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Three people each took 5 tests. If the ranges of their score

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

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

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New post 25 Jul 2017, 09:43
Is the question worded properly?I am not able to understand it
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Re: Three people each took 5 tests. If the ranges of their score  [#permalink]

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New post 26 Jul 2017, 09:48
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Anazeer wrote:
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.

Does this help?

I have given the solution here: https://gmatclub.com/forum/three-people ... l#p1212587
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Re: Three people each took 5 tests. If the ranges of their score  [#permalink]

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New post 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

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

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New post 04 Jan 2018, 07:22
Bunuel wrote:
GMATPASSION wrote:
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?

A. 17
B. 28
C. 35
D. 45
E. 80

Min possible range. That means the lowest possible difference in total 15 values.

0 0 0 0 17
0 0 0 0 28
0 0 0 0 35

Minimum possible range is 35. Oh got the trick.

But my question is If I am thrown a question like this in the test I might panic & try many different kind of values. Is there a particular strategy or pattern for this type of questions.


Try to look at it as overlapping sets problem:
# of people in group A is 17;
# of people in group B is 28;
# of people in group C is 35;

What is the minimum # of total people possible in all 3 groups? Clearly if two smaller groups A and B are subsets of bigger group C (so if all people who are in A are also in C and all people who are in B are also in C), then total # of people in all 3 groups will be 35. Minimum # of total people can not possibly be less than 35 since there are already 35 people in group C.

Answer: C.

Hope it's clear.

P.S. Notice that max range for the original question is not limited when the max # of people in all 3 groups for revised question is 17+28+35 (in case there is 0 overlap between the 3 groups).


Sorry Bunuel but I am still not convinced by this explanation..... for example if you have the following votes:

1 1 1 1 18
1 1 1 1 29
4 4 4 4 39

You would have range 35 for third group, but the range of all three groups would be 39-1= 38 > 35 ?
what am I missing?
Thanks
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Re: Three people each took 5 tests. If the ranges of their score  [#permalink]

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New post 04 Jan 2018, 07:40
teone83 wrote:
Bunuel wrote:
GMATPASSION wrote:
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?

A. 17
B. 28
C. 35
D. 45
E. 80

Min possible range. That means the lowest possible difference in total 15 values.

0 0 0 0 17
0 0 0 0 28
0 0 0 0 35

Minimum possible range is 35. Oh got the trick.

But my question is If I am thrown a question like this in the test I might panic & try many different kind of values. Is there a particular strategy or pattern for this type of questions.


Try to look at it as overlapping sets problem:
# of people in group A is 17;
# of people in group B is 28;
# of people in group C is 35;

What is the minimum # of total people possible in all 3 groups? Clearly if two smaller groups A and B are subsets of bigger group C (so if all people who are in A are also in C and all people who are in B are also in C), then total # of people in all 3 groups will be 35. Minimum # of total people can not possibly be less than 35 since there are already 35 people in group C.

Answer: C.

Hope it's clear.

P.S. Notice that max range for the original question is not limited when the max # of people in all 3 groups for revised question is 17+28+35 (in case there is 0 overlap between the 3 groups).


Sorry Bunuel but I am still not convinced by this explanation..... for example if you have the following votes:

1 1 1 1 18
1 1 1 1 29
4 4 4 4 39

You would have range 35 for third group, but the range of all three groups would be 39-1= 38 > 35 ?
what am I missing?
Thanks


The question asks: what is the MINIMUM possible range in scores of the three test-takers? The range could be 38, or 56, or 119 (or any other number for certain conditions)... but it CANNOT be less than 35, so the MINIMUM possible range is 35.
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Re: Three people each took 5 tests. If the ranges of their score &nbs [#permalink] 04 Jan 2018, 07:40

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