For a certain set, the value range of its members is 112.4. A new set

800score Official Solution:

A well-practiced student’s intuition should tell us that the new range will be 112.4/4 = 28.1. But to be rigorous about it:
Under the assumption that the range after the transformation will be the same for any set that has originally the range of 112.4, let the largest member of the old set be 0 and the smallest member be -112.4 . In the new set, the largest value will be (0 – 12)/4 and the smallest value will be (-112.4 – 12)/4. Thus, the range of the new set will be: (-12/4) – (-124.4 / 4) = -3 – (-31.1) = 31.1 – 3 = 28.1 . The correct answer is B.

The alternative method is the following:
Suppose the greatest and the least of the elements of the original set are G and s, thus giving the range = G – s = 112.4 .
Now after the transformation of subtracting 12 from each member and dividing the result by 4, the greatest and the least elements of the original set will be transformed into the greatest and the least elements of the new set. The range works out to be (G – 12)/4 – (s – 12)/4 which can be simplified: (G – s)/4 = 112.4 / 4 = 28.1 .

The correct answer is B.

Here is my approach to this question.

Let the set be {\(x,y,z\)}. Note, the number of elements in the set do not matter since the question only pertains to the range which is the difference between the first and the last element of the set.

Now the range of the above set is 112.4, which means that \(z - x = 112.4\)

Also, each member of the new set is the old member reduced by 12, and then divided by 4,

The new set becomes {\(\frac{x-12}{4},\frac{y-12}{4},\frac{z-12}{4}\)}

The range of the new set is \(\frac{z-12}{4} - \frac{x-12}{4}\), which simplifies to \(\frac{z - 12 - x + 12}{4}\), further simplifying to \(\frac{z - x}{4}\)

Which means the range of the old set is 4 times the range of the new set,

\(\frac{z - x}{4} = \frac{112.4}{4} = 28.1\)

Answer is B.

Range=max-min=112.4

It can easily calculated in 3 steps:

1) Consider max=212.4 & min=100 and one other number=150, just to make calculations easy.

2) Subtract 12 from each of the above and divide the result by 4.

3) Calculate the range again: 50.1-22=28.1. Hence the correct answer is B

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