Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49417

For a certain set, the value range of its members is 112.4. A new set
[#permalink]
Show Tags
10 Jul 2015, 02:26
Question Stats:
72% (01:27) correct 28% (01:06) wrong based on 148 sessions
HideShow timer Statistics



Current Student
Joined: 20 Mar 2014
Posts: 2638
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: For a certain set, the value range of its members is 112.4. A new set
[#permalink]
Show Tags
10 Jul 2015, 04:55
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 = 41=3 and if I subtract 'a' from each number : {1a,2a,3a,4a} range = 4a  (1a) = 4a1+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



SVP
Joined: 08 Jul 2010
Posts: 2347
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: For a certain set, the value range of its members is 112.4. A new set
[#permalink]
Show Tags
10 Jul 2015, 05:18
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 term3) 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 51 = 4 Range of {3, 6, 9, 12, 15} is 153 = 12 which 3 times the previous range because new set has each term 3 times each term of previous setGiven: Range = 112.4 Step1: A new set is created in which 12 is subtracted from a member of the old setRange will not change as depicted in concept abovei.e. Even now, Range = 112.4 Step2: the result is divided by 4The range also gets divided by 4i.e. now, Range = 112.4/4 = 28.1Answer: Option B
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Math Expert
Joined: 02 Sep 2009
Posts: 49417

Re: For a certain set, the value range of its members is 112.4. A new set
[#permalink]
Show Tags
13 Jul 2015, 02:37
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 wellpracticed 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Current Student
Affiliations: Scrum Alliance
Joined: 09 Feb 2010
Posts: 81
Location: United States (MI)
Concentration: Strategy, General Management
GMAT 1: 600 Q48 V25 GMAT 2: 710 Q48 V38
WE: Information Technology (Retail)

Re: For a certain set, the value range of its members is 112.4. A new set
[#permalink]
Show Tags
14 Jul 2015, 08:58
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 {\(\frac{x12}{4},\frac{y12}{4},\frac{z12}{4}\)} The range of the new set is \(\frac{z12}{4}  \frac{x12}{4}\), 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.
_________________
kudos please



Manager
Joined: 01 Apr 2015
Posts: 54

For a certain set, the value range of its members is 112.4. A new set
[#permalink]
Show Tags
21 Jul 2015, 07:22
Range=maxmin=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: 50.122=28.1. Hence the correct answer is B



NonHuman User
Joined: 09 Sep 2013
Posts: 8161

Re: For a certain set, the value range of its members is 112.4. A new set
[#permalink]
Show Tags
04 Jul 2018, 13:33
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: For a certain set, the value range of its members is 112.4. A new set &nbs
[#permalink]
04 Jul 2018, 13:33






