It is currently 20 Sep 2017, 17:03

### 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 certain chemical reaction is directly

Author Message
TAGS:

### Hide Tags

Manager
Joined: 23 Jun 2008
Posts: 140

Kudos [?]: 140 [11], given: 0

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

### Show Tags

05 Feb 2010, 13:06
11
KUDOS
55
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

55% (01:05) correct 45% (01:31) wrong based on 1317 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 percent, 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
[Reveal] Spoiler: OA

Kudos [?]: 140 [11], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 41640

Kudos [?]: 124200 [29], given: 12075

Re: GMAT Prep - Ratios [#permalink]

### Show Tags

05 Feb 2010, 13:16
29
KUDOS
Expert's post
36
This post was
BOOKMARKED
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

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 $$x^2=2$$ --> $$x\approx{1.41}$$, which is approximately 40% increase. $$R=\frac{A^2}{B}=\frac{(1.4A)^2}{2B}=\frac{2A^2}{2B}$$

_________________

Kudos [?]: 124200 [29], given: 12075

Manager
Joined: 18 Feb 2010
Posts: 171

Kudos [?]: 231 [5], given: 0

Schools: ISB

### Show Tags

20 Aug 2010, 23:14
5
KUDOS
CR = (A^2) * ( 1/B)

put any values

625 = 25*25

B increases by 100% so it becomes 50

CR remains same at 625
1/B becomes 50

so A^2 should be

625/50 = 12.5 or say decreased by 50% (b)
_________________

CONSIDER AWARDING KUDOS IF MY POST HELPS !!!

Kudos [?]: 231 [5], given: 0

Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 406

Kudos [?]: 237 [12], given: 50

Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB

### Show Tags

23 Aug 2010, 19:06
12
KUDOS
1
This post was
BOOKMARKED
Given equation = $$A^2/B$$

Also given that the concentration of B is increased by 100 %. Hence B becomes 2B.

New concentration = $$A^2/2B$$. In order to keep the new concentration the same as the original concentration, A should be equal to $$\sqrt{2}A$$ so that A^2/2B becomes $$A^2/B$$

$$\sqrt{2}A$$ == 1.414 * A or approximately 141% of A.

141% of A is 41 % increase of A.

_________________

Support GMAT Club by putting a GMAT Club badge on your blog

Kudos [?]: 237 [12], given: 50

Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 406

Kudos [?]: 237 [4], given: 50

Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB

### Show Tags

14 Sep 2010, 19:40
4
KUDOS
1
This post was
BOOKMARKED
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?

Given: Rate - $$(A^2/B)$$

B increased by 100%. New B is 2B.

Rate - $$(A^2)/2B$$. In order for the initial rate of chemical reaction to be the same as the final rate. A should be increased such that it should cancel out the 2 in the denominator.

Hence A should be $$A\sqrt{2}$$ and hence final rate of reaction is $$(A\sqrt{2}))^2/2B$$

$$2A^2/2B$$ which becomes the same as the initial rate of reaction. Hence A should be $$A\sqrt{2}$$.

Or final concentration of A is $$1.41A$$ or an increase of approximately 41%.

_________________

Support GMAT Club by putting a GMAT Club badge on your blog

Kudos [?]: 237 [4], given: 50

Manager
Joined: 08 Sep 2010
Posts: 224

Kudos [?]: 308 [2], given: 21

Location: India
WE 1: 6 Year, Telecom(GSM)

### Show Tags

19 Oct 2010, 02:37
2
KUDOS
satishreddy wrote:
the rate of certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of the 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.

100% decrease
50% increase
40% decrease
40% increase
50% increase

Let the rate of the reaction is r and concentration of chemical A is A and concentration of chemical B is B.

According to the question , r is proportional to A^2
and r is also proportional to 1/B

Combining these two condition , r =K (A^2/B) , where K is proportionality constant.

Now in the changed condition B has increased by 100 % means is has become 2B.

