 - Range 28 Candi - 20, 25, 39, 49, 55 - Range 35

So Candi has 2 scores such that they have a difference of 35 between them (the smallest and the greatest scores). When we put everyone's scores together and try to find the range, these two scores will still be there. There is a difference of 35 between them and that will stay. So no matter what, the range will be at least 35. In this case the lowest score out of all is 20 and highest is 55 so the range will be 35.

It could be more as well. E.g.

Anna - 30, 38, 45, 46, 47 - Range 17 Beth - 10, 19, 26, 29, 38 - Range 28 Candi - 20, 25, 39, 49, 55 - Range 35

Now taking all scores together, lowest score is 10 and highest is 55 so range becomes 45.

It can keep increasing in this way.

I'm trying to understand this question and the closest I can get to understanding is your answer. However, the original question does not tell us what their individual scores were. It only gives us ranges. Is your explanation still valid if their scores were:

Anna: 6, 12, 14, 16, 23 - range 17 Beth: 8, 10, 12, 14, 36 - range 28 Candi: 10, 12, 14, 20, 45 - range 35

Wouldn't now the minimum range be from 6-45, which is 39? The question tells us the ranges, it seems to me that everyone just assumes that Anna's lowest score was higher than Beth's and Candi's lowest score and that Anna's highest score is also lower than Beth's and Candi's (so that her scores fall right in the middle of the other two's scores and so on).

Can you please may be explain in a bit more detail the minimum part. I'm stuck with question of possibilities, I mean what if the first set had this value or that value.

thanks

The minimum range of the entire group will be the maximum range of individuals. Say there are 3 people: Anna - 30, 38, 45, 46, 47 - Range 17 Beth - 20, 29, 36, 39, 48 - Range 28 Candi - 20, 25, 39, 49, 55 - Range 35

So Candi has 2 scores such that they have a difference of 35 between them (the smallest and the greatest scores). When we put everyone's scores together and try to find the range, these two scores will still be there. There is a difference of 35 between them and that will stay. So no matter what, the range will be at least 35. In this case the lowest score out of all is 20 and highest is 55 so the range will be 35.

It could be more as well. E.g.

Anna - 30, 38, 45, 46, 47 - Range 17 Beth - 10, 19, 26, 29, 38 - Range 28 Candi - 20, 25, 39, 49, 55 - Range 35

Now taking all scores together, lowest score is 10 and highest is 55 so range becomes 45.

It can keep increasing in this way.

I'm trying to understand this question and the closest I can get to understanding is your answer. However, the original question does not tell us what their individual scores were. It only gives us ranges. Is your explanation still valid if their scores were:

Anna: 6, 12, 14, 16, 23 - range 17 Beth: 8, 10, 12, 14, 36 - range 28 Candi: 10, 12, 14, 20, 45 - range 35

Wouldn't now the minimum range be from 6-45, which is 39? The question tells us the ranges, it seems to me that everyone just assumes that Anna's lowest score was higher than Beth's and Candi's lowest score and that Anna's highest score is also lower than Beth's and Candi's (so that her scores fall right in the middle of the other two's scores and so on).

Thank you!

Yes, you are right that in this case the range will be 39. But note that we are looking for the minimum possible range. Is it possible to reduce the range? Yes. Try to make it as small as possible. Make Anna's and Beth's lowest scores higher than Candi's lowest score and make their highest scores lower than Candi's highest score. That ways, you can reduce the range of all scores to Candi's range.
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Re: Three people each took 5 tests. If the ranges of their score [#permalink]

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26 May 2017, 15:46

fameatop wrote:

Hey bunuel, I am able to get the analogy but I still can't apply that analogy to this case. Kindly explain once more You said "The main point is that the minimum possible range of the three test-takers can no way be less than the largest range of the three test-takers, which is 35." If the one of the possible distribution of marks is mentioned below - then the minimum possible range in scores of the three test-takers should be 7-0 = 7. 17 17 17 17 34 7 7 7 7 35 0 0 0 0 35

Thanks in advance

A small note to avoid that common issue is by taking few seconds to think about the question, I had the same misunderstanding at the beginning. By definition range is max - min and not difference between any two numbers in the set. For any range related question, it is better to lay down all numbers in increasing order. So the minimum range we can acquire is if all 3 sets are nested, which results with the biggest range of all three sets = 35.

Is the question worded properly?I am not able to understand it

Yes, the wording is fine. "range" for 5 test scores would be (Max score - Min score).

Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 28 and 35, what is the minimum possible range in scores of the three test-takers?

Range for person 1 was 17. So he tool 5 tests and got 5 scores. If Max is his maximum score of the 5 and Min is his minimum score of the 5, Max - Min = 17. Similarly, for the other two, Max - Min is 28 and 35 respectively.

So now we need the minimum possible range of all scores of all three test takers. So we have 15 test scores and we need the minimum value possible for their range.

Re: Three people each took 5 tests. If the ranges of their score [#permalink]

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09 Aug 2017, 01:28

Here is what I did on this one -> Since the range of set three is 35 that means when we combine the test scores => Those two data elements would prevail. Hence the minimum range would be 35

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