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KarishmaB
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Three people each took 5 tests. If the ranges of their score 21 Feb 2022, 23:21
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him0559
KarishmaB
Cant there be negative marking in case of calculating max range
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Where it will be relevant, the question will mention the scoring pattern (maximum, minimum scores possible, negative marking, the way negative marking is calculated etc).
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Three people each took 5 tests. If the ranges of their score 13 Jan 2026, 10:54
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explain this part: 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).
Bunuel


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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Bunuel
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Three people each took 5 tests. If the ranges of their score 13 Jan 2026, 10:59
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Goldenfuture
explain this part: 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).

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The point is simply this:

In the overlapping-sets example, the total has a clear maximum of 17 + 28 + 35 when there is no overlap.
In the original score-range problem, there is no such upper limit, because scores can be spread arbitrarily far apart on the number line.
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Three people each took 5 tests. If the ranges of their score 16 Jan 2026, 02:43
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Deconstructing the Question
Given ranges of scores for three people:
1. Person A: Range = 17
2. Person B: Range = 28
3. Person C: Range = 35

Target: Find the minimum possible range of the scores for the combined group.

Step 1: Understand the Constraint
The range of a dataset is defined as \(Max - Min\).
Let the set of all scores be \(S\).
Since Person C's scores are a subset of \(S\), and Person C has a range of 35, the set \(S\) must contain at least two values, \(x\) and \(y\), such that \(|x - y| = 35\).

Therefore, the range of the entire set \(S\) must be at least 35.
Mathematically: \(Range_{total} \ge \max(Range_A, Range_B, Range_C)\).

Step 2: Test for Minimum Possibility
To minimize the total range, we assume complete overlap of the score intervals.
Let's assign hypothetical scores to verify if a total range of 35 is possible:
- Person C scores: {0, ..., 35} -> Range is 35.
- Person B scores: {0, ..., 28} -> Range is 28. (Fits inside [0, 35])
- Person A scores: {0, ..., 17} -> Range is 17. (Fits inside [0, 35])

In this scenario:
Global Max = 35
Global Min = 0
Global Range = 35.

Thus, the minimum possible range is determined by the largest individual range.

Answer: C
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Three people each took 5 tests. If the ranges of their score 21 May 2026, 19:26
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Please help me understand:
Suppose Test Takes scores are
A-{0,0,0,0,17}
B-{0,0,0,0,28}
C-{35,35,35,35,70}

In this case, set of total scores are {0,0,0,0,0,0,0,0,17,28, 35,35,35, 35, 70} and the minimum range of total set would be |70-0|=70

Bunuel please help me straight my thinking!
Bunuel


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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Three people each took 5 tests. If the ranges of their score 21 May 2026, 21:36
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bishal128
Please help me understand:
Suppose Test Takes scores are
A-{0,0,0,0,17}
B-{0,0,0,0,28}
C-{35,35,35,35,70}

In this case, set of total scores are {0,0,0,0,0,0,0,0,17,28, 35,35,35, 35, 70} and the minimum range of total set would be |70-0|=70

Bunuel please help me straight my thinking!

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The question asks for “the minimum possible range,” and as shown in the solution on the previous pages, the minimum possible range is 35.
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Three people each took 5 tests. If the ranges of their score 30 May 2026, 01:57
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AMsac123
Is the question worded properly?I am not able to understand it
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I agree!!! If they had included "all" three test takers, I wouldn't have spent full 5 minutes just trying to understand the question. :(
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