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Word problem on rates

by emiflo » Sat Jul 31, 2010 6:13 am
hi guys. pls could someone solve this for me. the rate of a chemical reaction is directly proportional to the square of concentration of chemical A and inversely proportional to the concentration of chemical B. If the concentration of chemical B is increased by 100 percent, which of the following is closest to the percentage change in concentration of chemical A required to keep the reaction unchanged.
A 100% decrease
B 50% decrease
C 40% decrease
D 40% increase
E 50% increase
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by sumanr84 » Sat Jul 31, 2010 7:02 am
Here you go.

https://www.beatthegmat.com/gmat-prep-ch ... 16793.html

Please use search option before posting..
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by GMATGuruNY » Sat Jul 31, 2010 7:06 am
emiflo wrote:hi guys. pls could someone solve this for me. the rate of a chemical reaction is directly proportional to the square of concentration of chemical A and inversely proportional to the concentration of chemical B. If the concentration of chemical B is increased by 100 percent, which of the following is closest to the percentage change in concentration of chemical A required to keep the reaction unchanged.
A 100% decrease
B 50% decrease
C 40% decrease
D 40% increase
E 50% increase
The problem describes the following relationship:

r =(A^2)/B

Why? Two reasons:

1) The rate is directly proportional to A^2, and directly proportional means that as one value increases, the other also increases by a proportionate amount. In the equation above, if we double r, we'll have to double the value of A^2 for the equation to remain valid. So the equation represents the directly proportional relationship between r and A^2.

2) The rate is inversely proportional to B, and inversely proportional means as one value increases, the other decreases by a proportionate amount. In the equation above, if we double r, we'll have to halve the value of B for the equation to remain valid. (Multiplying the left side by 2 is the same as dividing the right side by 1/2). So the equation represents the inversely proportional represent between r and B.

Now let's plug in values.
Let A = 10 and B = 2.
r = (10^2)/2 = 100/2 = 50.
If we increase B by 100%, new B = 4.
If we want the rate to stay the same, we get:
50 = (A^2)/4
A^2 = 200
New A = Root200 = 10Root2 = 14 approximately

% change in A = Difference/(Original A) * 100 = (14-10)/10 * 100 = 4/10 * 100 = 40%.

The correct answer is D.
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by outreach » Sat Jul 31, 2010 7:14 am
A^2/B is ratio of chemical A to chemical B that must be maintained to keep this reaction rate unchanged.
R1 = the original ratio of the chemical reaction = A^2/B
R2 = a variation of this ratio in which B is doubled = A1^2/B(2)

A^2 / B = A1^2/2B2
A^2 * 2 = A1^2
A * sqrt 2 = A1
sqrt 2=1.4
1.4A=A1
D
emiflo wrote:hi guys. pls could someone solve this for me. the rate of a chemical reaction is directly proportional to the square of concentration of chemical A and inversely proportional to the concentration of chemical B. If the concentration of chemical B is increased by 100 percent, which of the following is closest to the percentage change in concentration of chemical A required to keep the reaction unchanged.
A 100% decrease
B 50% decrease
C 40% decrease
D 40% increase
E 50% increase
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by mepinoargote » Thu Sep 02, 2010 6:36 pm
directly proportional means that as one value increases, the other also increases by a proportionate amount.
Just a quick question, so lets say 2 values are proportional, if the first increases by 10%, the other must increase by 10%?? i get that when one value increases the other also increases, but is it always by the same amount?? Can you clarify this? thanx!
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by neerajkumar1_1 » Thu Sep 02, 2010 7:45 pm
mepinoargote wrote:
directly proportional means that as one value increases, the other also increases by a proportionate amount.
Just a quick question, so lets say 2 values are proportional, if the first increases by 10%, the other must increase by 10%?? i get that when one value increases the other also increases, but is it always by the same amount?? Can you clarify this? thanx!
it depends on what the proportion is...
for e.g ... in the same question if r is only proportional to A then
r=A/B

and now if u increase B by 100% then new rate = A/2B
to keep the rate constant A will also need to be doubled... Hence A will increase by the same amount....

If u want u can look at it algebraically ...

when we say r=a/b or any such formula...
u need to see how any two terms relate to each other...

in this case we need to keep r constant...

so a = rb
now if u notice a is directly proportional to b

so a increase or decrease in a or b is going to make a similar inc or dec in the other...


Also the amount of change will vary if the proportionality is different...

so in case a^2= kb

now the term a^2 is proportional to b...
Hence an increase or dec in b will make the same change to a^2... but then the actual quantity of a will only be under root of that change in a^2...


Hope this helps...
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