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# m04#08

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Director
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18 Apr 2009, 01:41
3
KUDOS
A 10 liter mixture of cranberry juice and water contains juice and water in the ratio of 3 : 2. 5 liters of the mixture are removed and replaced with pure juice and the operation is repeated once more. At the end of the two removals and replacements, what is the ratio of juice to water in the resulting mixture?

(A) 5 : 3
(B) 6 : 4
(C) 8 : 2
(D) 17 : 3
(E) 9 : 1

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

My solution:
Original mixture has CJ:6 lts and water 4 lts.
step 1:
5 lts are removed.Therefore,
CJ remaining: 6 - {3/5 x 5} = 3lts.
Water remaining: 4 - {2/5 x 5}=2lts.
now 5 lts of CJ are added bringing the mixture to CJ:8 lts and water:2 lts.

step 2:
5 more lts are removed.
amount of CJ removed: 8 x 3/5 = 4.8 lts
amount of wtr removed:8 x 2/5= 0.2lts.
5 lts of CJ added Resulting in CJ: 8.20lts and 1.80 lts of water.

where did i mess up???
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20 May 2010, 00:12
4
KUDOS
ratio is 3:2 and mixture ir 10 lit. It can be expressed as 3x+2x=10 where x is a constant.
5x=10 => x=2. We have 6 lit juice and 4 lit water in 10 lit mixture.

Similarly for 5 lit, we have 3 lit juice and 2 lit water. Taking out this 5 lit means we are left with 6-3=3 lit juice and 4-2 = 4 lit water in the remaing 5 lit mixture.

Now we add 5 lit pure juice , which means the total mix is again 10 lit with the new composition as 3+5=8 lit juice and 2 lit water. Hence the new ratio is 8:2 or 4:1

Now if we take out 5 lit of mixture again. it means we are taking out 4 lit juice and 1 lit water. So the remaing is 4 lit juice and 1 lit water.

Again adding 5 lit of juice to it.. new comp is 4+5 =9 lit juice and 1 lit water.

Hence 9:1
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27 May 2013, 18:15
2
KUDOS
A 10 liter mixture of cranberry juice and water contains juice and water in the ratio of 3 : 2. 5 liters of the mixture are removed and replaced with pure juice and the operation is repeated once more. At the end of the two removals and replacements, what is the ratio of juice to water in the resulting mixture?

10 = 6Juice + 4 Water

When 5 litre is removed ,because the ratio is 3:2 , 3L Juice and 2L Water is removed and when 5L juice is added then the above equation becomes

10=8Juice + 2 Water

In the second go , the ratio now is 4:1 , when we take out 5L of the mixture , 4L of Juice and 1L of Water is taken out and when we add 5L of pure juice the above equation becomes

10 = (8-4+5)Juice + (2-1+0)Water

Which is 9:1 and hence E is the answer
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20 Apr 2009, 17:53
1
KUDOS
Here's a simpler way to look at this:

Ratio : J:W = 3:2 In 10 liters that will be 6J and 4W

6J 4W , Remove 5 . 3J 2W remains
+5J
New Ratio: 8J 2W Remove 5 liters, 4J 1W remains
+5J
--------
Final: 9J 1W
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19 May 2010, 13:57
1
KUDOS
yep.. this is much simpler question to answer as the ratios result in very nice integers....

first round: 5 litres removed => remaining is 3L juice + 2L water
add 5L more juice => now 8L juice + 2L water => 8:2
second round: now remaining is 4L juice+ 1L water (5L is removed)...
add 5L more juice => 9L juice+1L water =>final ratio 9:1
Manager
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19 May 2010, 15:15
1
KUDOS
So without looking at the reveal I would say this. First of all we have ten liters in 3:2 ratio which is the same as 6L juice and 4 liters water. Then we take away 5L of fluid leaving 3L juice and 2L water and then add 5L juice. Now after one cycle we have 8 L juice and 2L water. We take away 5 L of fluid retaining 4L juice and 1L water. Then we add 5L juice. Now we have 9L juice and 1 L water. Ratio 9:1. ANSWER #5.

