Solution A contains 18 ounces of alcohol ...

[Night reader]

Solution A contains 18 ounces of alcohol and 32 ounces of water. Solution B contains 72 ounces of water and 8 ounces of alcohol. What percent of Solution B must be added to Solution A so that the resulting mixture contains 5/7 water?

(GMAT drill: mixture word problems)

[rishab1988]

solution A water = 32
solution A alcohol=18

solution A contains =32/50 [fraction of mixture water] =16/25

solution B water =72
solution B alcohol=8

solution B contains = 72/80 [fraction of mixture water] =9/10

Lets x be the percentage of solution B that is added to A to get a ratio of 5/7 [water to total micture]

16/25 + x/100 * [9/10] =5/7

9x/1000 = (125-112)/175
9x = (13*1000)/175
x = 520/63%

or x = approx 8%

[Night reader]

solution A water = 32
solution A alcohol=18

solution A contains =32/50 [fraction of mixture water] =16/25

solution B water =72
solution B alcohol=8

solution B contains = 72/80 [fraction of mixture water] =9/10

Lets x be the percentage of solution B that is added to A to get a ratio of 5/7 [water to total micture]

16/25 + x/100 * [9/10] =5/7

9x/1000 = (125-112)/175
9x = (13*1000)/175
x = 520/63%

or x = approx 8%

I can not understand your solution; 8% of what?

rethink problem

[rishab1988]

I made a blunder.

In solution A Water/Total = W/T=W/W+A

Now let the amount of water from B added =x
let the amount of alcohol added from B =y

Then as the question states -> (W+x)/(W+A+x+y) = 5/7 [right?]

7W+7x = 5W+5A+5x+5y
2W-5A = 5y-2x

Now let the % of solution B added = a

Water from Solution B (x) = a/100 *72
Alcohol from Solution B (y) = a/100*8

2*32-5*18 = a/100 [40-144]
64-90 = -(104)/100 *a
a = (26*100)/104 = 25%

Confirmation:

25% of 72 = 18
25% of 8 = 2

W+x/W+A+x+y = 50/70 = 5/7

[vishal_2804]

Rishab is perfect, 8% of sol. B to be added to sol A to get desired mixture

[rishab1988]

DUDE THIS IS A MUCH TOUGHER QUESTION THAN I PREVIOUSLY THOUGHT!!!!!

[Night reader]

Rishab is perfect, 8% of sol. B to be added to sol A to get desired mixture

Vishal: Rishab wasn't perfect first time.

answer 25%=1/4 is correct. It's not tough though, only 300-500 level

[rishab1988]

Who rated that problem -300 to 500?

If it is of that level is rated incorrectly.

3 out of 3 guys solved it incorrectly. My MGMAT quant score [48,48,48,51,51].Last GMAT attempt score -49.

A 300-500 question is solved correctly by most of the people.

The level of a question depends on the % of people who answer it correctly and not what you perceive that question to be theoretically.

The most accurate rating of levels,I believe,is done by MGMAT.A 700-800 questions is truly of that level and by no means a cakewalk.Similarly on MGMAT 600-700 questions,on which my accuracy is more like 90%,is still easier than this question.

Anyway,our objective was to understand the concepts and that we did.

Mind you this question with,answer choices,would have been a cakewalk for me,because i almost always solve such questions by pluggin-in. Solving algebraically is a much more tedious task.

In plugging in I would have taken 25% of 80 to get 20 and then 9/10 of 20 to get 18 and simply added 18 to 32 to get num=50 and 2 and 18 to denominator to get 70.The % that would give me 5/7 would have been the answer.

[rishab1988]

Who rated that problem -300 to 500?

If it is of that level is rated incorrectly.

3 out of 3 guys solved it incorrectly. My MGMAT quant score [48,48,48,51,51].Last GMAT attempt score -49.

A 300-500 question is solved correctly by most of the people.

The level of a question depends on the % of people who answer it correctly and not what you perceive that question to be theoretically.

The most accurate rating of levels,I believe,is done by MGMAT.A 700-800 questions is truly of that level and by no means a cakewalk.Similarly on MGMAT 600-700 questions,on which my accuracy is more like 90%,is still easier than this question.

Anyway,our objective was to understand the concepts and that we did.

Mind you this question with,answer choices,would have been a cakewalk for me,because i almost always solve such questions by pluggin-in. Solving algebraically is a much more tedious task.

In plugging in I would have taken 25% of 80 to get 20 and then 9/10 of 20 to get 18 and simply added 18 to 32 to get num=50 and 2 and 18 to denominator to get 70.The % that would give me 5/7 would have been the answer.

[Night reader]

answering 400-level question incorrectly doesn't kill the quant scaled score

Solution A contains 18 ounces of alcohol and 32 ounces of water. Solution B contains 72 ounces of water and 8 ounces of alcohol. What percent of Solution B must be added to Solution A so that the resulting mixture contains 5/7 water?

(GMAT drill: mixture word problems)


Solution A contains 18 ounces of alcohol and 32 ounces of water ---- 18/32
Solution B contains 72 ounces of water and 8 ounces of alcohol ----- 8/72

What percent of Solution B must be added to Solution A so that the resulting mixture contains 5/7 water (simplify further 5/7 water~ 2/7 alcohol~ alcohol/water 2/5 ---- this is very simple ratio conversion expected at 300-400 level)

equation is almost set: (18+8x)/ (32+72x) = 2/5
x=13/52, x=1/4 (25%) or 20 mill.

[rishab1988]

The question is why would I do algebra when I have the answers in front of me.

Doing this by algebra is sheer wastage of time

Setting up and equation and solving those equations would take you 2-3 minutes.Plugging in this question can be solved in under 1 minute.

Talking about equations

Combinatorics have the simplest equations but why do they only appear only when you are doing well ? at-least 45+ scaled score +.Because their logic ,usually,tends to be the most complex.

GMAT is not equations.It is about logic...

[Night reader]

The question is why would I do algebra when I have the answers in front of me.

Doing this by algebra is sheer wastage of time

Setting up and equation and solving those equations would take you 2-3 minutes.Plugging in this question can be solved in under 1 minute.

Talking about equations

Combinatorics have the simplest equations but why do they only appear only when you are doing well ? at-least 45+ scaled score +.Because their logic ,usually,tends to be the most complex.

GMAT is not equations.It is about logic...

good generalization, I should have known that