Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 28 May 2009
Posts: 156
Location: United States
Concentration: Strategy, General Management
GMAT Date: 03222013
GPA: 3.57
WE: Information Technology (Consulting)

In a certain industry, production index x is directly propor [#permalink]
Show Tags
05 Feb 2013, 18:25
1
This post received KUDOS
3
This post was BOOKMARKED
Question Stats:
41% (02:39) correct
59% (01:48) wrong based on 111 sessions
HideShow timer Statistics
In a certain industry, production index x is directly proportional to the square of efficiency index y, and indirectly proportional to investment index z. If a business in this industry halves its investment index, which of the following is closest to the percent change in the business’s efficiency index required to keep the production index the same? (A) 100% increase (B) 50% increase (C) 30% increase (D) 30% decrease (E) 50% decrease Source: Gmat Hacks 1800
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
New to GMAT Club? Start here
Kindle Flashcards  Quant (Official Gmat Club, miguemick's Quant topics), and Verbal (Official Gmat Club)  in Kindle (azw3) format



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7438
Location: Pune, India

Re: In a certain industry, production index x is directly [#permalink]
Show Tags
05 Feb 2013, 21:50
2
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
megafan wrote: In a certain industry, production index x is directly proportional to the square of efficiency index y, and indirectly proportional to investment index z. If a business in this industry halves its investment index, which of the following is closest to the percent change in the business’s efficiency index required to keep the production index the same?
(A) 100% increase
(B) 50% increase
(C) 30% increase
(D) 30% decrease
(E) 50% decrease
Source: Gmat Hacks 1800 I am discussing direct and inverse variation on my blog nowadays. http://www.veritasprep.com/blog/2013/01 ... directly/http://www.veritasprep.com/blog/2013/02 ... inversely/Next post will discuss a similar question using both. I have tried to show every step here to avoid confusion but on the blog, I am going to be more direct. By the way, the question is not very GMATlike. \(x = ky^2\) (x is directly proportional to y^2. k is any constant) \(xz = k\) (I am assuming that indirectly is actually inversely proportional) Both together, \(\frac{xz}{y^2} = k\) (Assume z to be constant, you get x is directly proportional to y^2. Assume y to be constant, you get x is inversely proportional to z) \(\frac{x_1*z_1}{(y_1)^2} = \frac{x_2*z_2}{(y_2)^2}\) Given that \(z_2 = (\frac{1}{2})z_1\) and that \(x_1\)should be equal to \(x_2\). What is the relation between \(y_1\) and \(y_2\)? \(\frac{x_1*z_1}{(y_1)^2} = \frac{x_1*(1/2)z_1}{(y_2)^2}\) \((y_2)^2 = \frac{(y_1)^2}{2}\) \(y_2 = \frac{y_1}{\sqrt{2}}\) \(y_2 = \frac{y_1*\sqrt{2}}{2}\) \(y_2 = 0.7*y_1\) (A decrease of 30%) Answer (D)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1382
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: In a certain industry, production index x is directly [#permalink]
Show Tags
05 Feb 2013, 21:58
megafan wrote: In a certain industry, production index x is directly proportional to the square of efficiency index y, and indirectly proportional to investment index z. If a business in this industry halves its investment index, which of the following is closest to the percent change in the business’s efficiency index required to keep the production index the same?
(A) 100% increase
(B) 50% increase
(C) 30% increase
(D) 30% decrease
(E) 50% decrease
Source: Gmat Hacks 1800 The entire expression can be written in the form \(x=k*y^2/z\). When z is halved, the expression becomes \(x=2k*y^2/z\). In order to make this expression equal to its initial form, we need to divide this expression by 2. This can be done by reducing \(y\) to \(y/\sqrt{2}\). Therefore percent change= \(yy/1.414\)=>\(0.414y/1.414\). This is almost equal to 30%. Hope this helps.
_________________
Prepositional Phrases ClarifiedElimination of BEING Absolute Phrases Clarified Rules For Posting www.UnivScholarships.com



Math Expert
Joined: 02 Sep 2009
Posts: 39589

Re: In a certain industry, production index x is directly propor [#permalink]
Show Tags
06 Feb 2013, 00:34
megafan wrote: In a certain industry, production index x is directly proportional to the square of efficiency index y, and indirectly proportional to investment index z. If a business in this industry halves its investment index, which of the following is closest to the percent change in the business’s efficiency index required to keep the production index the same?
(A) 100% increase
(B) 50% increase
(C) 30% increase
(D) 30% decrease
(E) 50% decrease
Source: Gmat Hacks 1800 Original question from GMAT Prep: Quote: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
A. 100% decrease B. 50% decrease C. 40% decrease D. 40% increase E. 50% increase Discussed here: therateofacertainchemicalreactionisdirectly90119.html (I guess many Gmat Hacks questions are just reworded problems from GMAT Prep).
_________________
New to the Math Forum? Please read this: 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



