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

Another approach is to think of range questions on the number line.

5 numbers have range of 17 means the smallest number and the largest number have a diff of 17 between them. Place them like this on the number line

..................................S1..........(17).............L1..............

5 numbers have range of 28 means the smallest number and the largest number have a diff of 28 between them. Place them like this on the number line

..........................S2...............(28)........................L2..............


5 numbers have range of 35 means the smallest number and the largest number have a diff of 35 between them. Place them like this on the number line


....................S3..................................(35).............................L3..............

The minimum range will be when S1 and L1 and S2 and L2 lie in between S3 and L3. The range of 35 will stay no matter what.

...................S3.......S2.....S1..............................L1......L2.......L3..............

The maximum range, on the other hand, depends on the total range the scores can have. If the score is out of 100, the maximum range will be 100, if they are out of 1000, the maximum range is 1000 and so on.

For example: S1 may lie at 0 and L3 may lie at 100 etc

(0)S1...........................L1..........S2....................................L2..................................S3.......................................................L3(100)
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Consider this as an overlapping sets problem:

• The number of people in Group A is 17.
• The number of people in Group B is 28.
• The number of people in Group C is 35.

What is the minimum number of total people possible in all three groups? Clearly, if the two smaller groups A and B are subsets of the larger group C (meaning all people in A and all in B are also in C), then the total number of people across all three groups would be 35. The minimum total cannot possibly be less than 35, as there are already 35 people in group C.

Answer: C.

Hope it's clear.

P.S. Note that the maximum range for the original question is not limited, whereas the maximum number of people in all three groups for my revised question is 17 + 28 + 35, which occurs if there is zero overlap between the groups.
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Your example:
{17, 17, 17, 17, 34} --> range=17;
{7, 7, 7, 7, 35} --> range=28;
{0, 0, 0, 0, 35} --> range=35.

All 15 scores: {0, 0, 0, 0, 7, 7, 7, 7, 17, 17, 17, 17, 34, 35, 35} --> range=35-0=35, not 7.

Hope it's clear.
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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.
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Just to clarify the approach here.

It may look like this and would be correct, or?

17 17 17 17 34
7 7 7 7 35
0 0 0 0 35

Would be the same minimum range?!?

Yes. 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.
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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

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.


Range = Max-Min
=35-0
=35 ?

Am i right?

This problem took me 27 seconds, according to the timer. I took note of my own thinking while I was solving this problem.

I visualized three intervals of length 17, 28, and 35, respectively. Then I felt, intuitively, that the intervals were independent, so I visualized the smaller intervals as covered by the larger one. So I felt that the answer should be the greatest of the numbers. I looked at the numbers again and chose 35. Then I spent a few seconds making sure that I was answering the right question since it seemed too easy.

On an actual exam I would've double-checked myself by coming up with an actual example of fifteen scores, as explained above - provided, of course, that I had enough time.

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

Hi Bunuel - Great explanation. Do we have similar kind of questions for practice?

Yes, check all min/max questions here: search.php?search_id=tag&tag_id=63

Hope it helps.
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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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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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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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KarishmaB
Cant there be negative marking in case of calculating max range