Find all School-related info fast with the new School-Specific MBA Forum

It is currently 09 Jul 2014, 20:06

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In a certain industry, production index x is directly propor

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Joined: 28 May 2009
Posts: 155
Followers: 4

Kudos [?]: 74 [0], given: 89

GMAT ToolKit User
In a certain industry, production index x is directly propor [#permalink] New post 05 Feb 2013, 17:25
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

33% (02:35) correct 66% (01:28) wrong based on 36 sessions
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
[Reveal] Spoiler: OA

_________________

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

Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesVeritas Prep GMAT Discount Codes
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4514
Location: Pune, India
Followers: 1010

Kudos [?]: 4296 [1] , given: 161

Re: In a certain industry, production index x is directly [#permalink] New post 05 Feb 2013, 20:50
1
This post received
KUDOS
Expert's post
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 GMAT-like.

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_1should 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

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1425
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 123

Kudos [?]: 545 [0], given: 62

GMAT ToolKit User GMAT Tests User Premium Member
Re: In a certain industry, production index x is directly [#permalink] New post 05 Feb 2013, 20:58
Expert's post
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= y-y/1.414=>0.414y/1.414. This is almost equal to 30%.
Hope this helps.
_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18474
Followers: 3184

Kudos [?]: 21142 [0], given: 2532

Re: In a certain industry, production index x is directly propor [#permalink] New post 05 Feb 2013, 23:34
Expert's post
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: the-rate-of-a-certain-chemical-reaction-is-directly-90119.html (I guess many Gmat Hacks questions are just reworded problems from GMAT Prep).
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
Moderator
Moderator
User avatar
Joined: 01 Sep 2010
Posts: 2279
Followers: 228

Kudos [?]: 1955 [0], given: 664

Re: In a certain industry, production index x is directly propor [#permalink] New post 06 Feb 2013, 08:50
Expert's post
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: the-rate-of-a-certain-chemical-reaction-is-directly-90119.html (I guess many Gmat Hacks questions are just reworded problems from GMAT Prep).




you are correct ........
_________________

COLLECTION OF QUESTIONS
Quant: 1. Bunuel Signature Collection - The Next Generation 2. Bunuel Signature Collection ALL-IN-ONE WITH SOLUTIONS 3. Veritas Prep Blog PDF Version
Verbal:1. Best EXTERNAL resources to tackle the GMAT Verbal Section 2. e-GMAT's ALL CR topics-Consolidated 3. New Critical Reasoning question bank by carcass 4. Meaning/Clarity SC Question Bank by Carcass_Souvik 5. e-GMAT's ALL SC topics-Consolidated-2nd Edition

TOEFL iBT
Best resources to tackle each section of the TOEFL iBT

Manager
Manager
avatar
Joined: 28 Feb 2012
Posts: 115
Concentration: Strategy, International Business
Schools: INSEAD Jan '13
GPA: 3.9
WE: Marketing (Other)
Followers: 0

Kudos [?]: 15 [0], given: 17

GMAT ToolKit User
Re: In a certain industry, production index x is directly propor [#permalink] New post 06 Feb 2013, 22:44
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!

Manager
Manager
User avatar
Joined: 24 Nov 2012
Posts: 161
Concentration: Sustainability, Entrepreneurship
GMAT 1: 770 Q50 V44
WE: Business Development (Internet and New Media)
Followers: 12

Kudos [?]: 57 [0], given: 73

Re: In a certain industry, production index x is directly [#permalink] New post 21 Apr 2013, 00:59
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= y-y/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 ... nprep-com/ - 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 - from-the-ashes-thou-shall-rise-770-q-50-v-44-awa-5-ir-162299.html#p1284542

Re: In a certain industry, production index x is directly   [#permalink] 21 Apr 2013, 00:59
    Similar topics Author Replies Last post
Similar
Topics:
Production index p is directly proportional to efficiency judokan 4 25 Jun 2008, 06:22
7 Experts publish their posts in the topic In a certain business, production index p is directly Superhuman 12 06 May 2008, 23:49
In a certain business, production index p is directly mrmikec 9 15 Jun 2006, 00:16
The rate of a certain chemical reaction is directly yaron 3 27 Aug 2005, 10:04
4 Experts publish their posts in the topic The rate of a certain chemical reaction is directly okdongdong 8 07 Aug 2005, 20:00
Display posts from previous: Sort by

In a certain industry, production index x is directly propor

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.