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

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Math Expert
Joined: 02 Sep 2009
Posts: 51263
For a certain set, the value range of its members is 112.4. A new set  [#permalink]

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10 Jul 2015, 01:26
1
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00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:52) correct 29% (01:29) wrong based on 151 sessions

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For a certain set, the value range of its members is 112.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set?

A. 25.1
B. 28.1
C. 56.4
D. 98.4
E. 112.4

Kudos for a correct solution.

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Re: For a certain set, the value range of its members is 112.4. A new set  [#permalink]

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10 Jul 2015, 03:55
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Bunuel wrote:
For a certain set, the value range of its members is 112.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set?

A. 25.1
B. 28.1
C. 56.4
D. 98.4
E. 112.4

Kudos for a correct solution.

The given range of the original set = 12. For the new set we subtract 12 from a member ---> the range does not change (Example : Let the set be {1,2,3,4}, range = 4-1=3 and if I subtract 'a' from each number : {1-a,2-a,3-a,4-a} range = 4-a - (1-a) = 4-a-1+a = 3 = same range as before).

Range (original set)= $$R_O$$ = $$Max_O - Min_O$$
Thus the subtraction of 12 from the values will not have an effect. But the division by 4 will reduce the members of the set by 1/4th of their previous values and hence the new range = $$R_N$$ = $$Max_N - Min_N$$ = $$(Max_O /4) - (Min_O /4)$$ = $$1/4 (Max_O - Min_O) = 1/4 * (R_O)$$ = 1/4 * 112.4 = 28.1. Thus B is the correct answer
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Re: For a certain set, the value range of its members is 112.4. A new set  [#permalink]

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10 Jul 2015, 04:18
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Bunuel wrote:
For a certain set, the value range of its members is 112.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set?

A. 25.1
B. 28.1
C. 56.4
D. 98.4
E. 112.4

Kudos for a correct solution.

CONCEPT: 1) Range = The Highest term of the set - The Smallest terms of the set

2) The Range of a set doesn't change if a constant is added to/subtracted from each terms of the set
e.g.{1, 2, 3, 4, 5} will have same Range as {1+10, 2+10, 3+10, 4+10, 5+10}

Reason: The deviation remains same as before if the constant is added to/Subtracted from each term

3) The Range of a set Multiplies or gets divided if a constant is Multiplied with or divides respectively each terms of the set
e.g. Range of {1, 2, 3, 4, 5} is 5-1 = 4
Range of {3, 6, 9, 12, 15} is 15-3 = 12 which 3 times the previous range because new set has each term 3 times each term of previous set

Given: Range = 112.4

Step-1: A new set is created in which 12 is subtracted from a member of the old set
Range will not change as depicted in concept above
i.e. Even now, Range = 112.4

Step-2: the result is divided by 4
The range also gets divided by 4
i.e. now, Range = 112.4/4 = 28.1

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Re: For a certain set, the value range of its members is 112.4. A new set  [#permalink]

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13 Jul 2015, 01:37
Bunuel wrote:
For a certain set, the value range of its members is 112.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set?

A. 25.1
B. 28.1
C. 56.4
D. 98.4
E. 112.4

Kudos for a correct solution.

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 .

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Re: For a certain set, the value range of its members is 112.4. A new set  [#permalink]

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14 Jul 2015, 07:58
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,

$$\frac{z - x}{4} = \frac{112.4}{4} = 28.1$$

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

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21 Jul 2015, 06:22
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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Re: For a certain set, the value range of its members is 112.4. A new set  [#permalink]

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04 Jul 2018, 12:33
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Re: For a certain set, the value range of its members is 112.4. A new set &nbs [#permalink] 04 Jul 2018, 12:33
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