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
The OA is the option D.
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In a certain industry, production index x is directly
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Shahrukh_mbabreakspace
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Since x is directly proportional to y^2 and inversely proportional to z
x=(ky^2)/z, where k is a constant
Now, if z becomes half, then to keep x unchanged, y^2 should also become 1/2
This means y will become 1/sqrt(2) times of y
Now, % change in y= (y-(1/sqrt(2)*y))/y * 100
Which approximately is 30%
________________________________________
Shahrukh Moin Khan
QA Mentor at Breakspace
https://www.mbabreakspace.com
PGDM: IIM Calcutta
B.Tech IIT Roorkee
x=(ky^2)/z, where k is a constant
Now, if z becomes half, then to keep x unchanged, y^2 should also become 1/2
This means y will become 1/sqrt(2) times of y
Now, % change in y= (y-(1/sqrt(2)*y))/y * 100
Which approximately is 30%
________________________________________
Shahrukh Moin Khan
QA Mentor at Breakspace
https://www.mbabreakspace.com
PGDM: IIM Calcutta
B.Tech IIT Roorkee
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Scott@TargetTestPrep
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"Production index x is directly proportional to the square of efficiency index y, and indirectly proportional to investment index z" means x = k * y^2/z for some positive value k.VJesus12 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
Now we are given that z becomes z/2 and we can let y become ty for some positive value t. So we have x = k * (ty)^2/(z/2). Since we are keeping x the same and recall that x = k * y^2/z, so we have:
k * y^2/z = k * (ty)^2/(z/2)
y^2/z = t^2 * y^2 * 2/z
1 = t^2 * 2
1/2 = t^2
t = √(1/2) ≈ 0.7
Thus we see that the efficiency index y has to become 0.7y, or a 30% decrease, in order to keep the production index x the same.
Answer: D
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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/1.41 4 --> 0.414y/1.414. This is almost equal to 30%.
Regards!
Therefore percent change = y−y/1.41 4 --> 0.414y/1.414. This is almost equal to 30%.
Regards!
