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

It is currently 22 Oct 2018, 11:44

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

M04-08

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50042
M04-08  [#permalink]

Show Tags

New post 16 Sep 2014, 00:22
1
1
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

78% (01:20) correct 22% (01:15) wrong based on 187 sessions

HideShow timer Statistics

A 10 liter mixture of cranberry juice and water contains juice and water in the ratio of \(3:2\). 5 liters of the mixture are removed and replaced with pure juice and the operation is repeated once more. At the end of the two removals and replacements, what is the ratio of juice to water in the resulting mixture?

A. 5 : 3
B. 6 : 4
C. 8 : 2
D. 17 : 3
E. 9 : 1

_________________

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50042
Re M04-08  [#permalink]

Show Tags

New post 16 Sep 2014, 00:22
1
1
Official Solution:

A 10 liter mixture of cranberry juice and water contains juice and water in the ratio of \(3:2\). 5 liters of the mixture are removed and replaced with pure juice and the operation is repeated once more. At the end of the two removals and replacements, what is the ratio of juice to water in the resulting mixture?

A. 5 : 3
B. 6 : 4
C. 8 : 2
D. 17 : 3
E. 9 : 1


The initial mixture contains 6 liters of juice and 4 of water. 50% of the mixture is removed each time (5 liters is 50% of 10 liters of initial mixture). This means we have to remove 50% of juice as well as 50% of water. After the first removal of 5 liters it has 3 liters of juice and 2 of water. Adding 5 liters of juice gives us a mixture of 8 liters of juice and 2 of water. Removing 5 liters of the mixture, we have 4 liters of juice and 1 of water. Adding 5 liters of juice again gives us a 9 : 1 ratio of juice to water.


Answer: E
_________________

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

Manager
Manager
User avatar
Status: PLAY HARD OR GO HOME
Joined: 25 Feb 2014
Posts: 150
Location: India
Concentration: General Management, Finance
Schools: Mannheim
GMAT 1: 560 Q46 V22
GPA: 3.1
GMAT ToolKit User
Re: M04-08  [#permalink]

Show Tags

New post 02 Nov 2014, 02:11
Bunuel wrote:
Official Solution:

A 10 liter mixture of cranberry juice and water contains juice and water in the ratio of 3 : 2. 5 liters of the mixture are removed and replaced with pure juice and the operation is repeated once more. At the end of the two removals and replacements, what is the ratio of juice to water in the resulting mixture?

A. 5 : 3
B. 6 : 4
C. 8 : 2
D. 17 : 3
E. 9 : 1


The initial mixture contains 6 liters of juice and 4 of water. 50% of the mixture is removed each time (5 liters is 50% of 10 liters of initial mixture). This means we have to remove 50% of juice as well as 50% of water. After the first removal of 5 liters it has 3 liters of juice and 2 of water. Adding 5 liters of juice gives us a mixture of 8 liters of juice and 2 of water. Removing 5 liters of the mixture, we have 4 liters of juice and 1 of water. Adding 5 liters of juice again gives us a 9 : 1 ratio of juice to water.


Answer: E


Hi Bunuel,
great solution..Could u please tell me why doesnt this mixture replacement formula work here ?Its working fine with other problem..m i missing something ?

Suppose a container contains x of liquid from which y units are taken out and replaced by water.
After n operations, the quantity of pure liquid = \(A = Q( 1-\frac{q}{Q} )^n\)

Heres how m trying to solve =
For juice=

\(A= 6(1 - \frac{5}{10}) ^2 + 10\)
\(=\frac{23}{2}\)

For water=
\(A2= 4(1-\frac{5}{10})^2\)
\(=1\)

\(\frac{A1}{A2}=\frac{11.5}{1}\)
_________________

ITS NOT OVER , UNTIL I WIN ! I CAN, AND I WILL .PERIOD.

Manager
Manager
User avatar
Status: PLAY HARD OR GO HOME
Joined: 25 Feb 2014
Posts: 150
Location: India
Concentration: General Management, Finance
Schools: Mannheim
GMAT 1: 560 Q46 V22
GPA: 3.1
GMAT ToolKit User
Re: M04-08  [#permalink]

Show Tags

New post 02 Nov 2014, 07:27
Hii Bunuel,
Please help me out with this..m totally confused..
thanks in advance.. :?
_________________

ITS NOT OVER , UNTIL I WIN ! I CAN, AND I WILL .PERIOD.

