A lab assistant at Wizard Labs, a leading chemistry research facility,

Question

A lab assistant at Wizard Labs, a leading chemistry research facility, is mixing a new batch of reagent for the upcoming experiment. She has access to Brand A, which comes in 30%, 50%, and 70% concentrations, and to Brand B, which comes in 20%, 40%, and 60% concentrations. She has an equal amount of each concentration for a given brand (the same amount at 30%, 50%, and 70% for A, for example), but she has twice as much of Brand B as Brand A. Once she picks the proper concentrations, she will use the entire amount of each, but only one concentration of each brand is used.

In the table below, select the concentration of Brand A and of Brand B to be used to create a reagent that is 50% concentrated.

In the table below, select the concentration of Brand A and of Brand B to be used to create a reagent that is 50% concentrated.

rocky620 · Accepted Answer

Let the quantity of Brand A solutions (of each concentration) be  100 , so the quantity of Brand B solutions (of each concentration) will be  200

Quantity of reagent in Brand A concentrations  
30% conc = 30
50% conc = 50
70% conc = 70

Quantity of reagent in Brand B concentrations  
20% conc = 40
40% conc = 80
60% conc = 120

When she mixes the solution of both Brands, total qty of the resultant mixture will be 300. Since, the resultant will have 50% concentration of the reagent, the quantity of the the reagent will be 150.

Only the below combinations will work.
 Combo-1  30% conc of Brand A with qty  30  & 60% conc of Brand B with qty  120 
 Combo-2  70% conc of Brand A with qty  70  & 40% conc of Brand B with qty  80

20% -   If this is the Conc of B (the qty will be 40), 110% of A needs to be mixed, which is impossible. Eliminate 
 40% -  As per the Combo-2, This will be the concentration of Brand B to be used  
 50% -   If this is the Conc of A (the qty will be 50), 50% of B needs to be mixed, which is not a concentration given. Eliminate 
 60% -   If this is the Conc of B (the qty will be 120), 30% of A needs to be mixed, which is not in the Options. Eliminate 
 70% -  As per the Combo-2, This will be the concentration of Brand A to be used

Concentration of Brand A - 70%
Concentration of Brand B - 40%

nikitachaudhary · Answer

30% of a and 40% of b 
70% of a and 60% of b

Posted from my mobile device

sayan640 · Answer

A => 30 % , 50% or 70%
B=> 20% , 40% and 60%

lets say , y% of A is mixed with z% of B to get the 50% in the combined reagent.

She has twice as much of Brand B as Brand A.

Hence , we get y + 2z= 150

lets try different values of z and y.
If z = 60 , then 30 + 120 = 150 
But there is no value of y as 30. Hence z cant be 60.

Lets take  y=70 and z=40 , 70 + 40*2 = 150 
 It works and is the answer. ( Keep trying only with the 6 values given i.e 30 , 50 , 70 , 20 , 40 and 60 ).

GMATinsight   chetan2u   KarishmaB  Am I right in my approach ?

cheshire · Answer

Yep this is correct. Your diagram is similar to the alligation method which might be faster but this is a good approach.

anushree01 · Answer

Good question, my learning is to not fixate and start eliminating, as my first thought was since its 50% net, A must be less which is incorrect

Mylastdance · Answer

Take A = 100 and B = 200. Total quantity = 300.

Required reagent = 50% × 300 = 150.

Check the options:
A = 50% → contributes 50, so B must contribute 100 → B = 50%. Not an option.
A = 70% → contributes 70, so B must contribute 80 → 80/200 = 40%. Valid.

Therefore, A = 70% and B = 40%.

A lab assistant at Wizard Labs, a leading chemistry research facility,

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A lab assistant at Wizard Labs, a leading chemistry research facility,

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

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My Rewards