GMAT Changed on April 16th - Read about the latest changes here

It is currently 24 Apr 2018, 07:18

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

M20-32

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44639
M20-32 [#permalink]

Show Tags

New post 16 Sep 2014, 01:09
Expert's post
13
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

63% (01:43) correct 37% (01:37) wrong based on 150 sessions

HideShow timer Statistics

A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain opened?

A. at 2:00 pm
B. at 2:30 pm
C. at 3:00 pm
D. at 3:30 pm
E. at 4:00 pm
[Reveal] Spoiler: OA

_________________

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

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44639
Re M20-32 [#permalink]

Show Tags

New post 16 Sep 2014, 01:09
Expert's post
5
This post was
BOOKMARKED
Official Solution:

A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain opened?

A. at 2:00 pm
B. at 2:30 pm
C. at 3:00 pm
D. at 3:30 pm
E. at 4:00 pm

When only the valve is open, the pool is filling at a rate of \(\frac{1}{4}\) an hour. When both the valve and the drain are open, the pool is filling at a rate of \(\frac{1}{4} - \frac{1}{5} = \frac{1}{20}\) an hour. Let \(x\) denote the time when only the valve was open. Then both the valve and the drain were open for \(11 - 1 - x = 10 - x\)hours. Now we can compose the equation \(\frac{1}{4}x + \frac{1}{20}(10 - x) = 1\) which reduces to \(\frac{x}{5} = 0.5\) from where \(x = 2.5\). Thus, the drain was opened at \(1:00 + 2:30 = 3:30\)pm.

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

2 KUDOS received
Intern
Intern
avatar
Joined: 22 Jul 2013
Posts: 19
Location: United States
Concentration: Technology, Entrepreneurship
Schools: IIM A '15
GMAT 1: 650 Q46 V34
GMAT 2: 720 Q49 V38
GPA: 3.67
WE: Engineering (Non-Profit and Government)
Reviews Badge
Re: M20-32 [#permalink]

Show Tags

New post 01 Dec 2014, 19:06
2
This post received
KUDOS
The Valve that Fills is working at a rate of 1/4 per hour
The Drain is working at a rate of 1/5 per hour

Now The valve is open for 10 hrs ( between 1 Pm to 11 Pm)
Let the drain be open for x hrs.

so work done is (10)/4 (Valve's work)
Drains work is (x)/5

==> (10/4 ) - (x/5) = 1 ( Assuming work is 1)

gives us x= 7.5 hrs ., Drain was open for 7.5 hrs which is 2.5 hrs from 1 Am = 3:30 Am

Hope that helps.

Regards,
Arun

Bunuel wrote:
Official Solution:

A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain opened?

A. at 2:00 pm
B. at 2:30 pm
C. at 3:00 pm
D. at 3:30 pm
E. at 4:00 pm

When only the valve is open, the pool is filling at a rate of \(\frac{1}{4}\) an hour. When both the valve and the drain are open, the pool is filling at a rate of \(\frac{1}{4} - \frac{1}{5} = \frac{1}{20}\) an hour. Let \(x\) denote the time when only the valve was open. Then both the valve and the drain were open for \(11 - 1 - x = 10 - x\)hours. Now we can compose the equation \(\frac{1}{4}x + \frac{1}{20}(10 - x) = 1\) which reduces to \(\frac{x}{5} = 0.5\) from where \(x = 2.5\). Thus, the drain was opened at \(1:00 + 2:30 = 3:30\)pm.

Answer: D
1 KUDOS received
Intern
Intern
avatar
Joined: 20 Jun 2014
Posts: 9
Schools: CBS '18
Re: M20-32 [#permalink]

Show Tags

New post 19 Feb 2015, 16:34
1
This post received
KUDOS
Bunuel wrote:
Official Solution:

A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain opened?

A. at 2:00 pm
B. at 2:30 pm
C. at 3:00 pm
D. at 3:30 pm
E. at 4:00 pm

When only the valve is open, the pool is filling at a rate of \(\frac{1}{4}\) an hour. When both the valve and the drain are open, the pool is filling at a rate of \(\frac{1}{4} - \frac{1}{5} = \frac{1}{20}\) an hour. Let \(x\) denote the time when only the valve was open. Then both the valve and the drain were open for \(11 - 1 - x = 10 - x\)hours. Now we can compose the equation \(\frac{1}{4}x + \frac{1}{20}(10 - x) = 1\) which reduces to \(\frac{x}{5} = 0.5\) from where \(x = 2.5\). Thus, the drain was opened at \(1:00 + 2:30 = 3:30\)pm.

