A bag contains a mixture of beans and pulses. To achieve 20 percent be

Hi pushpitkc,

Though I got the correct answer, but I am not sure if my approach is correct. Please tell me if there is any flaw in the below mentioned approach.

Initial : 40%(Beans) + 60%(Pulses)
Final : 20%(Beans) + 80%(Pulses)

Using allegation:
(w1/w2)=(100-80)/(80-60) w1-original weight of pulses in the mixture, w2-weight of pulses added to the mixture, concentration of pulses added=100%
(w1/w2)=1:1

Hence w2=1/2=50%

Hence 50% of the mixture should be removed.

Ans. C

Thanks
Dkingdom

Hi Dkingdom,

I don't seem to understand what you have done.
Also, we needn't solve for the quantity of pulses to be added
in order to achieve 20 percent beans in the mixture.

But for all DS questions, if either A or B is sufficient to answer the question
, we do not need to test for C. Option A is the correct answer.
Please ignore this if that was a typo!

Hope that helps

I am sorry! I was supposed to write A.
Using allegation method, I have calculated the additional amount of pulses needed in the mixture to reduce the concentration of Beans from 40% to 20%.
Does it make sense now? I hope I did not make a complete mess of it!

Bunuel

Is this a common question format on the gmat? Or is there a known OG question that is strikingly similar in wording to this?

I was stumped because I didn't know that when you remove a percentage of the total mixture, you are removing a uniform amount from the entire mixture.
I thought maybe it would tell us that we are removing parts in a distributed manner.

If so, happy to just assume from now on.

Hello,
I have a question with the first statement. Why not just taking out 20% of beans and replace it with pulses? why you have to take out that 30% of pulses and replace it again? I'm a little bit confused. I would appreciate if you might explain. Thank you.

Keep in mind the general criteria to face, GMAT Data Sufficiency questions.

Consider ideal mix:
20% beans + 80% legumes

1) Originally blend of 40% beans + 60% legumes

If we consider 40 beans and 60 legumes in the original mix.
Removing half the beans we have 20 beans left, removing half the legumes we have 30 legumes left.

If we add the amount of mixture withdrawn (50 units) replaced by legumes. We have 20 beans + (30 +50) legumes

that is, 20% beans and 80% legumes, which is what is requested.

Then you have to remove 50% of the mixture (50 units: 20 beans and 30 legumes) and replace it (50 units) with legumes.

So 1) is enough.

2) Knowing the total of the mixture does not allow us to form what is requested. IS NOT SUFFICIENT.

Answer A

A bag contains a mixture of beans and pulses. To achieve 20 percent beans in the mixture, what percent of the mixture should be taken out and replaced with pulses?

(1) The mixture originally has 40 percent beans and 60 percent pulses.
(2) Total quantity of the mixture is 20 lb.

Formula for replacement :
\(F/I\) = (1 - \(B/A\))^N
F = Final concentration of the element in the mixture that is being reduced
I = Initial concentration of the element in the mixture that is being reduced
B = Amount of mixture that is being replaced
N = No of iterations
Since only the percentage of the quantity replaced is asked we can assume the mixture total to be 100

(1) The mixture originally has 40 percent beans and 60 percent pulses.
Calculating from the pov of the element whose concentration is being reduced - Beans Since Pure pulses is being added to the replaced mixture
\(20/40\) = 1 - \(B/100\)
\(1/2\) = 1 - \(B/100\)
B = 50
Suff

(2) Total quantity of the mixture is 20 lb.
Not Sufficient we dont have the final ratio and we have 2 unknowns

A