Three solutions A, B and C having equal volume are made up

Question

Three solutions A, B and C having equal volume are made up of water and alcohol in the ratio 1:3, 2:5 and 3:4 respectively. 24 litres of A is taken out and mixed into B, then the composition of water and alcohol in B changes to 11:29. Had 14 litres been taken from the original B solution and mixed into C, what would had been the final ratio of C?

A. 2:3
B. 3:4
C. 4:5
D. 5:6
E. 6:7

(Source : Wizako)

A. 2:3
B. 3:4
C. 4:5
D. 5:6
E. 6:7

(Source : Wizako)

ThatDudeKnows · Accepted Answer

Read my signature below. Quantitative REASONING.

B has a smaller ratio than does C. We are going to add some of B to C. Will C stay at 3:4? No, so answer choice B is wrong. Do we want something more than 3:4 or less than 3:4? Less than, so answer choices C, D, and E are wrong. Answer choice A. . . . Orrrrrrr, go ahead and spend a bunch of time showing that you are a "quantitative" master...both ways get the same points on the test...your choice!

Can,Will · Answer

gmatophobia

stuck with this approach

ThatDudeKnows · Answer

AnujL

11:29, huh? I’m going out on a limb that once we add 24 liters to B, the volume of B is a multiple of 40.

Could it be 40? If it were, that would mean that we started with 16 liters in B and at least 24 liters in A. But the starting amounts are equal, so this doesn’t work.

Could it be 80? If it were, that would mean that we started with 56 liters in B (and therefore 56 liters in each). Hmm, see if you can make your ratio math work from here…(hint: you can!).

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Can,Will · Answer

chetan2u 
help with this one

ThatDudeKnows · Answer

AnujL

Did you try it with 56 liters of each, as I suggested?!?

Start
A: 14 water, 42 alcohol
B: 16 water, 40 alcohol
C: 24 water, 32 alcohol

Move 14 from B to C, so 4 water and 10 alcohol.

C: 28 water, 42 alcohol

28:42 = 2:3

Answer choice A.

Posted from my mobile device

chetan2u · Answer

24 litres of A 1:3 means 6:18 is mixed in B 2:5.
 Finding y and z 
Thus, 6+2y=11z and 18+5y=29z
Or 30+10y=55z and 36+10y=58z
Thus, 6=3z or z=2 and 6+2y=11*2 or y=8

Total volume of each 
(2+5)*8=56

14 litres of B2:5 means 4:10 is mixed into 3:4 of C. 3:4 of C, total of 56, means 24:32.
Thus final ratio = 4+24 : 10+32 = 28:42 = 2:3

A

KarishmaB · Answer

With 3 solutions, approximation would be the way to go else it will take too much time. Though here the options are such that no work is required.

Equal volumes of all 3 are available.

A = 1:3 i.e. 3/4 = 75% alcohol
B = 2:5 i.e. 5/7 = about 72% alcohol
C = 3:4 i.e. 4/7 = about 58% alcohol (you should know fraction percent equivalents:   https://youtu.be/HxnsYI1Rws8  
 
When 24 ltr of A is mixed with B, alcohol percentage will be between 72 and 75.
When 14 ltr of B is mixed into C, alcohol percentage will be between 72 and 58 and closer to 58.

A. 2:3 
-> 3/5 = 60% this is between 58 and 72

B. 3:4
-> 4/7. This is the same as C i.e. 58% approximately. But alcohol concentration will be more than this because B is added to it.

C. 4:5
-> 5/9 is less than 4/7 because numerator has increased by 25% but denominator has increased by a higher percentage. 
Same will be true for all other options too. Since answer cannot be less than 58%, options (C), (D) and (E) are eliminated too.

Answer (A)

Three solutions A, B and C having equal volume are made up

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GMAT Problem Solving (PS) Questions

Three solutions A, B and C having equal volume are made up

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