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50042
Re: M04-08  [#permalink]

Show Tags

New post 02 Nov 2014, 08:04
vards wrote:
Bunuel wrote:
Official Solution:

A 10 liter mixture of cranberry juice and water contains juice and water in the ratio of 3 : 2. 5 liters of the mixture are removed and replaced with pure juice and the operation is repeated once more. At the end of the two removals and replacements, what is the ratio of juice to water in the resulting mixture?

A. 5 : 3
B. 6 : 4
C. 8 : 2
D. 17 : 3
E. 9 : 1


The initial mixture contains 6 liters of juice and 4 of water. 50% of the mixture is removed each time (5 liters is 50% of 10 liters of initial mixture). This means we have to remove 50% of juice as well as 50% of water. After the first removal of 5 liters it has 3 liters of juice and 2 of water. Adding 5 liters of juice gives us a mixture of 8 liters of juice and 2 of water. Removing 5 liters of the mixture, we have 4 liters of juice and 1 of water. Adding 5 liters of juice again gives us a 9 : 1 ratio of juice to water.


Answer: E


Hi Bunuel,
great solution..Could u please tell me why doesnt this mixture replacement formula work here ?Its working fine with other problem..m i missing something ?

Suppose a container contains x of liquid from which y units are taken out and replaced by water.
After n operations, the quantity of pure liquid = \(A = Q( 1-\frac{q}{Q} )^n\)

Heres how m trying to solve =
For juice=

\(A= 6(1 - \frac{5}{10}) ^2 + 10\)
\(=\frac{23}{2}\)

For water=
\(A2= 4(1-\frac{5}{10})^2\)
\(=1\)

\(\frac{A1}{A2}=\frac{11.5}{1}\)


Not familiar with this formula but for juice it should be \((6(1 - \frac{5}{10})+5)(1 - \frac{5}{10})+5\)
_________________

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
avatar
Joined: 05 Jan 2015
Posts: 9
Re: M04-08  [#permalink]

Show Tags

New post 01 Jul 2015, 21:18
May be you wrongly applied the formula. The original statement said: "Remove the liquid and replace by water", or in general "remove one, and replace by another"

Therefore, the formula in this case can be applied for the water only (remove water and replace by juice), and cannot be applied for the juice (remove juice and replace by juice!!!!).

Once you get the amount of water remained 1l, you know that juice remain 9l (10-1).


vards wrote:
Bunuel wrote:
Official Solution:

A 10 liter mixture of cranberry juice and water contains juice and water in the ratio of 3 : 2. 5 liters of the mixture are removed and replaced with pure juice and the operation is repeated once more. At the end of the two removals and replacements, what is the ratio of juice to water in the resulting mixture?

A. 5 : 3
B. 6 : 4
C. 8 : 2
D. 17 : 3
E. 9 : 1


The initial mixture contains 6 liters of juice and 4 of water. 50% of the mixture is removed each time (5 liters is 50% of 10 liters of initial mixture). This means we have to remove 50% of juice as well as 50% of water. After the first removal of 5 liters it has 3 liters of juice and 2 of water. Adding 5 liters of juice gives us a mixture of 8 liters of juice and 2 of water. Removing 5 liters of the mixture, we have 4 liters of juice and 1 of water. Adding 5 liters of juice again gives us a 9 : 1 ratio of juice to water.


Answer: E


Hi Bunuel,
great solution..Could u please tell me why doesnt this mixture replacement formula work here ?Its working fine with other problem..m i missing something ?

Suppose a container contains x of liquid from which y units are taken out and replaced by water.
After n operations, the quantity of pure liquid = \(A = Q( 1-\frac{q}{Q} )^n\)

Heres how m trying to solve =
For juice=

\(A= 6(1 - \frac{5}{10}) ^2 + 10\)
\(=\frac{23}{2}\)

For water=
\(A2= 4(1-\frac{5}{10})^2\)
\(=1\)

\(\frac{A1}{A2}=\frac{11.5}{1}\)
Manager
Manager
avatar
B
Joined: 16 Feb 2016
Posts: 52
Concentration: Other, Other
GMAT ToolKit User Premium Member Reviews Badge
Re: M04-08  [#permalink]

Show Tags

New post 27 Apr 2016, 00:08
kimnguyen wrote:
May be you wrongly applied the formula. The original statement said: "Remove the liquid and replace by water", or in general "remove one, and replace by another"

Therefore, the formula in this case can be applied for the water only (remove water and replace by juice), and cannot be applied for the juice (remove juice and replace by juice!!!!).

