Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 19 Oct 2008
Posts: 94

The rate of a certain chemical reaction is directly proportional to th [#permalink]
Show Tags
23 Mar 2009, 11:03
1
This post received KUDOS
19
This post was BOOKMARKED
Question Stats:
57% (02:15) correct
43% (01:14) wrong based on 446 sessions
HideShow timer Statistics
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%, 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
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 06 Aug 2016, 23:02, edited 2 times in total.
Edited the question and added the OA



Senior Manager
Joined: 06 Mar 2006
Posts: 494

Re: The rate of a certain chemical reaction is directly proportional to th [#permalink]
Show Tags
23 Mar 2009, 13:19
Accountant wrote: The rate of a chemical reaction is directly proportional to the square of concentration of chemcial A present and invesrsly proportional to the concentration of chemical B present. If chemical B is increased by 100% which of the following is the change in concentration of chemical A required to keep teh reaction rate unchanged:
A. 100% decrease B. 50% decrease C. 40% decrease D. 40% increase E. 50% increase
Please explain your answer. The rate of reaction is invesrsly proportional to the concentration of chemical B present. It used to have B=1 . Now that B is increased by 100%. So the new equation would be 2B=(1/2). In order for the rate of reaction to still be 1, we need to change the concentration of A to yield a 2. It used to be A^2=1, now the new equation should be (sqrt(2)*A)^2=2. The change in the concentration of A can be calculated as (sqrt(2) 1)/1 or approximately 40% increase. Answer D.



Intern
Joined: 25 Dec 2008
Posts: 18
Schools: HBS, Stanford

Re: The rate of a certain chemical reaction is directly proportional to th [#permalink]
Show Tags
23 Mar 2009, 16:13
1
This post received KUDOS
CA: Concentration A CB: Concentration B R: Reaction rate
Formula for reaction rate:
R = (CA^2) / CB
Thus if CB is increased by 100% >> means concentration doubles >> 2xCB
Thus, for R to remain the same (CA^2) also has to double.
>> 2 x (CA^2) >> to see what happens to CA, take the 2 into the bracket by taking its root
>> (SQRT2 CA)^2
SQRT 2 is roughly 40% >> answer D



Math Expert
Joined: 02 Sep 2009
Posts: 39637

Re: The rate of a certain chemical reaction is directly proportional to th [#permalink]
Show Tags
27 Nov 2009, 19:43
5
This post received KUDOS
Expert's post
6
This post was BOOKMARKED



Manager
Joined: 30 Mar 2010
Posts: 83

Re: The rate of a certain chemical reaction is directly proportional to th [#permalink]
Show Tags
27 Nov 2010, 18:06
Bunuel wrote: NOTE: Put directly proportional in nominator and inversely proportional in denominator. \(RATE=\frac{A^2}{B}\), (well as it's not the exact fraction it should be multiplied by some constant but we can ignore this in our case).
We are told that B increased by 100%, hence in denominator we have 2B. We want the rate to be the same. As rate is directly proportional to the SQUARE of A, A should also increase (nominator) by x percent and increase of A in square should be 2. Which means x^2=2, x=~1.41, which is approximately 40% increase. \(R=\frac{A^2}{B}=\frac{(1.4A)^2}{2B}\)
Answer: D. Brunel, why do you put the directly proportional in the nominator and inversely proportional in the denoimnator?



Math Expert
Joined: 02 Sep 2009
Posts: 39637

Re: The rate of a certain chemical reaction is directly proportional to th [#permalink]
Show Tags
28 Nov 2010, 02:12
2
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
afyl128 wrote: Bunuel wrote: NOTE: Put directly proportional in nominator and inversely proportional in denominator. \(RATE=\frac{A^2}{B}\), (well as it's not the exact fraction it should be multiplied by some constant but we can ignore this in our case).
We are told that B increased by 100%, hence in denominator we have 2B. We want the rate to be the same. As rate is directly proportional to the SQUARE of A, A should also increase (nominator) by x percent and increase of A in square should be 2. Which means x^2=2, x=~1.41, which is approximately 40% increase. \(R=\frac{A^2}{B}=\frac{(1.4A)^2}{2B}\)
Answer: D. Brunel, why do you put the directly proportional in the nominator and inversely proportional in the denoimnator? \(a\) is directly proportional to \(b\) means that as the absolute value of \(b\) gets bigger, the absolute value of \(b\) gets bigger too, so there is some nonzero constant \(x\) such that \(a=xb\); \(a\) is inversely proportional to \(b\) means that as the absolute value of \(b\) gets bigger, the absolute value of \(a\) gets smaller, so there is some nonzero constant constant \(y\) such that \(a=\frac{y}{b}\). So, when we are told that the rate (R) is directly proportional to the square of A and inversely proportional to B we can write \(R=\frac{(A^2x)y}{B}\). Hope it's clear.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 30 Mar 2010
Posts: 83