Moderator
Joined: 01 Sep 2010
Posts: 3211

Re: In a certain industry, production index x is directly propor [#permalink]
Show Tags
06 Feb 2013, 09:50
Bunuel wrote: megafan wrote: In a certain industry, production index x is directly proportional to the square of efficiency index y, and indirectly proportional to investment index z. If a business in this industry halves its investment index, which of the following is closest to the percent change in the business’s efficiency index required to keep the production index the same?
(A) 100% increase
(B) 50% increase
(C) 30% increase
(D) 30% decrease
(E) 50% decrease
Source: Gmat Hacks 1800 Original question from GMAT Prep: Quote: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
A. 100% decrease B. 50% decrease C. 40% decrease D. 40% increase E. 50% increase Discussed here: therateofacertainchemicalreactionisdirectly90119.html (I guess many Gmat Hacks questions are just reworded problems from GMAT Prep). you are correct ........
_________________
COLLECTION OF QUESTIONS AND RESOURCES Quant: 1. ALL GMATPrep questions Quant/Verbal 2. Bunuel Signature Collection  The Next Generation 3. Bunuel Signature Collection ALLINONE WITH SOLUTIONS 4. Veritas Prep Blog PDF Version 5. MGMAT Study Hall Thursdays with Ron Quant Videos Verbal:1. Verbal question bank and directories by Carcass 2. MGMAT Study Hall Thursdays with Ron Verbal Videos 3. Critical Reasoning_Oldy but goldy question banks 4. Sentence Correction_Oldy but goldy question banks 5. Readingcomprehension_Oldy but goldy question banks



Manager
Joined: 28 Feb 2012
Posts: 115
Concentration: Strategy, International Business
GPA: 3.9
WE: Marketing (Other)

Re: In a certain industry, production index x is directly propor [#permalink]
Show Tags
06 Feb 2013, 23:44
1
This post received KUDOS
Normally i plug numbers to see what happens if certain change applies, i am not sure whether i am doing correct but please comment if anything wrong in my method: Let say the efficiency index y=10 and investment index=1, so, per question terms, production index x=y^2/x=10^2/1=100; now we change the investment index to half (i assumed that it has been decreased to half since it is not clear in the question) and we have the following: 100=y^2/0.5=(y^2)*2=100 > y=\sqrt{50} > equals to about 7, then we can see that efficiency index should be reduced to approximately 30% (from 10 to 7). I hope that my way of thinking is correct.
_________________
If you found my post useful and/or interesting  you are welcome to give kudos!



Current Student
Joined: 24 Nov 2012
Posts: 176
Concentration: Sustainability, Entrepreneurship
WE: Business Development (Internet and New Media)

Re: In a certain industry, production index x is directly [#permalink]
Show Tags
21 Apr 2013, 01:59
Marcab wrote: The entire expression can be written in the form \(x=k*y^2/z\). When z is halved, the expression becomes \(x=2k*y^2/z\). In order to make this expression equal to its initial form, we need to divide this expression by 2. This can be done by reducing \(y\) to \(y/\sqrt{2}\). Therefore percent change= \(yy/1.414\)=>\(0.414y/1.414\). This is almost equal to 30%. Hope this helps. I used the same method but skipped the calculations since you know that since z is being halved y also has to decrease. There are only 2 options that decrease. If i plug in 50, the condition isn't met and hence 30 is the answer. You should be able to deduce this in less than 30 secs.
_________________
You've been walking the ocean's edge, holding up your robes to keep them dry. You must dive naked under, and deeper under, a thousand times deeper!  Rumi
http://www.manhattangmat.com/blog/index.php/author/cbermanmanhattanprepcom/  This is worth its weight in gold
Economist GMAT Test  730, Q50, V41 Aug 9th, 2013 Manhattan GMAT Test  670, Q45, V36 Aug 11th, 2013 Manhattan GMAT Test  680, Q47, V36 Aug 17th, 2013 GmatPrep CAT 1  770, Q50, V44 Aug 24th, 2013 Manhattan GMAT Test  690, Q45, V39 Aug 30th, 2013 Manhattan GMAT Test  710, Q48, V39 Sep 13th, 2013 GmatPrep CAT 2  740, Q49, V41 Oct 6th, 2013
GMAT  770, Q50, V44, Oct 7th, 2013 My Debrief  http://gmatclub.com/forum/fromtheashesthoushallrise770q50v44awa5ir162299.html#p1284542



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15918

Re: In a certain industry, production index x is directly propor [#permalink]
Show Tags
30 Jul 2014, 02:25
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



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15918

Re: In a certain industry, production index x is directly propor [#permalink]
Show Tags
18 Sep 2016, 17:40
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: In a certain industry, production index x is directly propor
[#permalink]
18 Sep 2016, 17:40







