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Bag A contains red, white and blue marbles such that the red [#permalink]

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29 Jun 2007, 15:38

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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?

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.

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.

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?

1 3 4 6 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).
_________________

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)

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

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

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? ==
_________________

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

Solution - Combined ratio of Red:White:Blue marbles in bag A is 2:6:9.

And ratio of Red:White in Bag B = 1:4

So total white marbled in 2 bags combined = 30 (given) => 6x + 4x = 30 => x = 3

Your ratios are right. 2/6/9 in A 1/4 in B That makes 6x + 4y=30 This is where you have done wrong. After it. We must look at the choices. Red no's must be even (2/6/9 ratio) So it may be 4, 6 or 8. If red is 4 => whites in A becomes 12; whites in B becomes 18 (30-12) => 1/4 ratio becomes impossible thus 4 is wrong. If red is 8 => whites in A becomes 24; whites in B becomes 6 => 1/4 ratio becomes impossible When red is 6 => whites in A becomes 18; in B becomes 12 thus 1/4 ratio becomes possible

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

Please explain. I did not understand the explanation given. Thanks

BAG A: R to W to B is 2 to 6 to 9 BAG B: R W is 1 to 4

white in both is 30 therefore using 4+6 = 10 30/10 = 3

therefore 3 *6 = 18 white in bag a ration is 2 to 6 therefore if 18w, 18*2/6 = 6red

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