Re: The rate of a certain chemical reaction is directly proportional to th [#permalink]
Show Tags
28 Nov 2010, 09:56
Bunuel wrote: afyl128 wrote: Bunuel wrote: NOTE: Put directly proportional in nominator and inversely proportional in denominator. \(RATE=\frac{A^2}{B}\), (well as it's not the exact fraction it should be multiplied by some constant but we can ignore this in our case).
We are told that B increased by 100%, hence in denominator we have 2B. We want the rate to be the same. As rate is directly proportional to the SQUARE of A, A should also increase (nominator) by x percent and increase of A in square should be 2. Which means x^2=2, x=~1.41, which is approximately 40% increase. \(R=\frac{A^2}{B}=\frac{(1.4A)^2}{2B}\)
Answer: D. Brunel, why do you put the directly proportional in the nominator and inversely proportional in the denoimnator? \(a\) is directly proportional to \(b\) means that as the absolute value of \(a\) gets bigger, the absolute value of \(b\) gets bigger too, so there is some nonzero constant \(x\) such that \(a=xb\); \(a\) is inversely proportional to \(b\) means that as the absolute value of \(a\) gets bigger, the absolute value of \(b\) gets smaller, so there is some nonzero constant constant \(y\) such that \(a=\frac{y}{b}\). So, when we are told that the rate (R) is directly proportional to the square of A and inversely proportional to B we can write \(R=\frac{(A^2x)y}{B}\). Hope it's clear. Thanks =) do you have any links to similar questions? i'm very shaky on these



Math Expert
Joined: 02 Sep 2009
Posts: 39637

Re: The rate of a certain chemical reaction is directly proportional to th [#permalink]
Show Tags
28 Nov 2010, 10:27



Manager
Joined: 04 Dec 2011
Posts: 80

Re: The rate of a certain chemical reaction is directly proportional to th [#permalink]
Show Tags
29 Sep 2013, 10:12
Hi Bunuel, I am a bit shaky with variation concepts and hence decided to get the basics clear, I was referring to Karishma's blog here http://www.veritasprep.com/blog/2013/02 ... gjointly/Now I understand that if a rate varies directly for Eg X varies directly with Y than we have X/Y = K(some value) because in direct variation the ratio remains same. and in inverse variation it will be XY = K(some value) because x=1/y Please correct me if I misunderstood any concept till this point. now to your explanation Bunuel wrote: NOTE: Put directly proportional in nominator and inversely proportional in denominator how can we put a direct variation in numerator? because if I understand the concept correctly it should be in denominator? and an inverse in numerator..how did you arrived at this quick formula? another question to may be both karishma and you Bunuel ( sorry karishma I am asking questions pertaining to your blog on this forum, but I thought this question can serve as a common reference.) As per me It should be B/A^2 (infect If I look at karishma's sample question in same page its essentially the same question with just values swapped with N and M) another point of confusion when B becomes double (i.e 2B) why don't we simply say A^2 also doubles(i.e 2 A^2) why do we say if a^2 has to double it has to be A^2 = 2 ? if its a ratio than it should be multiplied and divided by same value in numerator and denominator (i.e 2)
_________________
Life is very similar to a boxing ring. Defeat is not final when you fall down… It is final when you refuse to get up and fight back!
1 Kudos = 1 thanks Nikhil



Manager
Joined: 04 Dec 2011
Posts: 80

Re: The rate of a certain chemical reaction is directly proportional to th [#permalink]
Show Tags
01 Oct 2013, 12:22
Hi Bunuel...waiting for reply.. have exam this week so a bit nervous
_________________
Life is very similar to a boxing ring. Defeat is not final when you fall down… It is final when you refuse to get up and fight back!
1 Kudos = 1 thanks Nikhil



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15940

Re: The rate of a certain chemical reaction is directly proportional to th [#permalink]
Show Tags
17 Oct 2014, 00:38
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15940

Re: The rate of a certain chemical reaction is directly proportional to th [#permalink]
Show Tags
20 Nov 2015, 00:25
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Intern
Joined: 06 Nov 2015
Posts: 28

Re: The rate of a certain chemical reaction is directly proportional to th [#permalink]
Show Tags
29 Apr 2016, 07:54
Bunuel wrote: \(a\) is directly proportional to \(b\) means that as the absolute value of \(b\) gets bigger, the absolute value of \(b\) gets bigger too, so there is some nonzero constant \(x\) such that \(a=xb\);
\(a\) is inversely proportional to \(b\) means that as the absolute value of \(b\) gets bigger, the absolute value of \(a\) gets smaller, so there is some nonzero constant constant \(y\) such that \(a=\frac{y}{b}\).
So, when we are told that the rate (R) is directly proportional to the square of A and inversely proportional to B we can write \(R=\frac{(A^2x)y}{B}\).
Hope it's clear.
Hi, Could someone help to explain this one, how can we come up with the final result, which is \(R=\frac{(A^2x)y}{B}\)? As far as I understand, according to the case in question, we have: 1. The rate is directly proportional to the square of concentration of chemical A > R = \(xA^2\) (1) 2. The rate is inversely proportional to the concentration of chemical B > R = \(\frac{y}{B}\) (2) So next, how can we infer that \(R=\frac{(A^2x)y}{B}\)? What steps used to modify/combine (1) and (2) to get this one? Actually, from (1) and (2), I am thinking of \(\frac{(A^2x)*y}{B}\) as \(R*R\) = \(R^2\) instead Please help to clarify. Thanks



