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The rate of a certain chemical reaction is directly

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

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New post 01 Jul 2015, 21:30
Sample numbers really help one in these percentage problems.
r = A^2/B
A = 10, B=5 => r = 20
r = A^2/10=20
A^2=20 => A=14
(14-10)/10=4/10=40% increase => D is the best answer

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GMAT Prep Test - Proportion Problem [#permalink]

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New post 25 Jun 2016, 10:48
I encountered the following proportion question in the GMAT Prep test.

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?

From what I understand A^2 is inversely proportional to B. So if B increases that A^2 decreases and consequently A decreases. However, the answer is 40% increase. I am not quite able to figure this one out. Can anyone help me on this....Thanks!

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

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New post 25 Jun 2016, 10:51
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gourav16183 wrote:
I encountered the following proportion question in the GMAT Prep test.

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?

From what I understand A^2 is inversely proportional to B. So if B increases that A^2 decreases and consequently A decreases. However, the answer is 40% increase. I am not quite able to figure this one out. Can anyone help me on this....Thanks!


Your post is merged. Please refer to the above discussion and search before posting.

Rules for posting: rules-for-posting-please-read-this-before-posting-133935.html#p1092822

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

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New post 25 Jun 2016, 11:22
balboa 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 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


R =\(\frac{a^2}{b}\)

a = 4 ; b = 2

R = 16/2 =>8

Now B increases by 100%

So, a = x ; b = 4

R = 8

So, 8 = \(\frac{a^2}{4}\)

or, a^2 = 32

Or, a ~ 5.65

So % increase in a is \(\frac{(5.65 - 4)}{4}\)*100 => 41.xx %

So, Answer will be (D) 40%

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

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New post 26 Jun 2016, 00:42
Bunuel 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

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. \(R=\frac{A^2}{B}=\frac{(1.4A)^2}{2B}=\frac{2A^2}{2B}\)

Answer: D.


This is the credited response. I have nothing to add. :-D
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The rate of a certain chemical reaction is directly proportional to th [#permalink]

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New post 25 Aug 2016, 06:09
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 present 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
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Re: The rate of a certain chemical reaction is directly [#permalink]

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New post 25 Aug 2016, 08:08
OluOdekunle 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 percent, which of the following is closest to the present 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


Merging topics.

Please refer to the discussion on previous pages.
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Re: The rate of a certain chemical reaction is directly [#permalink]

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New post 09 Apr 2017, 11:18
Bunuel 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

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. \(R=\frac{A^2}{B}=\frac{(1.4A)^2}{2B}=\frac{2A^2}{2B}\)

Answer: D.


@Bunnuel, can you please help me understand why this set up below is incorrect? Thank you.

R=A^2=1/B

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

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New post 09 Apr 2017, 21:55
Andy24 wrote:
Bunuel 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

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. \(R=\frac{A^2}{B}=\frac{(1.4A)^2}{2B}=\frac{2A^2}{2B}\)

Answer: D.


@Bunnuel, can you please help me understand why this set up below is incorrect? Thank you.

R=A^2=1/B


You should put directly proportional in nominator and inversely proportional in denominator.
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Re: The rate of a certain chemical reaction is directly [#permalink]

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New post 15 May 2017, 18:14
balboa 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 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


Using "=" as the "directly proportional to" symbol.

R=C(A)^2=1/C(B)

Subbing in values for C(A) and C(B):

R=2^2=1/2

If we increase C(B) by 100%), we must halve C(A)^2.

So:

C(A)^2 will become 2 and C(A) root2. Now, we need to make C(A) 2 again. root2=1.41. So we need to add 0.6 to 1.4. That's an increase of approx. 40%.

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

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New post 04 Jun 2017, 13:16
Hi.
You all could also refer to Mitch Hunt's approach on beatthegmat.com.
It can be helpful
http://www.beatthegmat.com/the-rate-of- ... 60321.html

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

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New post 15 Aug 2017, 05:45
Its a easy question if the though process is right.
I could not get it initially but was able to get the logical flow
Let rate be R and it is directly proportional to A² ie if A² increases than R also increases
we can represent it as follows
R∝A²-❶
R is also inversely proportion to B ie if B increases than R reduces
R∝1/B-❷
combining ❶ and❷
R∝A²/B or R=A²₁/B₁
Now B₁ is increased by 100% or is 2B₁
R=A²₁/B₁=A²₂/B₂
B₂=2B₁
A²₁/B₁=A²₂/2B₁
A²₂=A²₁*2B₁/B₁
A²₂=A²₁*2
A₂=√A²₁*2
A₂=A₁√2
A₂=A₁*1.41(√2=1.41)
or A has to increase by 40% to maintain the same rate.

The other way is just plug in the values
we have the equation A²/B=R
Let A=10 and B=5
R=100/5=20 ie the rate is 20 and has to remain the same when B increase by 100% or is 2B
20=A²/2*5
20=A²/10
20*10=A²
A²=200
A=√200=14 ie increase of (14-10)/100=40% increase

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

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New post 12 Oct 2017, 14:29
Can someone help me explain why it shouldn't be a 100% increase? See below for my workflow...

R = A^2 / B
A = 2
B = 1
R = 2^2 / 1 = 4 / 1 = 4
B is increased by 100% = 1 --> 2
R = 2^2 / 2 = 2
If you increased 2^2 by 4 --> 8 / 2 = 4 (the same rate)

Thanks for your help.

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

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New post 12 Oct 2017, 21:06
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Raffio wrote:
Can someone help me explain why it shouldn't be a 100% increase? See below for my workflow...

R = A^2 / B
A = 2
B = 1
R = 2^2 / 1 = 4 / 1 = 4
B is increased by 100% = 1 --> 2
R = 2^2 / 2 = 2
If you increased 2^2by 4 --> 8 / 2 = 4 (the same rate)

Thanks for your help.


A in your example is 2 not 2^2. A should be increased by 44%. Please read the previous pages of discussion, which explain this in great detail.
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Re: The rate of a certain chemical reaction is directly   [#permalink] 12 Oct 2017, 21:06

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