Thanks,
Skip
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18 Apr 2009, 17:05
J = (3/5)(10) = 6
W = 4

after 5 liter mixture is removed and 5 liter juice is added:
J = 6 - 5(3/5) + 5 = 8
water = 4 - 5(3/5) = 2

after one more time 5 liter mixture is removed and 5 liter juice is added:

J = 8 - 5(4/5) + 5 = 9
water = 2 - 5(1/5) = 1

so J:W = 9:1. Thats E.
Hope you got it.

suyashjhawar wrote:
A 10 liter mixture of cranberry juice and water contains juice and water in the ratio of 3 : 2. 5 liters of the mixture are removed and replaced with pure juice and the operation is repeated once more. At the end of the two removals and replacements, what is the ratio of juice to water in the resulting mixture?

1. 5 : 3
2. 6 : 4
3. 8 : 2
4. 17 : 3
5. 9 : 1

My solution:
Original mixture has CJ:6 lts and water 4 lts.
step 1:
5 lts are removed.Therefore,
CJ remaining: 6 - {3/5 x 5} = 3lts.
Water remaining: 4 - {2/5 x 5}=2lts.
now 5 lts of CJ are added bringing the mixture to CJ:8 lts and water:2 lts.

step 2:
5 more lts are removed.
amount of CJ removed: 8 x 3/5 = 4.8 lts
amount of wtr removed:8 x 2/5= 0.2lts.
5 lts of CJ added Resulting in CJ: 8.20lts and 1.80 lts of water.

where did i mess up???

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19 May 2010, 08:44
Your approach is somewhat correct. What you're messing up in the 2nd round is that you're keeping the ratio of Juice to Water at 3:2, as per the original ratio, instead of realizing that the ratio of Juice to Water is now different in the 2nd time. The ratio had changed after we removed 5 liters of the mixture and replaced it with Juice in the first round.

Hope that helps.

suyashjhawar wrote:
GMAT TIGER wrote:
J = (3/5)(10) = 6
W = 4

after 5 liter mixture is removed and 5 liter juice is added:
J = 6 - 5(3/5) + 5 = 8
water = 4 - 5(3/5) = 2

after one more time 5 liter mixture is removed and 5 liter juice is added:

J = 8 - 5(4/5) + 5 = 9
water = 2 - 5(1/5) = 1

so J:W = 9:1. Thats E.
Hope you got it.

suyashjhawar wrote:
A 10 liter mixture of cranberry juice and water contains juice and water in the ratio of 3 : 2. 5 liters of the mixture are removed and replaced with pure juice and the operation is repeated once more. At the end of the two removals and replacements, what is the ratio of juice to water in the resulting mixture?

1. 5 : 3
2. 6 : 4
3. 8 : 2
4. 17 : 3
5. 9 : 1

My solution:
Original mixture has CJ:6 lts and water 4 lts.
step 1:
5 lts are removed.Therefore,
CJ remaining: 6 - {3/5 x 5} = 3lts.
Water remaining: 4 - {2/5 x 5}=2lts.
now 5 lts of CJ are added bringing the mixture to CJ:8 lts and water:2 lts.

step 2:
5 more lts are removed.
amount of CJ removed: 8 x 3/5 = 4.8 lts
amount of wtr removed:8 x 2/5= 0.2lts.
5 lts of CJ added Resulting in CJ: 8.20lts and 1.80 lts of water.

where did i mess up???

did'nt get the later part dude..missing something when the things getting replaced the second time.
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20 May 2010, 05:55
10 lit Juice = 6lit Juice + 4 lit Water
5 lit taking out
= 3lit + 2 lit water
and 5 lit pure juice added
= 8lit + 2lit water
5 lit taking out
= 4lit + 1 lit water
and 5 lit pure juice added
= 9lit + 1lit water

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SD

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20 May 2010, 16:39
The best answer is 9:1 as explained by all previous posts.
I don't have any problem with this one.
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20 Aug 2010, 02:08
Its E.

