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.

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

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KarishmaB

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21 Feb 2022, 23:21

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him0559

KarishmaB
Cant there be negative marking in case of calculating max range

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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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.

Bunuel

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13 Jan 2026, 10:59

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Goldenfuture

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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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