Manager
Joined: 06 Jun 2014
Posts: 57

Re: The rate of a certain chemical reaction is directly proportional to th [#permalink]
Show Tags
06 May 2016, 02:06
1
This post received KUDOS
thuyduong91vnu wrote: Bunuel wrote: \(a\) is directly proportional to \(b\) means that as the absolute value of \(b\) gets bigger, the absolute value of \(b\) gets bigger too, so there is some nonzero constant \(x\) such that \(a=xb\);
\(a\) is inversely proportional to \(b\) means that as the absolute value of \(b\) gets bigger, the absolute value of \(a\) gets smaller, so there is some nonzero constant constant \(y\) such that \(a=\frac{y}{b}\).
So, when we are told that the rate (R) is directly proportional to the square of A and inversely proportional to B we can write \(R=\frac{(A^2x)y}{B}\).
Hope it's clear.
Hi, Could someone help to explain this one, how can we come up with the final result, which is \(R=\frac{(A^2x)y}{B}\)? As far as I understand, according to the case in question, we have: 1. The rate is directly proportional to the square of concentration of chemical A > R = \(xA^2\) (1) 2. The rate is inversely proportional to the concentration of chemical B > R = \(\frac{y}{B}\) (2) So next, how can we infer that \(R=\frac{(A^2x)y}{B}\)? What steps used to modify/combine (1) and (2) to get this one? Actually, from (1) and (2), I am thinking of \(\frac{(A^2x)*y}{B}\) as \(R*R\) = \(R^2\) instead Please help to clarify. Thanks Hello my friend. This is how I solved this question. First I didnt assign those variebels x and y as above in the quote. I think those are used just as reference in order to show the proportonality. Now to the question. I did assign variable x to be the factor of percent increase or decrease, r to be the rate, and a and b for the concetrations. So start with first formula \(r=a^2/b\) where a is directly proportonal ans is nuumerator and b is denominator since it is inversly proportinal. note u have to put \(a^2\) because it is given that the square root is directly proportonal now the second equation , the question asks to have same value for the rate but b is doubled or increase for 100% \(r=(xa)^2/2b\) or \(r=x^2a^2/2b\) now from here we can use the short way given by Bunuel or the long way to solve for x, either way it will come out as x^2=2 and\(x=1.41\). now earlier we said x is a factor of percentage change \(1+0.41\) or we have an increase of 41%



Manager
Joined: 15 Feb 2016
Posts: 65

Re: The rate of a certain chemical reaction is directly proportional to th [#permalink]
Show Tags
06 Aug 2016, 15:04
Accountant wrote: The rate of a chemical reaction is directly proportional to the square of concentration of chemcial A present and invesrsly proportional to the concentration of chemical B present. If chemical B is increased by 100% which of the following is the change in concentration of chemical A required to keep teh reaction rate unchanged:
A. 100% decrease B. 50% decrease C. 40% decrease D. 40% increase E. 50% increase Please edit the question. It is " which of the following is the closest to the change". Makes a lot of difference.
_________________
It is not who I am underneath but what I do that defines me.



Math Expert
Joined: 02 Sep 2009
Posts: 39637

Re: The rate of a certain chemical reaction is directly proportional to th [#permalink]
Show Tags
06 Aug 2016, 23:03



Intern
Joined: 03 Nov 2016
Posts: 1

Re: The rate of a certain chemical reaction is directly proportional to th [#permalink]
Show Tags
26 Dec 2016, 14:26
1
This post received KUDOS
1
This post was BOOKMARKED
This question can also be solved by plugging in values for a and b and comparing the results:  The rate of this reaction at first is \(r=\frac{A^2}{B}\)  If \(A=1\) and \(B=2\) the result of the equation is \(r=\frac{1}{2}\)  When \(B\) is increased by 100% the equation becomes \(r=\frac{A^2}{2B}\)  Since the question asks by how much \(A\) would need to increase in order for the reaction rate to remain the same, the second equation can be rewritten as \(\frac{1}{2}=\frac{A^2}{4}\) where \(r=\frac{1}{2}\), the same as in the first equation.  The second equation can then be rewritten as \(2=A^2\) and then as \(\sqrt{2}=A\)  The percent increase from \(A=1\) in the first equation to \(A=\sqrt{2}\) in the second equation is approximately 40% since\(\sqrt{2}=1.4\)  The answer is




Re: The rate of a certain chemical reaction is directly proportional to th
[#permalink]
26 Dec 2016, 14:26







