3 containers have their volumes in the ratio 3:4:5.. They are full of mixtures of milk and water. The mixture contain milk and water in the ratio of (4:1), (3:1) and (5:2) respectively. the contents of all these 3 containers are poured into a fourth container. the ratio of milk and water in the 4th container is
A 4:1
B 151:48
C 157:53
D 5:2
E none of these
ratios
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 138
- Joined: Mon May 01, 2017 11:56 pm
- Thanked: 4 times
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi vaibhav101,
We're told that 3 containers have their volumes in the ratio 3:4:5 and the 3 mixtures contain milk and water in the ratio of (4:1), (3:1) and (5:2) respectively. We're asked for the ratio of all milk to all water in the 3 containers. This question can be solved in a couple of different ways, including by TESTing VALUES.
The most 'ugly' of the 3 ratios is 5:2 (for every 5 parts of milk, there are 2 parts of water - with a total of 7 parts). With the given 3:4:5 ratio of total volumes, we can set the largest volume to 35 liters (which is 5x7, and will help make the math for the other containers a bit easier to deal with). Thus, the ratio of the volumes will be 21:28:35.
IF....
the containers hold 21 liters, 28 liters and 35 liters respectively, then
the 1st container holds (4/5)(21) liters of milk and (1/5)(21) liters of water
the 2nd container holds (3/4)(28) liters of milk and (1/4)(28) liters of water
the 3rd container holds (5/7)(35) liters of milk and (2/7)(35) liters of water
Total milk = 84/5 + 21 + 25 =
84/5 + 46 =
84/5 + 230/5
314/5
Total water = 21/5 + 7 + 10 =
21/5 + 17 =
21/5 + 85/5 =
106/5
Thus, the ratio of total milk to total water = (314/5)/(106/5) = 314/106 = 157/53
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
We're told that 3 containers have their volumes in the ratio 3:4:5 and the 3 mixtures contain milk and water in the ratio of (4:1), (3:1) and (5:2) respectively. We're asked for the ratio of all milk to all water in the 3 containers. This question can be solved in a couple of different ways, including by TESTing VALUES.
The most 'ugly' of the 3 ratios is 5:2 (for every 5 parts of milk, there are 2 parts of water - with a total of 7 parts). With the given 3:4:5 ratio of total volumes, we can set the largest volume to 35 liters (which is 5x7, and will help make the math for the other containers a bit easier to deal with). Thus, the ratio of the volumes will be 21:28:35.
IF....
the containers hold 21 liters, 28 liters and 35 liters respectively, then
the 1st container holds (4/5)(21) liters of milk and (1/5)(21) liters of water
the 2nd container holds (3/4)(28) liters of milk and (1/4)(28) liters of water
the 3rd container holds (5/7)(35) liters of milk and (2/7)(35) liters of water
Total milk = 84/5 + 21 + 25 =
84/5 + 46 =
84/5 + 230/5
314/5
Total water = 21/5 + 7 + 10 =
21/5 + 17 =
21/5 + 85/5 =
106/5
Thus, the ratio of total milk to total water = (314/5)/(106/5) = 314/106 = 157/53
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Container 1 : Container 2 : Container 3 = 3:4:5.vaibhav101 wrote:3 containers have their volumes in the ratio 3:4:5.. They are full of mixtures of milk and water. The mixture contain milk and water in the ratio of (4:1), (3:1) and (5:2) respectively. the contents of all these 3 containers are poured into a fourth container. the ratio of milk and water in the 4th container is
A 4:1
B 151:48
C 157:53
D 5:2
E none of these
In Container 1, M:W = 4:1, implying that water constitutes 1/5 of Container 1.
In Container 2, M:W = 3:1, implying that water constitutes 1/4 of Container 2.
In Container 3, M:W = 5:2, implying that water constitutes 2/7 of Container 3.
The LCM for the denominators of the blue fractions = 5*4*7 = 140.
To make the math easier, multiply the red ratio by this LCM:
Container 1: Container 2: Container 3 = 3(140) : 4(140) : 5(140) = 420:560:700.
Resulting total volume = 420+560+700 = 1680.
Applying the blue fractions to 420:560:700, we get:
Water in Container 1 = (1/5)(420) = 84.
Water in Container 2 = (1/4)(560) = 140.
Water in Container 3 = (2/7)(700) = 200.
Total water = 84 + 140 + 200 = 424.
Thus:
Total milk = (total volume) - (total water) = 1680 - 424 = 1256.
Resulting ratio:
M:W = 1256:424 = 157:53.
The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
We can let the volume of the largest container be 35, thus the volume of the middle one is 28 and the volume of the largest one is 21.vaibhav101 wrote:3 containers have their volumes in the ratio 3:4:5.. They are full of mixtures of milk and water. The mixture contain milk and water in the ratio of (4:1), (3:1) and (5:2) respectively. the contents of all these 3 containers are poured into a fourth container. the ratio of milk and water in the 4th container is
A 4:1
B 151:48
C 157:53
D 5:2
E none of these
Since the milk and water in the smallest container are in a ratio of 4:1, we have:
4x + x = 21
5x = 21
x = 4.2
So, we have milk = 16.8 and water = 4.2 in the smallest container.
Since the milk and water in the middle container are in a ratio of 3:1, we have:
3y + y = 28
4y = 28
y = 7
So, we have mike = 21 and water = 7 in the middle container.
Since the milk and water in the largest container are in a ratio of 5:2, we have:
5z + 2z = 35
7z = 35
z = 5
So, we have mike = 25 and water = 10 in the largest container.
When the contents of all these 3 containers are poured into a fourth container, we have milk = 16.8 + 21 + 25 = 62.8 and water = 4.2 + 7 + 10 = 21.2. Thus the ratio of milk and water is:
62.8/21.2 = 628/212 = 157/53
Answer: C
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews