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

It is currently 19 Jan 2019, 03:12

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 in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • FREE Quant Workshop by e-GMAT!

     January 20, 2019

     January 20, 2019

     07:00 AM PST

     07:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

S99-16

  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: 52294
S99-16  [#permalink]

Show Tags

New post 16 Sep 2014, 00:53
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

53% (02:39) correct 47% (02:38) wrong based on 73 sessions

HideShow timer Statistics

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

A. 5 and \(\frac{5}{11}\) minutes
B. 6 minutes
C. 10 minutes
D. 19 minutes
E. 30 minutes

_________________

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: 52294
Re S99-16  [#permalink]

Show Tags

New post 16 Sep 2014, 00:53
Official Solution:

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

A. 5 and \(\frac{5}{11}\) minutes
B. 6 minutes
C. 10 minutes
D. 19 minutes
E. 30 minutes


Let \(t\) stand for the desired time, so that the drain can empty the tub in \(t\) minutes and faucet Q can fill the tub in \((t - 4)\) minutes. Also, the drain does negative work as it empties the tub. The rates for the pipes and the drain are thus

P: 1 tub in \(10\) min \(= \frac{1}{10}\) tub per min

Q: 1 tub in \((t - 4)\) min \(= \frac{1}{t - 4}\) tub per min

Drain: -1 tub in \(t\) min \(= -\frac{1}{t}\) tub per min

Using the fact that all three fixtures together take 6 minutes to fill 1 tub, set up an RTW chart, and use the chart to calculate the total work quantities in the last column.
Rate (tub/min) \(\times\) Time (min) \(=\) Total Work (tubs) P \(\frac{1}{10}\) \(\times\) 6 \(=\) \(\frac{3}{5}\) Q \(\frac{1}{t - 4}\) \(\times\) 6 \(=\) \(\frac{6}{t - 4}\) Drain \(\frac{-1}{t}\) \(\times\) 6 \(=\) \(\frac{-6}{t}\) Total n/a n/a 1
Set up an equation summing up the work:
\(\frac{3}{5} + \frac{6}{t - 4} - \frac{6}{t} = 1\)

Multiply by the common denominator, \(5t(t - 4)\):
\(3t(t - 4) + 6(5t) - 6(5)(t - 4) = 5t(t - 4)\)
\(3t^2 - 12t + 30t - 30t + 120 = 5t^2 - 20t\)
\(0 = 2t^2 - 8t - 120\)
\(0 = t^2 - 4t - 60\)
\(0 = (t - 10)(t + 6)\)

\(t = 10\) or \(t = -6\)

The negative value is absurd, so \(t = 10\); the drain can empty the tub in 10 minutes.


Answer: C
_________________

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: 02 Oct 2014
Posts: 9
Re: S99-16  [#permalink]

Show Tags

New post 22 Oct 2016, 19:48
any other quick solution to this.......
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52294
Re: S99-16  [#permalink]

Show Tags

New post 22 Oct 2016, 23:39
1
VIJAYTHAPLIYAL wrote:
any other quick solution to this.......


A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

A. 5 and \(\frac{5}{11}\) minutes
B. 6 minutes
C. 10 minutes
D. 19 minutes
E. 30 minutes

Let \(p\) and \(q\) be the times in minutes needed for faucets P and Q working alone to fill the tub and d be the time in minutes needed for drain to empty the tub.

Given:
Faucet P alone can fill the whole tub in ten minutes --> \(p=10\);
Faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub --> \(q=d-4\);
Faucets P and Q both running and the drain unstopped, the tub fills in six minutes --> \(\frac{1}{p}+\frac{1}{q}-\frac{1}{d}=\frac{1}{6}\) --> \(\frac{1}{10}+\frac{1}{d-4}-\frac{1}{d}=\frac{1}{6}\) --> \(\frac{1}{d-4}-\frac{1}{d}=\frac{1}{15}\) --> substituting the values from the answer choices we'll get \(d=10\).

Answer: C.
_________________

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: 18 Jan 2018
Posts: 1
Re: S99-16  [#permalink]

Show Tags

New post 24 Jan 2018, 06:51
The question is not clear. The question should be "How long would the drain take to empty the whole tub WHEN BOTH FAUCETS ARE ON". Am I wrong?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52294
Re: S99-16  [#permalink]

Show Tags

New post 24 Jan 2018, 07:07
susig27 wrote:
The question is not clear. The question should be "How long would the drain take to empty the whole tub WHEN BOTH FAUCETS ARE ON". Am I wrong?


The question is: How long would the drain take to empty the whole tub, when none of the faucets is working?

Check solution here: https://gmatclub.com/forum/s99-184744.html#p1752472
_________________

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
B
Joined: 20 May 2018
Posts: 17
CAT Tests
Re: S99-16  [#permalink]

Show Tags

New post 14 Oct 2018, 02:48
susig27 wrote:
The question is not clear. The question should be "How long would the drain take to empty the whole tub WHEN BOTH FAUCETS ARE ON". Am I wrong?

You probably are.
maybe you did not thoroughly read the second part of the passage! I am claiming this just 'cause did the same mistake at the beginning. I did the equation considering a "stopped" drain ( so just the combination of the faucets' rates, without considering the drain).
In realty the text says "unstopped" so the equation have to be
1/x + 1/10 - 1/(4+x) = 1/6
solving it you get x=6 (i considered 1/x the rate of P and 1/(x+4) the drain's rate)
Hope it helps!
Intern
Intern
avatar
B
Joined: 10 Feb 2017
Posts: 5
GMAT ToolKit User CAT Tests
Re: S99-16  [#permalink]

Show Tags

New post 22 Oct 2018, 05:27
A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

finding answer from answer choices.

go with the most easy choice that you can handle

always choose LCM method

P takes 10 mins
From the option you take for ex 6(option-b) for drain D
SO Q MUST TAKE 6-4=2 MINS
so now find LCM(10,6,2)=30
FOR MIN P WILL DO 30/10=3(SINCE WORK IS NOT 1 NOW,ITS 30 NOW)
Q=15 WORKS PER MIN
D=5 WORKS/MIN

ALL TOGETHER TOTAL WORK WILL BE =3+15-5=13/MIN.

NOW LOOK 13 WORKS*6 MINS (WHY 6 IS MULTIPLIED,BKZ ITS GIVEN IN THE QN THAT WHEN ALL WORK TOGETHER THEIR WAY IT TAKES 6 MINS TO FEEL THE TANK)
BUT ITS NOT,SO OPTION -B OUT
NEXT OPTION C
P=10
D=10(OPTION)
Q=10-4=6
LCM(10,10,6)=30
PER MIN WORK=3-3+5=5
NOW OUT OF 30 WORKS

IF ALL WORKING THEIR WAY AND 5 IS THE NET WORK PER MINUTE,CAN THEY FEEL THE TANK IN 6 MINUTES?
ANSWER IS YES 5*6=30(TOTAL Capacity as per our lcm work out.

think rethink practice and get the correct choice as dont forget to help for 1 kudo.
GMAT Club Bot
Re: S99-16 &nbs [#permalink] 22 Oct 2018, 05:27
Display posts from previous: Sort by

S99-16

  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®.