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

 It is currently 18 Jun 2019, 18:39

### 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

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

# If Samson is filling a bathtub with COLD water, it will take

Author Message
TAGS:

### Hide Tags

Manager
Joined: 16 Jul 2009
Posts: 191
If Samson is filling a bathtub with COLD water, it will take  [#permalink]

### Show Tags

08 Apr 2010, 01:31
2
6
00:00

Difficulty:

55% (hard)

Question Stats:

72% (02:47) correct 28% (03:25) wrong based on 299 sessions

### HideShow timer Statistics

If Samson is filling a bathtub with COLD water, it will take him 6 minutes and 40 seconds, and if he fills it with HOT water, it will take him 8 minutes. If draining the tub takes 13 minutes and 20 seconds, how many minutes will it take to fill up the bath tub with both HOT and COLD water running while the plug is out, so the water is constantly draining?

A. 16
B. 12
C. 8.6
D. 5
E. 4.75

M04-37

Wanted to understand the way the numbers 12, 10 and 6 are arrived at in the net speed calculation.
Math Expert
Joined: 02 Sep 2009
Posts: 55670

### Show Tags

08 Apr 2010, 03:03
5
1
abhi758 wrote:
If Samson is filling a bathtub with COLD water, it will take him 6 minutes and 40 seconds, and if he fills it with HOT water, it will take him 8 minutes. If draining the tub takes 13 minutes and 20 seconds, how many minutes will it take to fill up the bath tub with both HOT and COLD water running while the plug is out, so the water is constantly draining?

a) 16
b) 12
c) 8.6
d) 5
e) 4.75

Wanted to understand the way the numbers 12, 10 and 6 are arrived at in the net speed calculation.

Times:
$$c=6\frac{2}{3}=\frac{20}{3}$$;
$$h=8$$;
$$d=13\frac{1}{3}=\frac{40}{3}$$.

Remember that we can sum the rates. As rate is the reciprocal of time:
$$\frac{1}{c}+\frac{1}{h}-\frac{1}{d}=\frac{3}{20}+\frac{1}{8}-\frac{3}{40}=\frac{1}{5}=\frac{1}{t}$$ --> $$\frac{1}{5}=\frac{1}{t}$$ --> $$t=5$$.

_________________
##### General Discussion
Manager
Joined: 16 Jul 2009
Posts: 191

### Show Tags

08 Apr 2010, 04:14
Bunnel, Thanks for the prompt explanation!
Manager
Joined: 07 Jan 2010
Posts: 164

### Show Tags

09 Apr 2010, 23:16
Did same same Bunuel ...calculated the net gain per minute ...5 min.
Manager
Joined: 28 Aug 2010
Posts: 170

### Show Tags

06 Feb 2011, 15:03
Bunuel, please can you explain the concept behind summing the rate. if you could also point me to more questions like these on the forum ..it would be really helpful. Thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 55670

### Show Tags

06 Feb 2011, 15:27
ajit257 wrote:
Bunuel, please can you explain the concept behind summing the rate. if you could also point me to more questions like these on the forum ..it would be really helpful. Thanks.

This is very simple concept. For example if printer A can print 3 pages per hour and printer B can print 2 pages per hour then working simultaneously they can print 2+3=5 pages per hour.

Check this: word-translations-rates-work-104208.html#p812628

PS work problems: search.php?search_id=tag&tag_id=66
DS work problems: search.php?search_id=tag&tag_id=46
_________________
Manager
Joined: 06 Mar 2014
Posts: 89
Re: If Samson is filling a bathtub with COLD water, it will take  [#permalink]

### Show Tags

29 Dec 2014, 10:55
Hi Bunuel,

Why can't we directly add the times, as we need to calculate time only at the end
Math Expert
Joined: 02 Sep 2009
Posts: 55670
Re: If Samson is filling a bathtub with COLD water, it will take  [#permalink]

### Show Tags

31 Dec 2014, 04:39
Shree9975 wrote:
Hi Bunuel,

Why can't we directly add the times, as we need to calculate time only at the end

_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14351
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If Samson is filling a bathtub with COLD water, it will take  [#permalink]

### Show Tags

31 Dec 2014, 12:22
1
Hi All,

While the approach would be slightly longer, you could use the Work Formula and some rate-based calculations to answer this question.

Work Formula = (A)(B)/(A+B)

We're told the two rates to "fill" the tub:

A = 6 mins 40 secs = 6 2/3 mins = 20/3 mins
B = 8 mins

(20/3)(8)/(20/3 + 8) = (160/3)/(44/3) = 160/44 mins to fill the tub

160/44 = 40/11 mins to fill the tub.

In 1 minute, 11/40 of the tub will be filled

We're also told how long it takes to drain the tub:

Drain = 13 mins 20 secs = 13 1/3 mins = 40/3 mins to drain the tub

In 1 minute, 3/40 of the tub will be drained

Now that we have the rates of the water going "in" and the water coming "out", we can combined them:

11/40 - 3/40 = 8/40 = 1/5

The "net effect" is that 1/5 of the tub is filled every minute.

For a full tub, we need (1/5)(5 minutes).