So for keeping the rate constant we have to change the concentration of A, from A to ((Square root of 2)*A)

As K (((square root of 2)A)^2)/2B = K (A^2/B) =r

Now, let after increase of x% ,A has become ((square root of 2)A) i.e 1.414*A

A+(xA/100)=1.414 A
Hence x=41.4%

Please consider KUDOS if it helped u in some way.Thanks

Kudos [?]: 308 [2], given: 21

Intern
Joined: 15 Jan 2011
Posts: 6

Kudos [?]: 9 [3], given: 0

Re: % increase , proportions [#permalink]

### Show Tags

31 Jan 2011, 07:40
3
KUDOS
1
This post was
BOOKMARKED
The rate of a 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 percent , which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?

100% decrease
50% decrease
40% decrease
40% increase
50% increase

Let r be the rate of chemical reaction and A and B be the concentration of chemical A and chemical B respectively.

r is proportional to A^2
r is inversely proportional to B

thus, r = k(A^2/B), where k is some constant.

now B becomes 2B (100% increase). Let x be the new concentration of A.

The new equation becomes

r=k(x^2/2B)

Since r remains the same, we have

k(A^2/B)=k(x^2/2B)

so, x=1.4A which is an increase of 40%

Kudos [?]: 9 [3], given: 0

VP
Joined: 24 Jul 2011
Posts: 1342

Kudos [?]: 636 [1], given: 20

GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Re: Direct and Inverse Proportion Q [#permalink]

### Show Tags

18 Mar 2012, 21:26
1
KUDOS
Rate= r = k (A^2) (1/B) [where k is a constant]

If B is replaced by 2B, then
r = k (A^2) (1/2B)
=> k (A'^2) (1/2B) = k (A^2) (1/B) [where A' is the new concentration of A]
=> A'^2 = 2(A^2)
=> A' = sqrt (2) * A = 1.414 *A

Therefore the concentration of A must increase by ~40% [option D]
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Kudos [?]: 636 [1], given: 20

Senior Manager
Joined: 13 Mar 2012
Posts: 354

Kudos [?]: 191 [1], given: 31

Concentration: Operations, Strategy
Re: Direct and Inverse Proportion Q [#permalink]

### Show Tags

19 Mar 2012, 01:16
1
KUDOS
A-> (sq rt 2)*A

as R=K A^2/B

HENCE
((sq rt 2)-1)/1 =41% increase

hence D
_________________

Practice Practice and practice...!!

If there's a loophole in my analysis--> suggest measures to make it airtight.

Kudos [?]: 191 [1], given: 31

Math Expert
Joined: 02 Sep 2009
Posts: 41640

Kudos [?]: 124200 [2], given: 12075

Re: Direct and Inverse Proportion Q [#permalink]

### Show Tags

19 Mar 2012, 01:37
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
dddmba2012 wrote:
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 present is increased by 100 percent, which of the following is closest to the percent change in the 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

Also discussed here: the-rate-of-a-chemical-reaction-is-directly-proportional-to-76921.html

the-amount-of-coal-a-train-burns-each-mile-is-directly-93667.html

a-is-directly-proportional-to-b-when-a-8-b-88971.html
in-a-certain-formula-p-is-directly-proportional-to-s-and-80941.html

Hope it helps.
_________________

Kudos [?]: 124200 [2], given: 12075

Senior Manager
Joined: 15 Jun 2010
Posts: 359

Kudos [?]: 439 [0], given: 50

Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Re: The rate of a certain chemical reaction [#permalink]

### Show Tags

24 Oct 2012, 08:33
danzig wrote:
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

From Q Stem Chemical reaction R =K (A^2/B)
Now if B is increased by 100%----> it becomes R=K (A^2/2B)
Now To bring the relationship to its initial condition we need to cancel out 2 in denominator. So my multiplying root 2 we can do that. So root2 = 1.4 approx.
That means we need to increase 40% of A.

