GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Sep 2018, 11:48

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

Bag A contains red, white and blue marbles such that the red

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
Joined: 23 Sep 2009
Posts: 132
Bag A contains red, white and blue marbles such that the red  [#permalink]

Show Tags

New post Updated on: 31 Jul 2012, 03:01
12
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

70% (02:13) correct 30% (02:42) wrong based on 343 sessions

HideShow timer Statistics

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?

Explanation:
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.

The correct answer is D.

_________________

Thanks,
VP


Originally posted by vigneshpandi on 08 Sep 2010, 20:56.
Last edited by Bunuel on 31 Jul 2012, 03:01, edited 1 time in total.
Edited the question and added the OA.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49251
Re: Ratio problem with Marbles  [#permalink]

Show Tags

New post 08 Sep 2010, 21:27
12
12
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 multiple \(x\), 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 multiple \(y\), 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 \(2x=2\);

Only 6 is in the answer choices.

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Manager
Manager
avatar
Joined: 11 Sep 2009
Posts: 129
Re: Red + White Marbles  [#permalink]

Show Tags

New post 07 Nov 2011, 16:40
4
Bag A
R:W = 1:3
W:B = 2:3
R:W:B = 2:6:9

Because the proportion of 2:6:9 must hold constant, the number of white marbles in Bag A has to equal 6n, where n is a positive integer.

Bag B
R:W = 1:4

Because the proportion of 1:4 must hold constant, the number of white marbles in Bag B has to equal 4m, where m is a positive integer.

Given that there are a total of 30 white marbles, 30 = 6n + 4m. Given that m and n are both positive integers:

(m,n) = (3,3),(6,1)

If n = 1, the number of red marbles in Bag A = 2.
If n = 3, the number of red marbles in Bag A = 6.

Since 6 is the only answer among the 5 that satisfies the above conditions, the answer is D.
VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1097
Re: Red + White Marbles  [#permalink]

Show Tags

New post 07 Nov 2011, 23:36
white marbles in A are both multiple of 2 & 3.
hence possible numbers are 6,12,18 etc.

checking for 6, Red in A = 2,Blue = 9 and White in B= 24.
but 2 is not an answer option.

so checking for 18, in A, Red = 6,Blue = 27,White in B = 12.

hence 6 it is.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8281
Location: Pune, India
Re: Red + White Marbles  [#permalink]

Show Tags

New post 10 Nov 2011, 23:01
7
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.

Answer (D).
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Intern
Intern
avatar
Joined: 22 Aug 2011
Posts: 3
ne  [#permalink]

Show Tags

New post 13 Feb 2012, 04:51
R:W 1:3 = 2:6
W:B 2:3 = 6:9
R:W:B = 2:6:9

Open Ratio Box
R W B Total
Bag A 2 6 9 17
Multiplier X X X X
Total


R W B Total
Bag B 1 4 0 5
Multiplier X X X X
Total



R W B Total
Bag A+B 3 10 9 22
Multiplier X X X X
Total 30


find the multiplier X from the Bag A+B ratio box

10*X=30
X=3

substitute X value in the first box
R=2*(3)=6


It might be clearer if you go through attached excel sheet
Attachments

Ratio Box.xlsx [11.31 KiB]
Downloaded 130 times

To download please login or register as a user

Intern
Intern
User avatar
Joined: 21 Apr 2014
Posts: 39
Re: Bag A contains red, white and blue marbles such that the red  [#permalink]

Show Tags

New post 13 Nov 2014, 16:30
The ratio for bag A is 2:6:9 for red to white to blue marbles. You can get this number by multiplying the ration of red to white marbles by two to get 2:6, then multiplying the white to blue ration by three to get 6:9 and you can put them all together to get 2:6:9

The ratio of bag B equals 1:4 of red to white marbles and 0 blue marbles.

The problem also tells us that together the two bags contain 30 white marbles. This means that 6x+4y=30. There are two different combinations that work for this. x and y could both be 3. That would mean the total number of red marbles in bag A would be 6, which is D.

You could also have y=6 and x=1 and the total number of red marbles in bag A would be 2, but that is not an answer choice, so you would have to keep looking.
_________________

Eliza
GMAT Tutor
bestgmatprepcourse.com

Manager
Manager
User avatar
Joined: 13 Jun 2016
Posts: 125
Location: United States
Concentration: Finance, Technology
Re: Bag A contains red, white and blue marbles such that the red  [#permalink]

Show Tags

New post 01 Jul 2016, 15:58
30 white marbles just went over my head while I was doing this problem. I thought it was the total. smh
Intern
Intern
User avatar
B
Joined: 16 Jul 2011
Posts: 42
Concentration: Marketing, Real Estate
GMAT 1: 550 Q37 V28
GMAT 2: 610 Q43 V31
Reviews Badge
Re: Bag A contains red, white and blue marbles such that the red  [#permalink]

Show Tags

New post 30 Aug 2016, 13:01
Bunuel wrote:
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 multiple \(x\), 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 multiple \(y\), 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 \(2x=2\);

Only 6 is in the answer choices.

Answer: D.


How did you solve that equation to get those values? (I have marked the same in red in your answer) Could not understand it.. :(
_________________

"The fool didn't know it was impossible, so he did it."

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49251
Re: Bag A contains red, white and blue marbles such that the red  [#permalink]

Show Tags

New post 30 Aug 2016, 13:09
1
sam2016 wrote:
Bunuel wrote:
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 multiple \(x\), 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 multiple \(y\), 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 \(2x=2\);

Only 6 is in the answer choices.

Answer: D.


How did you solve that equation to get those values? (I have marked the same in red in your answer) Could not understand it.. :(

_____________
By trial and error.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
User avatar
B
Joined: 08 Jul 2016
Posts: 38
Location: Singapore
GMAT 1: 570 Q43 V25
GMAT 2: 640 Q42 V36
WE: Underwriter (Insurance)
Bag A contains red, white and blue marbles such that the red  [#permalink]

Show Tags

New post 10 Feb 2018, 09:19
Bunuel,

it took me 3 minutes to solve this one. can you please suggest some more questions like this one to practice upon?
Senior Manager
Senior Manager
avatar
G
Joined: 15 Oct 2017
Posts: 299
Reviews Badge CAT Tests
Re: Bag A contains red, white and blue marbles such that the red  [#permalink]

Show Tags

New post 10 Feb 2018, 12:15
In A, R:W=1:3, W:B=2:3; Therefore, R:W:B=2:6:9
In B, R:W=1:4

Total W=30
Therefore, 6x + 4y=30; Possible combinations are x=3 & y=3 or 1 & 6. But checking with given solutions we get x=3.
Hence, if x=3, Total R in A= 2x = 2*3 = 6.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49251
Re: Bag A contains red, white and blue marbles such that the red  [#permalink]

Show Tags

New post 11 Feb 2018, 01:08
1
prachigautam wrote:
Bunuel,

it took me 3 minutes to solve this one. can you please suggest some more questions like this one to practice upon?


3. Fractions, Decimals, Ratios and Proportions



For more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread


Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Re: Bag A contains red, white and blue marbles such that the red &nbs [#permalink] 11 Feb 2018, 01:08
Display posts from previous: Sort by

Bag A contains red, white and blue marbles such that the red

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.