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Bag A contains red, white and blue marbles such that the red [#permalink]
 29 Jun 2007, 15:38
Question Stats:
61% (03:31) correct
38% (00:45) wrong based on 7 sessions
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? A. 1 B. 3 C. 4 D. 6 E. 8 OPEN DISCUSSION OF THIS QUESTION IS HERE: bag-a-contains-red-white-and-blue-marbles-such-that-the-red-to-127477.html
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is there a strategy for this....i solved by brute force.
# white marbles in A + # white marbles in B = 30
# white marbles in A is div 3
# white marbles in B is div 4
Bag A..................Bag B
30 w, 10 r...........0 w, 0 r
18 w, 6 r...........12 w, 3 r
6 red marbles in A works
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Even I went by brute force ;
Its only when red marbles in Bag A are 6, the # of White marbles in A is 18 and thus # of white marbles in B is 12 which is Div by 4. For rest of other %s # of white marbles in B is not div by 4. hence 6.
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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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[spoiler]OA is D[/spoiler]
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Re: PS: Marble Ratios [#permalink]
01 Feb 2008, 18:30
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# of Red marbles in Bag A can be either 2 or 6. No 2 in the choices, so 6. D. Explanation Bag A: R:W:B = 2:6:9 Bag B R:W = 1:4 6X + 4Y = 30 i.e 3X + 2Y = 15 X has to be odd to make an odd sum from the eq. X = 1 , Y = 6 OR X = 3, Y = 3 So R can be 2X i.e 2 or 6.
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Re: PS: Marble Ratios [#permalink]
01 Feb 2008, 19:15
white(a)+white(b) = 30
white(a)=3*red(a)
white(b)=4*red(b)
3*red(a) + 4*red(b) = 30
now just see what number from the answer choices work, i.e. plug in the answer choices for red(a) and see if red(b) comes out to an integer value. Lets try a, 1:
3*1 + 4*red(b)=30 =>red(b) = 27/4 , which is not an integer and so cant be the answer.
The only value that works is 6.
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Marbles Bag A and Bag B [#permalink]
24 Feb 2008, 13:48
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?
This was a MGMAT CAT question. Can you tell me how to solve it with algebra?
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Re: Marbles Bag A and Bag B [#permalink]
24 Feb 2008, 17:42
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Manbehindthecurtain 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?
This was a MGMAT CAT question. Can you tell me how to solve it with algebra?
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8 (D) 6 I'd rather use basic ratio arithmetic for a problem like this. I imagine algebra will be a little tedious. Bag A: R:W = 1:3; and W:B = 2:3 R:W:B = 2:6:9 -- (I) Bag B: R:W = 1:4 Given: there are 30 white marbles. If we are to split this between the two bags, the split amounts must be multiples of 6 and 4, respectively. That is, [number of white marbles in Bag A, number of white marbles in Bag B] could be either [6, 24] or [18, 12]. Substitute both values of 6 and 18 white marbles in ratio (I) above and you'll see that in Bag A, you can have either 2 or 6 red marbles. Hence (D).
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From Manhattan CAT - 3
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)1
2)3
3)4
4)6
5)8
Sorry wrong forum!!
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Re: Ratio question [#permalink]
01 Jul 2008, 11:48
6
Bag A = 2x (Red), 6x (White) and 9x (Blue)
Bag B = x(Red), 4x (white)
6x + 4x = 30
x= 3
Red in Bag A = 2x = 6
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Re: Ratio question [#permalink]
01 Jul 2008, 23:53
i think u have assumed that both the bags contain equal no balls ( x is the total no of balls in the bag). The euation should be 6x+4y=30
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Re: Ratio question [#permalink]
02 Jul 2008, 00:21
rajesh04 wrote: From Manhattan CAT - 3
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)1
2)3
3)4
4)6
5)8
Sorry wrong forum!! Number of reds in A # number of red in B. So can not assume Xa=Xb (here I call Y) 6x+4y =30 ==> x=3, y=3 (Ra=6) or x =1, y=6 (Ra=2) D is best answer.
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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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Is it 6 red balls in A?
If there are 6 red balls in A , then there will be 18 while balls in A , leaving 12 (30 - 12) white balls for B .
Now we can divide 12 by 4 .. so i will go for this answer.
for all other option we will not get white balls values ,so that it will be divide by 4.. (keeping we have 1:4ratio in bag b)
Thanks
Vishal Shah
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dancinggeometry 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?
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8 W1 + W2 = 30 Where W1 is divisible by 6 and w2 is divisible by 4 6 12 18 24 4 8 12 16 20 24 28 only 18 and 12 can be correct values. W1=18 if W1=18, Red=6 (1:3) D
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If x is number of white marbles in A and y is number of white marbles in B then
x + y = 30.
We need to find out x/3 + y/4 or (4x+3y)/12 = (x + 90)/12
In order for the above expression to be integer, (x+90) should be a multiple of 12.....this is possible for x=6, 18, ........
or x/3 = 2, 6, .....
Since 2 is not an answer choice.....6 should be the answer.
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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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Director
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Its 6 R:W:B wise A will have ratio of---> 2:6:9 and B---------------> 1:4 Total White marbles =30=10(k) so red marbel wise , A will have 6. 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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I also think the answer is 6.
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Yes ans is 6. Thanks Nitya for such an esy explanation. The OE GIVEN FOR THIS QUESTION WAS SCARY
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