T J W
10 6 4
5 3 2 (5 litres removed)
10 8 2 (5 litres added)
5 4 1 (5 litres removed)
10 9 1 (5 litres added)

So the ratio of J to W is 9:1!
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23 May 2011, 04:38
Initially, J - 6L, W - 4 L

1st time -> 5L was removed

=> 3L J + 2L W was removed

Then after adding 5 L of J -> 8L J + 2 L W

2nd time -> 5L was removed

=> 4L J + 1 L W was removed

=> Total 9L J + 1 L W

So ratio = 9:1

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23 May 2011, 04:48
Removing half of mixture and replacing it with pure juice simply removes half of water. Repeat it twice and you get 1/4 of initial amount or 1/10 of total.
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23 May 2011, 07:30
1st - 60 % juice ; 40% water in 10 litres
after 5 litres is removed; the composition still remains same
2nd - 5 litre pure juice (100%) is added
in resultant mixture; juice= (60*5)/100 + 5 = 8 and water = 40 * 5/100 = 2
i.e. 80-20% in 10 litres
again after 5 litres is removed; the composition still remains same
3rd - 5 litre pure juice (100%) is added
in resultant mixture; juice = (80*5/100) + 5 = 9 and water =20*5/100 = 1
i.e. 9:1
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23 May 2011, 08:28

No need of any explaination everyone knows how to solve it.
Lets try a little different one. Give it a try
posting.php?mode=post&f=140
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24 May 2011, 07:59
J:W=3:2
So 10 litter= 6J + 4W
So 10 Litter=6J-3J+5J+4W-2W
=8J+2W
New Ratio for 5 litter
J:W= 4:1

10 Litter= 8J-4J+5J+2W-1W
=9J+1W
=9:1
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18 Apr 2012, 12:10
so first for total 10 lts of mix contain juice and water in the ratio 3:2 the for total 5 lts 3 lts of juice is there then for total 10 lts of mixture contain 6 lts of juice and remaining 4 lts of water(we can also calculate as juice but waste of time)

The ratio of Juice to water is 6:4

if 5 liters of mixture is removed then we can calculate the removing ratio of juice to water as for 10 lts we have 6 lts of juice so for 5 lts we can have 3 lts (5 is half of the 10 so the ratio of juice and water must also be halved ) and remaining 2 lts water

now in present mixture we have 3 lts of juice and 2 lts of water then 5 liters of juice is added to the resultant mixture after removing 5 lts of juice and water so if we add 5 lts of juice the present 3 lts the latest ratio of juice to water is 8:2

then from latest mixture again 5 lts or mixture is removed ie for 10 lts of mixture we have 8 lts of juice so for 5 lts we can remove 4 lts of juice (just halved) and 1 lts of water then the ratio of juice to water before adding pure juice is 4:1 then if we add 5 lts of juice to existing 4 lts the the total resulting juice would be 9 and remaining l ltr is water so final ratio is 9:1 i.e E.
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25 May 2012, 10:56
Given: Solution = 10 liters
Juice: Water = 3:2
So, Juice = 6 liters and Water = 4 liters

First Draw: Take out 5 liters of solutions. The remaining solution contains:
Juice = 3 liters and Water = 2 liters
Add 5 liters of juice. Resulting solutions will contain:
Juice = 8 liters and Water = 2 liters

Second Draw: Take out 5 liters of solutions. The remaining solution contains:
Juice = 4 liters and Water = 1 liters
Add 5 liters of juice. Resulting solutions will contain:
Juice = 9 liters and Water = 1 liters

So, Juice:Water = 9:1

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27 May 2013, 21:24
Seems like an easy one.

Initial J: 10*3/5 W 10*2/5
round1: J: 10*3/5*1/2+5 W 10*2/5*1/2
10 in the numerator and 5*2 in denominator cancel out
J: 8 W 2
round2: J: 8*1/2+5 = 9 W 2*1/2 =1

9:1

I know I could've calculated out the initial amounts, but I prefer to skip a step or two in the calculations when I can.
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28 May 2013, 10:23
Juice to Water Ratio is 3:2 which is 6 L of Juice and 4 L of Water in the total quantity of 10 L.
Step 1: Remove 5 L, which leaves 3 L of juice and 2 L of water.
Step 2: Add 5 L of only Juice, which makes 8 L of juice and 2 L of water.
Step 3: Remove 5 L, which leaves 4 L of juice and 1 L of water.
Step 4: Add 5 L of only juice, which make 9 L of juice and 1 L of water.

Re: m04#08   [#permalink] 28 May 2013, 10:23
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# m04#08

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