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Nice Ratio problem

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by chaitanya.mehrotra » Mon Jul 25, 2011 10:55 am
Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 30 white marbles. How many red marbles could be in bag A?
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6
8

OA 6
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by winniethepooh » Mon Jul 25, 2011 11:15 am
The answer is 6.

_______Red:White:Blue

Bag A-_ 1:__3
and ________2:____3

OR______2:__6:____9

Bag B-__1:__4

Total White marbles in the two bags = 30
So, in one Bag A there will be 30 * 6 /10 = 18 White Marbles (I get 10 by adding the ratio of White marbles in both bags)

As in Bag A 6 = 18
So__________2 = ?
= 18 * 2/6 = 6 Red marbles in Bag A.

Hence, 6.
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by chaitanya.mehrotra » Mon Jul 25, 2011 12:27 pm
winniethepooh wrote:The answer is 6.

_______Red:White:Blue

Bag A-_ 1:__3
and ________2:____3

OR______2:__6:____9

Bag B-__1:__4

Total White marbles in the two bags = 30
So, in one Bag A there will be 30 * 6 /10 = 18 White Marbles (I get 10 by adding the ratio of White marbles in both bags)

As in Bag A 6 = 18
So__________2 = ?
= 18 * 2/6 = 6 Red marbles in Bag A.

Hence, 6.
i dont think u can assume 6/10 directly .here you are ignoring the situation where Bag A ratios are multiplied by a different number and Bag B ratios by another number
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by winniethepooh » Mon Jul 25, 2011 1:19 pm
The information provided says that the total number of White marbles are 30.
In that case if I know that the ratios I have for White marbles is 10, why can I not multiply it by 6 then divide it by 10?(I have no option but to consider the number of items the same in absence of information)
Had this been a data sufficiency problem my answer would have been E.
But in problem solving I have to get an answer!

Also, you can multiply the ratios by a common factor 3.
You get in Bag A- R:W:B = 2:6:9 = 6:18:27

In Bag B- R:W: = 1:4 = 3:12.

White gives you 18 + 12 =30 and hence, Red = 6.
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by kevincanspain » Mon Jul 25, 2011 1:30 pm
chaitanya.mehrotra wrote:Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 30 white marbles. How many red marbles could be in bag A?
1
3
4
6
8

OA 6
We known that in bag a, the ratio r:w:b =2:6:9

Whereas in bag B r:w = 1:4

Use answer choices: 4 reds in A would be accompanied by 12 whites. This would mean that there are 18 whites in b (impossible). 6 reds in A would be accompanied by 18 whites, meaning that there would be 12 whites in B (possible)
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by MBA.Aspirant » Fri Aug 05, 2011 4:26 pm
R:W x:3x
W:B 2x:3x


R:W:B

2x:6x:9x 17x

bag 2

R:w x : 4x


6x+4x = 30

x = 3


bag 1

6:18:27


bag 2
3:12

12+18 = 30 white

R = 6
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by GMATGuruNY » Sat Aug 06, 2011 2:20 am
chaitanya.mehrotra wrote:Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 30 white marbles. How many red marbles could be in bag A?
1
3
4
6
8

OA 6
We can plug in the answers, which represent the number of red marbles in bag A and will indicate the number of white marbles in Bag A, since R:W = 1:3.

Answer choices:
R.......W
1.......3
3.......9
4.......12
6.......18
8.......24

Since W:B = 2:3 in Bag A, the number of white marbles must be even.
Eliminate A and B.

The total number of white marbles is 30.
Since R:W = 1:4 in Bag B, the number of white marbles in Bag B must be a multiple of 4.

Answer choices C, D and E:
W(A)......W(B)
12............18
18............12
24............6

Only answer choice D yields a multiple of 4 for the number of white marbles in Bag B.

The correct answer is D.
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