Hence D.
_________________

Regards
SD
-----------------------------
Press Kudos if you like my post.
Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Kudos [?]: 439 [0], given: 50

Intern
Joined: 11 Jul 2012
Posts: 46

Kudos [?]: 7 [0], given: 0

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

### Show Tags

04 Nov 2012, 02:38
Hello Bunuel
I saw this question coming around couple of times.
But doesn't the answer depend on how you express the concentration reaction?
If I said CR = A^2 - B, (or in general a*A^2 + b*B, where a >0 and b <0) the answer will still be D?
Brother Karamazov

Kudos [?]: 7 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 41640

Kudos [?]: 124200 [0], given: 12075

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

### Show Tags

08 Jul 2013, 01:09
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

To find DS questions by Kudos, sort by Kudos here: gmat-data-sufficiency-ds-141/
To find PS questions by Kudos, sort by Kudos here: gmat-problem-solving-ps-140/

_________________

Kudos [?]: 124200 [0], given: 12075

Manager
Joined: 13 Jul 2013
Posts: 71

Kudos [?]: 10 [0], given: 21

GMAT 1: 570 Q46 V24
Re: The rate of a certain chemical reaction is directly [#permalink]

### Show Tags

04 Jan 2014, 01:49
I am unable to understand this question.

Rate= a^2
Rate= 1/b

Where is constant K coming from? And why are we multiplying all the there i.e. K, a^2 and 1/b?

Kudos [?]: 10 [0], given: 21

Manager
Joined: 20 Dec 2013
Posts: 131

Kudos [?]: 103 [1], given: 1

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

### Show Tags

04 Jan 2014, 05:12
1
KUDOS
theGame001 wrote:
I am unable to understand this question.

Rate= a^2
Rate= 1/b

Where is constant K coming from? And why are we multiplying all the there i.e. K, a^2 and 1/b?

Lets make your life more easy.

Let us say x = 4, y = 2 then R = 16/2 = 8

Now keep R same and double y to see what is the change in X.

R = X^2/Y
8 = X^2/4
X = 4\sqrt{2}

X got multiplied by \sqrt{2} which means a 40 % increase

OR

R = X^2/Y
If Y got multiplied by 2 X will have to get multiplied by \sqrt{2} to keep R same. Still 40 % increase
_________________

76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org

Kudos [?]: 103 [1], given: 1

Manager
Joined: 13 Jul 2013
Posts: 71

Kudos [?]: 10 [0], given: 21

GMAT 1: 570 Q46 V24
Re: The rate of a certain chemical reaction is directly [#permalink]

### Show Tags

04 Jan 2014, 05:19
PerfectScores wrote:
theGame001 wrote:
I am unable to understand this question.

Rate= a^2
Rate= 1/b

Where is constant K coming from? And why are we multiplying all the there i.e. K, a^2 and 1/b?

Lets make your life more easy.

Let us say x = 4, y = 2 then R = 16/2 = 8

Now keep R same and double y to see what is the change in X.

R = X^2/Y
8 = X^2/4
X = 4\sqrt{2}

X got multiplied by \sqrt{2} which means a 40 % increase

OR

R = X^2/Y
If Y got multiplied by 2 X will have to get multiplied by \sqrt{2} to keep R same. Still 40 % increase

Thank you but what I am unable to understand is why are we multiplying?

x=4 and y=2
Squared 4= 16 ----- I understood this
Inversely proportional = 1/2 ------ Understood this
16*1/2 ------Unable to understand this part

Kudos [?]: 10 [0], given: 21

Manager
Joined: 20 Dec 2013
Posts: 131

Kudos [?]: 103 [1], given: 1

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

### Show Tags

04 Jan 2014, 05:22
1
KUDOS
theGame001 wrote:
PerfectScores wrote:
theGame001 wrote:
I am unable to understand this question.

Rate= a^2
Rate= 1/b

Where is constant K coming from? And why are we multiplying all the there i.e. K, a^2 and 1/b?

Lets make your life more easy.

Let us say x = 4, y = 2 then R = 16/2 = 8

Now keep R same and double y to see what is the change in X.

R = X^2/Y
8 = X^2/4
X = 4\sqrt{2}

X got multiplied by \sqrt{2} which means a 40 % increase

OR

R = X^2/Y
If Y got multiplied by 2 X will have to get multiplied by \sqrt{2} to keep R same. Still 40 % increase

Thank you but what I am unable to understand is why are we multiplying?

x=4 and y=2
Squared 4= 16 ----- I understood this
Inversely proportional = 1/2 ------ Understood this
16*1/2 ------Unable to understand this part

R is directly proportional to X^2 and inversely proportional to Y which means that R is directly proportional to X^2/Y

So if x = 4 and y = 2 R is directly proportional to (4^2)/2 which is equivalent to X^2/Y
_________________

76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org

Kudos [?]: 103 [1], given: 1

Current Student
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 960

Kudos [?]: 1810 [2], given: 229

Location: India
GPA: 3.51
WE: Information Technology (Computer Software)
The rate of a certain chemical reaction is directly [#permalink]

### Show Tags

09 Apr 2014, 14:26
2
KUDOS
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

$$Rate = \frac{k*A^2}{B}$$

$$Rate = \frac{k*NewA^2}{2B}$$

$$\frac{k*NewA^2}{2B} = \frac{k*A^2}{B}$$

$$NewA = sqrt{2} * A$$

$$%change = \frac{sqrt{2}*A - A}{A}*100$$

$$%change= 0.414*100=41.4% increase$$

_________________

Piyush K
-----------------------
Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison
Don't forget to press--> Kudos
My Articles: 1. WOULD: when to use? | 2. All GMATPrep RCs (New)
Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".

Kudos [?]: 1810 [2], given: 229

Intern
Status: Going the extra mile
Joined: 08 Feb 2014
Posts: 20

Kudos [?]: 16 [1], given: 57

Location: Netherlands
GMAT 1: 470 Q37 V18
GMAT 2: 570 Q36 V32
GMAT 3: 560 Q37 V30
GMAT 4: 610 Q41 V34
Re: The rate of a certain chemical reaction is directly [#permalink]

### Show Tags

03 May 2014, 02:50
1
KUDOS
Ratio A to B : A^2 = B

Say B = 100
Then A = 10^2

B Increases 100% ==> 200
x^2 = 200 ?
14^2=196 (almost 200, so x is a slightly bigger)

10 ==> 14 ==> increase of 40%.

_________________

Structural persistence is the key to succes .
Party hard, study harder.

Still bashing, will continue to do so , although it's important to chill aswell ; )
STUDY+CHILL=VICTORY

Kudos [?]: 16 [1], given: 57

Current Student
Joined: 03 Feb 2013
Posts: 942

Kudos [?]: 1034 [0], given: 548

Location: India
Concentration: Operations, Strategy
GMAT 1: 760 Q49 V44
GPA: 3.88
WE: Engineering (Computer Software)
The rate of a certain chemical reaction is directly [#permalink]

### Show Tags

21 Dec 2014, 08:40
$$\sqrt{2}$$= 1.414
Option D)
_________________

Thanks,
Kinjal

My Application Experience : http://gmatclub.com/forum/hardwork-never-gets-unrewarded-for-ever-189267-40.html#p1516961

Kudos [?]: 1034 [0], given: 548

The rate of a certain chemical reaction is directly   [#permalink] 21 Dec 2014, 08:40

Go to page    1   2    Next  [ 32 posts ]

Similar topics Replies Last post
Similar
Topics:
The volume of a certain substance is always directly proportional to 1 20 Dec 2015, 06:45
7 In a certain industry, production index x is directly propor 8 18 Sep 2016, 17:40
16 In a certain formula, p is directly proportional to s and 6 26 Dec 2016, 15:46
12 The rate of a certain chemical reaction is directly proportional to th 5 17 Jul 2015, 10:15
45 The rate of a certain chemical reaction is directly proportional to th 17 12 Sep 2017, 00:41
Display posts from previous: Sort by