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ Manager Joined: 18 Mar 2015 Posts: 120 Location: India Schools: ISB '19 GMAT 1: 600 Q47 V26 GPA: 3.59 Re: If Samson is filling a bathtub with COLD water, it will take [#permalink] ### Show Tags 08 Sep 2017, 10:35 I understood the logic but I converted time into sec and then into mins at the last steps but I'm not getting ans as 5.can anyone solve for me with detail steps in seconds please? EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14351 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If Samson is filling a bathtub with COLD water, it will take [#permalink] ### Show Tags 08 Sep 2017, 14:44 Hi r19, Can you list out your 'steps' and the work that you did? It might be that you knew how to answer the question, but you made a little math mistake (and that would be easier for another member to explain). GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Manager
Joined: 18 Mar 2015
Posts: 120
Location: India
Schools: ISB '19
GMAT 1: 600 Q47 V26
GPA: 3.59
If Samson is filling a bathtub with COLD water, it will take  [#permalink]

### Show Tags

09 Sep 2017, 06:12
rich ,
Sorry, I should have posted before
cold water = 6 mins 40 sec = 6*60=360+40 = 400 secs
hot water = 8 mins = 8*60 = 480 secs
drain = 13 mins 20 secs = 13*8=780+20=800 secs

equation
1/400+1/480-1/800
taking 10 out
1/40+1/48-1/80
taking 4 out
1/10+1/12-1/20
taking 2 out
1/5+1/6-1/10
lcm = 30
(6+5-1)/30 = 8/30
tell me where I made mistake
Manager
Joined: 19 Jul 2017
Posts: 85
Location: India
Concentration: General Management, Strategy
GPA: 3.5
Re: If Samson is filling a bathtub with COLD water, it will take  [#permalink]

### Show Tags

10 Sep 2017, 20:26
Bunuel wrote:
abhi758 wrote:
If Samson is filling a bathtub with COLD water, it will take him 6 minutes and 40 seconds, and if he fills it with HOT water, it will take him 8 minutes. If draining the tub takes 13 minutes and 20 seconds, how many minutes will it take to fill up the bath tub with both HOT and COLD water running while the plug is out, so the water is constantly draining?

a) 16
b) 12
c) 8.6
d) 5
e) 4.75

Wanted to understand the way the numbers 12, 10 and 6 are arrived at in the net speed calculation.

Times:
$$c=6\frac{2}{3}=\frac{20}{3}$$;
$$h=8$$;
$$d=13\frac{1}{3}=\frac{40}{3}$$.

Remember that we can sum the rates. As rate is the reciprocal of time:
$$\frac{1}{c}+\frac{1}{h}-\frac{1}{d}=\frac{3}{20}+\frac{1}{8}-\frac{3}{40}=\frac{1}{5}=\frac{1}{t}$$ --> $$\frac{1}{5}=\frac{1}{t}$$ --> $$t=5$$.

Since there are 2 reverse operations fill and drain going on, we need to find the net fill - drain in 1 min .

In 1 min 3/20 of cold water is filled and 1/8 of hot water.

So net fill = 3/20+1/8 =11/40;

Water drained in a min = 3/40.

So in a min when 3 operations are simultaneous, it will fill 11/40-3/40 of water tub.
ie 1/5 of tub in 1 min. So the tub will be fully filled in 5mins.

Ans:D
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14351
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If Samson is filling a bathtub with COLD water, it will take  [#permalink]

### Show Tags

11 Sep 2017, 12:26
2
Hi r19,

From a math standpoint, you cannot "reduce" the fractions the way you did without changing their values. Here's a simple example:

1/10 + 1/20 = 2/20 + 1/20 = 3/20

However, if you "take 2 out" the way you did, then you would then end up with:

1/5 + 1/10 = 2/10 + 1/10 = 3/10

This is NOT the same end result (it's actually DOUBLE what it should be).

Your initial 'step' was to convert information into what occurs each second:

1/400 + 1/480 are the two "intakes" and the - 1/800 is the "outtake." Adding those fractions up, we get...

12/4800 + 10/4800 - 6/4800 = 16/4800 = 1/300

This means that with each second that goes by, 1/300 of the bathtub is filled. Thus, it takes 300 seconds = 5 minutes to fill the tub.

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Manager
Joined: 18 Mar 2015
Posts: 120
Location: India
Schools: ISB '19
GMAT 1: 600 Q47 V26
GPA: 3.59
Re: If Samson is filling a bathtub with COLD water, it will take  [#permalink]

### Show Tags

12 Sep 2017, 11:01
@rich....thank you..goot my mistake
Intern
Joined: 21 Sep 2016
Posts: 29
Re: If Samson is filling a bathtub with COLD water, it will take  [#permalink]

### Show Tags

17 Sep 2017, 17:13
So, let C be cold water and H, hot water. Thus, D stands for draining.

$$1/T = 1/C + 1/H - 1/D$$

Converting times:
C -> 6 minutes and 40 seconds are 400 seconds.
H -> 8 minutes are 480 seconds.
D -> 13 minutes and 20 seconds are 800 seconds.

So:

$$1/T = 1/400 + 1/480 - 1/800$$

$$1/T = (12+10-6)/4800$$

$$1/T = 16/4800$$

So, T = 4800/16 -> 300 seconds, or 5 minutes.
Non-Human User
Joined: 09 Sep 2013
Posts: 11393
Re: If Samson is filling a bathtub with COLD water, it will take  [#permalink]

### Show Tags

18 Sep 2018, 00:38
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.
_________________
Re: If Samson is filling a bathtub with COLD water, it will take   [#permalink] 18 Sep 2018, 00:38
Display posts from previous: Sort by