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megafan
Joined: 28 May 2009
Last visit: 15 Oct 2017
Posts: 137
Given Kudos: 91
Location: United States
Concentration: Strategy, General Management
Schools: Stern PT Fall'18 Booth PT '18
GMAT Date: 03-22-2013
GPA: 3.57
WE:Information Technology (Consulting)
05 Feb 2013, 18:25
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
52% (02:24) correct
48%
(02:18)
wrong
based on 757
sessions
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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
(A) 100% increase
(B) 50% increase
(C) 30% increase
(D) 30% decrease
(E) 50% decrease
Source: Gmat Hacks 1800
megafan
I have discussed Variation in this video in detail: https://youtu.be/AT86tjxJ-f0
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 \(x_1\)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)
General Discussion
05 Feb 2013, 21:58
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megafan
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.
