rates

Expert replies

divya23: Master | Next Rank: 500 Posts; Posts: 113; Joined: Mon Apr 26, 2010 8:58 amFollowed by: 14 members; Thanked: 2 times

by divya23 » Wed Jun 15, 2011 5:53 am

the rate of a certain chemical reaction is directly prop to square of conc of chemical A and inversely prop to conc of chemical B present.if conc of chemical B is increased by 100% which of the follow is the closest to he percentage change in the conc of chemical a required to keep the reaction rate unchanged.
ans = 40%increase

Like this post

Source: Beat The GMAT — Problem Solving | Wed Jun 15, 2011 5:53 am

Roy@MasterGmat: GMAT Instructor; Posts: 19; Joined: Mon Feb 21, 2011 7:28 amFollowed by: 3 members; Thanked: 6 times

by Roy@MasterGmat » Wed Jun 15, 2011 6:08 am

Let x = chemical reaction,

A = Chemical A

B = Chemical B

Since x is directly proportional to the square of A and inversely proportional to B:

x=A^2/B

B increased by 100% becomes 2B. Denote the percentage change in A as n:

x = (nA)^2/2B

Finally, solve for n by equating (nA)^2/2B with the original A^2/B:

(nA)^2/2B = A^2/B

n^2A^2 / 2B = A^2 / B \:A^2

n^2 / 2B = 1/B \*2B

n^2 = 2

n = âˆš2

âˆš2 = approx' 1.4, so the percent increase is approx' 40%.

This is a *very* straightforward algebraic approach to this question. For a more qualitative explanation, see Geva's recent post on the matter:

https://www.beatthegmat.com/mba/2011/05/ ... n#comments

Roy
Master GMAT

Like this post

vineeshp: Legendary Member; Posts: 965; Joined: Thu Jan 28, 2010 12:52 amFollowed by: 34 members; Thanked: 156 times; GMAT Score:720

by vineeshp » Wed Jun 15, 2011 6:12 am

R = k A^2 / B

R1 = k A1^2 / B
R2 = k A2^2 / 2B

Given R1 = R2.

k A1^2 / B = k A2^2 / 2B

Cancelling common factors.
A1^2 = A2^2 / 2
A2^2 = 2 * A1^2
A2/A1 = root(2) =1.414
In %,
(A2/A1) * 100 = 141.4 ~ 140

i.e. A2 is 140 % of A1.
which is 40% increase over A1.

Vineesh,
Just telling you what I know and think. I am not the expert.

Like this post

divya23: Master | Next Rank: 500 Posts; Posts: 113; Joined: Mon Apr 26, 2010 8:58 amFollowed by: 14 members; Thanked: 2 times

by divya23 » Wed Jun 15, 2011 6:12 am

i got till root 2 and i cnaged it to 1.414 also but could not figure it out after that

Like this post

Roy@MasterGmat: GMAT Instructor; Posts: 19; Joined: Mon Feb 21, 2011 7:28 amFollowed by: 3 members; Thanked: 6 times

by Roy@MasterGmat » Wed Jun 15, 2011 6:38 am

Let's go over that part:

To keep the reaction unchanged, A needs to increase into 1.4*A. That means A needs to increase by 0.4A (to increase A into 1.4A, add 0.4A, or in math: A+0.4A = 1.4*A).

Since 0.4 is 40%, 0.4A is 40% of A. Therefore, A needs to increase by 40%.

As another example, 1.5x is 50% greater than x, since 0.5 is 50%. 1.7y is 70% greater than y, since 0.7 is 70%.

Hope it's clear now

Roy
Master GMAT

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