A solution contains 8 parts of water for every 7 parts of

x=fraction of solution replaced
8/15-8x/15+x=9/15
x=1/7
1/7*15=2.14 parts of solution replaced
C

HI Karishma,

I am just wondering if we can apply scale method to this problem?! The reason is - we know desired %, we have relevant proportions of water & lemonade which can be converted into %
Or Is my approach not right?

Responding to a pm:


Sure, the use of "parts" is fine. All measurements are in terms of the same "part". That part could 1 ml, 10 ml or 100 ml etc. There are total 15 of these parts in the solution.
When we get f = 1/7, f is the fraction of the solution removed. (1/7)th divides the whole solution into 7 equal parts and removes 1. These parts are not the same as the parts above. The total solution has 15 of the "parts" discussed above. Of these 15 parts, we remove 1/7th which is 2.14 "parts".

use C final = C initial (Volume original / volume final ) , final concentration is 40/100 , initial concentration is 7/15 , volume original is volume of the solution after removing part of it and before adding water to dilute it , V final is the total volume after replacing of x parts of the solution by x parts of water and thus total volume remains the same ( 15)

40/100 = 7/15 ( 15-x / 15 ) thus x = 15/7 = 2.14

y = amount removed from original = amount replaced with water
x = original amount

(8/15)x - (8/15)y + y = (3/5)x
(8/15)x + (7/15)y = (3/5)x
8x+7y = 9x
7y = x --> y = (1/7)x

There are 15 parts in the original --> so... 15/7 is our answer

C.

1. (Initial quantity of solution- quantity of solution removed)* strength of solution + (Quantity of water added *strength of water)/ Initial quantity= 40/100
2. Let x be the initial quantity and y be the quantity removed
3.( (x-y)*7/15 + y*0) / x = 0.4, x/y=7/1
4. If initial quantity is 7 parts, 1 part is removed, if 15 parts 15/7=2.14

Great solution. But I think you meant unitary method.

VeritasKarishma : Can we do this with scaling method? I've tried it, but got stuck somewhere in the middle.

Taking lemonade syrup into consideration,

7/15.....................4/10............................0

got the ratio as 1:6, but not sure how to get to the answer from here.
Since this method is a real time saver i would love to know how can we solve this using this scaling method.

Please help.

I have discussed the scale method for it here:
https://gmatclub.com/forum/a-solution-c ... l#p1624227

Hi,

Suppose if the solution is 30L then water = 16L and lemonade syrup = 14L
Also, we have to make the lemonade 40% of the solution.

so, (14-x)/30 = 40%
x = 2

What am I doing wrong? can you anyone please explain?

Hi Krish728,

The 'key' this question is that since we're dealing with a mixture, you cannot simply remove "1 part water" or "1 part syrup" - whatever you remove is a mix of the two ingredients. Your equation assumes that you can 'pour out' pure syrup from the mixture - which you can't.

My explanation (higher up in the thread) assumed that there were 15 liters total, but the same approach can be used if there were 30 liters total:

The prompt tells us to REPLACE some of the existing mixture with pure water (with the goal of turning the new mixture into a 40% syrup mix.
To start, we have 30 total liters -->a mixture that is 16 liters water and 14 liters syrup.

If we pour 1 liter of this mixture into a glass, we would have a liquid that is 14/30 = 7/15 syrup (so a little less than half syrup).

For the mixture to be 30 total liters and 40% syrup, we need the mixture to be 18 liters water and 12 liters syrup. In basic math terms, we need to pour out enough of the mixture that we remove 2 full liters of syrup; when we pour an equivalent amount of water back in, we'll have 30 total liters (and 12 of them will be syrup). Since each liter is 7/15 syrup......

We need to remove (2)(15/7) = 30/7 liters and replace them with 30/7 liters of pure water.

30/7 is a little more than 4 liters (about 4.28 liters). Remember that the prompt talks about the number of "PARTS" that need to be replaced though (not the number of liters) - since you 'doubled' all of the numbers to start off with 30 liters, we then have to reduce the result (by dividing by 2) to get the correct answer. 4.28/2 = 2.14

Final Answer:

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