In a certain industry, production index x is directly

Expert replies

VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Wed Jul 04, 2018 2:54 am

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.

What? I didn't understand the question. Please, help. <i class="em em-sob"></i>

Like this post

Source: Beat The GMAT — Problem Solving | Wed Jul 04, 2018 2:54 am

Shahrukh_mbabreakspace: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Mon Jul 02, 2018 1:56 amFollowed by: 2 members

by Shahrukh_mbabreakspace » Wed Jul 04, 2018 3:11 am

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

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Jul 09, 2018 7:01 pm

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

"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.

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 = âˆš(1/2) â‰ˆ 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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Fri Jul 13, 2018 9:21 am

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 = yâˆ’y/1.41 4 --> 0.414y/1.414. This is almost equal to 30%.

Regards!

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review