Rate Problem

[garuhape]

Hi there, can someone help me please?

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

[GMATGuruNY]

Hi there, can someone help me please?

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

We can plug in the answer choices, which represent the number of red marbles in Bag A.

Let R=red, W=white, B=blue.

Answer choice C: R=4 in bag A
Bag A:
R:W = 1:3 = 4:12, so W=12.
Bag B:
Since the total number of white marbles is 30, W = 30-12 = 18.
Doesn't work, because R:W = 1:4, and 18 is not a multiple of 4.
Eliminate C.

Answer choice D: R=6 in bag A
Bag A:
R:W = 1:3 = 6:18, so W=18.
Bag B:
Since the total number of white marbles is 30, W = 30-18 = 12.
R:W = 1:4 = 3:12. So R=3.
Success!

The correct answer is D.

[force5]

easy question once you know the direction

bag A - Red White Blue

ratio 2x : 6x : 9x

check RED:WHITE is 2x/6x = 1:3 ( as given)
WHITE: BLUE is 6x/9x = 2:3 ( as given)

Similarly
In Bag B - RED WHITE
Ratio 1y : 4y

now this means 6x+ 4y= 30 ( given)
or 3x+2y=15

hence if x = 1 ......... y = 6
if x = 3 ........ y = 3

putting in BAG A----
red balls are 2x. that means red balls can be 2, 6 ....

Hence the answer is D

EASY!!!