Once you get the amount of water remained 1l, you know that juice remain 9l (10-1).


vards wrote:
Bunuel wrote:
Official Solution:

A 10 liter mixture of cranberry juice and water contains juice and water in the ratio of 3 : 2. 5 liters of the mixture are removed and replaced with pure juice and the operation is repeated once more. At the end of the two removals and replacements, what is the ratio of juice to water in the resulting mixture?

A. 5 : 3
B. 6 : 4
C. 8 : 2
D. 17 : 3
E. 9 : 1


The initial mixture contains 6 liters of juice and 4 of water. 50% of the mixture is removed each time (5 liters is 50% of 10 liters of initial mixture). This means we have to remove 50% of juice as well as 50% of water. After the first removal of 5 liters it has 3 liters of juice and 2 of water. Adding 5 liters of juice gives us a mixture of 8 liters of juice and 2 of water. Removing 5 liters of the mixture, we have 4 liters of juice and 1 of water. Adding 5 liters of juice again gives us a 9 : 1 ratio of juice to water.


Answer: E


Hi Bunuel,
great solution..Could u please tell me why doesnt this mixture replacement formula work here ?Its working fine with other problem..m i missing something ?

Suppose a container contains x of liquid from which y units are taken out and replaced by water.
After n operations, the quantity of pure liquid = \(A = Q( 1-\frac{q}{Q} )^n\)

Heres how m trying to solve =
For juice=

\(A= 6(1 - \frac{5}{10}) ^2 + 10\)
\(=\frac{23}{2}\)

For water=
\(A2= 4(1-\frac{5}{10})^2\)
\(=1\)

\(\frac{A1}{A2}=\frac{11.5}{1}\)



Trying to remember formulas on the day might be an issue, so I would recommend understanding the solution. Then you can solve the question every time.
Manager
Manager
avatar
G
Joined: 14 Oct 2012
Posts: 167
Premium Member Reviews Badge
Re: M04-08  [#permalink]

Show Tags

New post 01 Apr 2017, 08:28
My 2 cents:
>> !!!

You do not have the required permissions to view the files attached to this post.

Intern
Intern
avatar
B
Joined: 29 May 2017
Posts: 3
Re: M04-08  [#permalink]

Show Tags

New post 17 Aug 2017, 06:12
Please change how the question is written, 2 . 5 is totally misleading, & providing multiple meanings whether 5 litre of solution was removed or .5 . It is also not giving clarity on ratio.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50042
Re: M04-08  [#permalink]

Show Tags

New post 17 Aug 2017, 06:20
1
Intern
Intern
User avatar
B
Joined: 15 Nov 2017
Posts: 41
Location: United States (OR)
Concentration: Marketing, Entrepreneurship
Schools: McCombs
GMAT 1: 630 Q40 V40
GPA: 2.99
WE: Education (Consulting)
Premium Member Reviews Badge
Re: M04-08  [#permalink]

Show Tags

New post 25 Dec 2017, 14:28
You guys are really smart! I pause the exam and still get the wrong answer. Half the time, I can't understand the question! I've taken all the relevant classes. But the classes are taught in a linear fashion: a+b+c=d. But the CAT presents the questions as: xa^3+yb^2-d=zc. I should just stay retired...=( It is very frustrating to work on a problem for 15 minutes (even with a calculator) and still get the wrong answer!...This is akin to the medieval "trial by morsel!"
_________________

McCombs MBA 1990, Hook'Em Horns. I am helping my son prep for 2019, while trying to keep a 66 y.o. brain active. ;-)

GMAT Club Bot
Re: M04-08 &nbs [#permalink] 25 Dec 2017, 14:28
Display posts from previous: Sort by

M04-08

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

Moderators: chetan2u, Bunuel



Copyright

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®.