Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 27 Jul 2016, 09:15

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The rate of a chemical reaction is directly proportional to

Author Message
TAGS:

Hide Tags

Manager
Joined: 19 Oct 2008
Posts: 95
Followers: 1

Kudos [?]: 30 [1] , given: 0

The rate of a chemical reaction is directly proportional to [#permalink]

Show Tags

23 Mar 2009, 11:03
1
KUDOS
16
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

55% (02:15) correct 45% (01:21) wrong based on 323 sessions

HideShow timer Statistics

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
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Mar 2012, 14:04, edited 1 time in total.
Edited the question and added the OA
Senior Manager
Joined: 06 Mar 2006
Posts: 496
Followers: 7

Kudos [?]: 141 [0], given: 1

Re: PS Rate of chemical reaction GMAT prep [#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

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
Followers: 0

Kudos [?]: 3 [1] , given: 2

Re: PS Rate of chemical reaction GMAT prep [#permalink]

Show Tags

23 Mar 2009, 16:13
1
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: 34091
Followers: 6091

Kudos [?]: 76640 [5] , given: 9978

Re: GMATPrep Percent change of chemical reaction [#permalink]

Show Tags

27 Nov 2009, 19:43
5
KUDOS
Expert's post
6
This post was
BOOKMARKED
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. $$R=\frac{A^2}{B}=\frac{(1.4A)^2}{2B}$$

_________________
Manager
Joined: 30 Mar 2010
Posts: 84
GMAT 1: 730 Q48 V42
Followers: 0

Kudos [?]: 22 [0], given: 5

Re: GMATPrep Percent change of chemical reaction [#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. $$R=\frac{A^2}{B}=\frac{(1.4A)^2}{2B}$$

Brunel, why do you put the directly proportional in the nominator and inversely proportional in the denoimnator?
Math Expert
Joined: 02 Sep 2009
Posts: 34091
Followers: 6091

Kudos [?]: 76640 [2] , given: 9978

Re: GMATPrep Percent change of chemical reaction [#permalink]

Show Tags

28 Nov 2010, 02:12
2
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. $$R=\frac{A^2}{B}=\frac{(1.4A)^2}{2B}$$

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 non-zero 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 non-zero 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.
_________________
Manager
Joined: 30 Mar 2010
Posts: 84
GMAT 1: 730 Q48 V42
Followers: 0

Kudos [?]: 22 [0], given: 5

Re: GMATPrep Percent change of chemical reaction [#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. $$R=\frac{A^2}{B}=\frac{(1.4A)^2}{2B}$$

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 non-zero 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 non-zero 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: 34091
Followers: 6091

Kudos [?]: 76640 [0], given: 9978

Re: GMATPrep Percent change of chemical reaction [#permalink]

Show Tags

28 Nov 2010, 10:27
Expert's post
afyl128 wrote:

Thanks =) do you have any links to similar questions? i'm very shaky on these

ds-question-93667.html
og-proportional-index-63570.html

easy-proportion-question-88971.html
vic-80941.html

Hope it helps.
_________________
Manager
Joined: 04 Dec 2011
Posts: 81
Schools: Smith '16 (I)
Followers: 0

Kudos [?]: 17 [0], given: 13

Re: GMATPrep Percent change of chemical reaction [#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 ... g-jointly/
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.

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: 81
Schools: Smith '16 (I)
Followers: 0

Kudos [?]: 17 [0], given: 13

Re: The rate of a chemical reaction is directly proportional to [#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: 10614
Followers: 495

Kudos [?]: 129 [0], given: 0

Re: The rate of a chemical reaction is directly proportional to [#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 Club Legend
Joined: 09 Sep 2013
Posts: 10614
Followers: 495

Kudos [?]: 129 [0], given: 0

Re: The rate of a chemical reaction is directly proportional to [#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.
_________________
Intern
Joined: 06 Nov 2015
Posts: 20
Followers: 0

Kudos [?]: 1 [0], given: 107

Re: The rate of a chemical reaction is directly proportional to [#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 non-zero 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 non-zero 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

Intern
Joined: 06 Jun 2014
Posts: 44
Followers: 0

Kudos [?]: 3 [1] , given: 100

Re: The rate of a chemical reaction is directly proportional to [#permalink]

Show Tags

06 May 2016, 02:06
1
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 non-zero 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 non-zero 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

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%
Re: The rate of a chemical reaction is directly proportional to   [#permalink] 06 May 2016, 02:06
Similar topics Replies Last post
Similar
Topics:
28 If the price of a commodity is directly proportional to m^3 12 07 Apr 2013, 05:45
104 The rate of a certain chemical reaction is directly 24 05 Feb 2010, 13:06
10 a is directly proportional to b. When a = 8, b = 6. 5 09 Jan 2010, 14:04
11 The rate of a certain chemical reaction is directly proportional to th 5 27 Aug 2009, 06:09
13 In a certain formula, p is directly proportional to s and 5 16 Jul 2009, 03:00
Display posts from previous: Sort by