Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Bag A contains red, white and blue marbles such that the red [#permalink]
08 Sep 2010, 19:56

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

76% (02:59) correct
24% (03:07) wrong based on 49 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

The explanation given is little confusing. Can anyone suggest a easy method to approach such types of problems?

We are told that bag B contains red and white marbles in the ration 1:4. This implies that WB, the number of white marbles in bag B, must be a multiple of 4.

What can we say about WA, the number of white marbles in bag A? We are given two ratios involving the white marbles in bag A. The fact that the ratio of red to white marbles in bag A is 1:3 implies that WA must be a multiple of 3. The fact that the ratio of white to blue marbles in bag A is 2:3 implies that WA must be a multiple of 2. Since WA is both a multiple of 2 and a multiple of 3, it must be a multiple of 6.

We are told that WA + WB = 30. We have already figured out that WA must be a multiple of 6 and that WB must be a multiple of 4. So all we need to do now is to test each candidate value of WA (i.e. 6, 12, 18, and 24) to see whether, when plugged into WA + WB = 30, it yields a value for WB that is a multiple of 4. It turns out that WA = 6 and WA = 18 are the only values that meet this criterion.

Recall that the ratio of red to white marbles in bag A is 1:3. If there are 6 white marbles in bag A, there are 2 red marbles. If there are 18 white marbles in bag A, there are 6 red marbles. Thus, the number of red marbles in bag A is either 2 or 6. Only one answer choice matches either of these numbers.

Re: Ratio problem with Marbles [#permalink]
08 Sep 2010, 20:27

3

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

vigneshpandi 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. 1 2. 3 3. 4 4. 6 5. 8

Bag A: R/W=1/3=2/6; W/B=2/3=6/9; So R/W/B=2/6/9 --> # of marbles in bag A would be 2x, 6x, and 9x, for some positive integer multiplex, where 6x corresponds to the # of white marbles and 2x corresponds to the # of red marbles (so # of red marbles must be a multiple of 2, so answers A and B are out at this stage);

Bag B: R/W=1/4 --> # of marbles in bag B would be y and 4y, for some positive integer multipley, where 4y corresponds to the # of white marbles;

Given:6x+4y=30 --> 3x+2y=15 --> there are two positive integer solutions for this equation: x=3 and y=3 --> in this case # of red marbles equals to 2x=6; Or: x=1 and y=6 --> in this case # of red marbles equals to 2x=2;

Red + White Marbles [#permalink]
07 Nov 2011, 12:39

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

Guys - can someone please help by explaining this problem? _________________

Re: Red + White Marbles [#permalink]
10 Nov 2011, 22:01

2

This post received KUDOS

Expert's post

enigma123 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?

A) 1 B) 3 C) 4 D) 6 E) 8

Guys - can someone please help by explaining this problem?

Responding to a pm:

We need the relation between number of red, white and total number of marbles.

We don't know what that relation in bag A. Let's find it out first. Red:White = 1:3 = 2:6 White:Blue = 2:3 = 6:9 Red:White:Blue = 2:6:9 In bag A, if you have 17 marbles, 2 will be Red, 6 will be White and 9 will be Blue. If you have 34 marbles, 4 will be Red, 12 will be White and 18 will be Blue etc No of white marbles could be 6/12/18/24... etc No of red marbles could be 2/4/6/8/... etc

In bag B, Red:White = 1:4 If you have 5 marbles, 1 will be Red, 4 will be White. If you have 10 marbles, 2 will be Red, 8 will be White. etc No of white marbles could be 4/8/12/16... etc No of red marbles could be 1/2/3/4... etc

Total number of white marbles = 30 There are two ways in which we could have obtained 30. White marbles in (Bag A, Bag B) = (6, 24) or (18, 12)

If Bag A has 6 white marbles, it will have 2 red marbles. If Bag A has 18 white marbles, it will have 6 red marbles.

Re: Red + White Marbles [#permalink]
11 Dec 2013, 16:48

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________