Answer: D


Bunuel,

can you please explain why we have \(\frac{1}{4}x + \frac{1}{20}(10 - x) = 1\) equalling to 1 instead of 1/10?

Thanks
Current Student
User avatar
Joined: 12 Aug 2015
Posts: 293
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
Re: M20-32 [#permalink]

Show Tags

New post 26 Jan 2016, 22:22
Combined approach: where back-solving meets algebra half-way.

Combined rate is 1/20 as correctly noted above. Assume that hose 1 had worked for 2 hours thus completing half of the job. Hence hose 2 joined in at 3 pm. By testing this value we will be able to cut off 2 options that are either too high or too low.

So rt=d formula helps us here: 1/20 * t = 1/2 ---> t = 10. 10+2 is way too much because the work was done in 10 hours as per prompt. Hence hose 1 worked for longer than 2 hours and completed more than half a job to fit the 10 hour requirement. We can safele eliminate A and B.

I don't like ugly numbers so I will test E - hose 1 worked for 3 hours hence having completed 3/4 of the job. 1/20 * t = 1/4 ---> t = 5. 5+2 is way too low.. So E is also wrong and D is the answer.
_________________

KUDO me plenty

Intern
Intern
avatar
B
Joined: 10 May 2016
Posts: 1
GMAT ToolKit User
Re: M20-32 [#permalink]

Show Tags

New post 13 Jul 2016, 20:15
1
This post was
BOOKMARKED
Work done by 1st for 10 hours = 10/4 = 2.5W
Total work done = w
Work for drain pipe = 1.5 W
Time for drain pipe = 1.5 * 5 = 7.5 hours
Intern
Intern
avatar
B
Joined: 07 Mar 2011
Posts: 31
GMAT ToolKit User Premium Member
Re: M20-32 [#permalink]

Show Tags

New post 25 Jul 2016, 07:57
Just a thought without equations.

Given that
1. in 4 hrs the pool can be filled.
2. in 5 hrs the pool can be drained.

in 10 hrs the valve can fill 2.5 times the pool [ 10/4 = 2.5 ].
So it means in 10 hrs 1.5 times of the pool water can be drained out if together both fill and drain valves are kept open and the pool is full. Finally, to drain out 1.5 times of the pool it requires 7.5 hrs [= 5hrs + 2.5 hrs ]. So drain valve would have kept opened at 11pm- 7.5 hrs = 3.5 hrs => 3:30Pm
Intern
Intern
avatar
Joined: 20 Jan 2013
Posts: 9
GMAT 1: 660 Q49 V30
Reviews Badge
M20-32 [#permalink]

Show Tags

New post 04 Sep 2016, 03:27
Let total work = 100%

Work completed each hour for filling A =25% (Total work completed in 4 hours, therfore work completed in 1 hour = 25%)

Work by Drain (B) = -20% (negative because it is acting against natural force of filling tank, finding 20% same as above)

Let time taken for filling = x , therfore time taken by A and B together = (10- x)

Now work = time * rate

100% = 25*x + (25-20=5) *(10-x)

Solving, x=2.5 hours

Therfore drain was opened 2.5 hours after A was opened. Therefore drain was opened at 1:00 p.m.+2.5 hrs =3:30 p.m.
Senior Manager
Senior Manager
User avatar
S
Joined: 08 Jun 2015
Posts: 478
Location: India
GMAT 1: 640 Q48 V29
Premium Member CAT Tests
Re: M20-32 [#permalink]

Show Tags

New post 26 Oct 2017, 08:18
+1 for option D.
_________________

" The few , the fearless "

Intern
Intern
avatar
Joined: 20 Oct 2014
Posts: 2
Re: M20-32 [#permalink]

Show Tags

New post 14 Nov 2017, 05:13
Bunuel,

can you please explain why we are equating it to 1 instead of 1/10?

Thanks
Re: M20-32   [#permalink] 14 Nov 2017, 05:13
Display posts from previous: Sort by

M20-32

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

Moderators: chetan2u, Bunuel



cron

GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.