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.

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?!?

Thanks Bunuel, always a great help.

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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I see no similarities between this problem (statistics) and overlapping sets problems.
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what is Maximum possible range is asked?
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Yes, there actually was no math to be applied here, except the concept of "range". The easiest way is simply to figure out how low could the lowest score among the 15 have been, and how high the highest one might have been.

Result is 35(max) - 0(min) = 35, answer C.

Thanks to anyone who clarified this problem.
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Andy

What would the answer be if it asked for maximum possible range?

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 17 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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