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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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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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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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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.

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

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

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

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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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Thank you for that kudos

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

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

R=A^2=1/B

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

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

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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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%.

Agree? Kudos.

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

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04 Jun 2017, 13:16
Hi.
You all could also refer to Mitch Hunt's approach on beatthegmat.com.
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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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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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)

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

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12 Oct 2017, 21:06
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Expert's post
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)

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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