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

It is currently 20 Aug 2019, 15:52

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

Question of the Week- 24 (Three pipes, A, B , C can fill a tank in...)

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

Hide Tags

Find Similar Topics 
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3019
Question of the Week- 24 (Three pipes, A, B , C can fill a tank in...)  [#permalink]

Show Tags

New post Updated on: 27 Feb 2019, 04:12
19
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

53% (03:01) correct 47% (02:47) wrong based on 131 sessions

HideShow timer Statistics

e-GMAT Question of the Week #24

Three pipes A, B and C can fill a tank in 10, 15 and 25 minutes respectively. All the three taps are used simultaneously to fill the tank. But, due to a leak at the bottom of the tank, only \(\frac{1}{3}\)rd of the tank was filled by the time it was supposed to be full. In how much time could the leak empty a full tank?

    A. \(\frac{75}{31}\)

    B. \(\frac{150}{31}\)

    C. \(\frac{225}{31}\)

    D. \(\frac{15}{2}\)

    E. \(\frac{450}{31}\)


Image

_________________

Originally posted by EgmatQuantExpert on 23 Nov 2018, 06:57.
Last edited by EgmatQuantExpert on 27 Feb 2019, 04:12, edited 1 time in total.
Most Helpful Expert Reply
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3019
Re: Question of the Week- 24 (Three pipes, A, B , C can fill a tank in...)  [#permalink]

Show Tags

New post 28 Nov 2018, 05:55
1
4

Solution


Given:
    • Three pipes, A, B and C can fill a tank in 10, 15 and 25 days respectively
    • All the three taps are used simultaneously to fill the tank
    • Only \(\frac{1}{3}^{rd}\) of the tank was filled by the time it was supposed to be full, due to a leak

To find:
    • The time in which the leak can empty a full tank

Approach and Working:
    • Three taps together can fill the tank in \(\frac{1}{((1/10) + (1/15) + (1/25))} = \frac{150}{31}\) days
      o But only \(\frac{1}{3}^{rd}\) of the tank was filled in \(\frac{150}{31}\) days, which implies that the leak can empty \(\frac{2}{3}^{rd}\) of the tank in \(\frac{150}{31}\) days

    • Thus, it can empty a full tank in \((\frac{150}{31}) * (\frac{3}{2})\) days = \(\frac{225}{31}\) days

Hence the correct answer is Option C.

Answer: C

Image

_________________
General Discussion
Intern
Intern
avatar
B
Joined: 20 Aug 2018
Posts: 4
Location: United States
Schools: HBS '22, CBS '22, Yale '22
GMAT 1: 740 Q49 V41
Re: Question of the Week- 24 (Three pipes, A, B , C can fill a tank in...)  [#permalink]

Show Tags

New post 23 Nov 2018, 10:03
1
3
This took me a little over 3 minutes but...

First let's figure out how much time it SHOULD take the pipes to fill the tank:

Individual rates of the three pipes are 1/10, 1/15, and 1/25, respectively.

Using W = R*T, and setting W = 1, we know that together, the three pipes can fill the tank in 1/((15+10+6)/150), or 150/31 units of time.

Next we need to find the rate that the tank is leaking. We know that 1/3 of the tank is left after this period (150/31) of time, so we set a new equation with the W = R*T formula:

(1/3) = ((31/150) - (leaking rate)) * (150/31)

After some "quick" algebra, we identify that:

31/450 = 31/150 - leaking rate

Leaking rate = (93/450) - (31/450) = 62/450 or 31/225

FINALLY, we need to know how long it would take the lead to drain an entire tank:

Back to W=R*T, we know that if unit of work is 1, then R and T are reciprocals of each other, so t=225/31 or ANSWER C

I really hope that's right...

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 21 Mar 2016
Posts: 20
GMAT ToolKit User
Re: Question of the Week- 24 (Three pipes, A, B , C can fill a tank in...)  [#permalink]

Show Tags

New post 14 Dec 2018, 10:00
Hi
Thank you for the solution.
But can you please explain the highlighted part?
Thanks again!

EgmatQuantExpert wrote:

Solution


Given:
    • Three pipes, A, B and C can fill a tank in 10, 15 and 25 days respectively
    • All the three taps are used simultaneously to fill the tank
    • Only \(\frac{1}{3}^{rd}\) of the tank was filled by the time it was supposed to be full, due to a leak

To find:
    • The time in which the leak can empty a full tank

Approach and Working:
    • Three taps together can fill the tank in \(\frac{1}{((1/10) + (1/15) + (1/25))} = \frac{150}{31}\) days
      o But only \(\frac{1}{3}^{rd}\) of the tank was filled in \(\frac{150}{31}\) days, which implies that the leak can empty \(\frac{2}{3}^{rd}\) of the tank in \(\frac{150}{31}\) days

    Thus, it can empty a full tank in \((\frac{150}{31}) * (\frac{3}{2})\) days = \(\frac{225}{31}\) days
Hence the correct answer is Option C.

Answer: C

Image
Director
Director
User avatar
P
Joined: 20 Sep 2016
Posts: 638
Location: India
Concentration: Strategy, Operations
GPA: 3.95
WE: Operations (Real Estate)
GMAT ToolKit User
Re: Question of the Week- 24 (Three pipes, A, B , C can fill a tank in...)  [#permalink]

Show Tags

New post 15 Dec 2018, 06:44
EgmatQuantExpert wrote:
Three pipes A, B and C can fill a tank in 10, 15 and 25 minutes respectively. All the three taps are used simultaneously to fill the tank. But, due to a leak at the bottom of the tank, only \(\frac{1}{3}\)rd of the tank was filled by the time it was supposed to be full. In how much time could the leak empty a full tank?

    A. \(\frac{75}{31}\)

    B. \(\frac{150}{31}\)

    C. \(\frac{225}{31}\)

    D. \(\frac{15}{2}\)

    E. \(\frac{450}{31}\)


Image


TIme taken : 1 min 16 seconds
used the choices :
approach :
first calculate the together rate = \(\frac{150}{3}\)
check the choices ...option B has \(\frac{150}{3}\) then the tank would have filled halfway ...because the leak and the filling pipes are working at the same rate and hence the work done by them will be equal ...but we are given work done is less than half...eliminate B
( proabibility of answering correct = 1/4)

from the above cognition we can undertsnad that the empty rate is greater than\(\frac{150}{3}\)
eliminate A
(P(correct answer) =1/3)

answer choice C is just plain wrong as we have a prime number in the denominator so no matter what we do we still are going to end up up 31
eliminate D
P(correct answer(=1/2

Option E = \(\frac{450}{3}\) ...this is 3 times the rate of together filling... if the empty rate were 3 times the filling the rate then the tank may not even be filled 10 percent let alone 33%

only plausible answer choice is C
Intern
Intern
User avatar
B
Status: when you say,"I can or I can't", Both times you are right!
Joined: 26 Nov 2018
Posts: 31
Location: India
Re: Question of the Week- 24 (Three pipes, A, B , C can fill a tank in...)  [#permalink]

Show Tags

New post 11 Jan 2019, 20:59
total time: 150/31 is required to empty the tank to 2/3 or to fill the tank to 1/3

time: 150/3

work is done: 2/3

2/3 work is done in 150/31(time)

complete work is done: 150/31*3/2 = 225/31


let me know if it is helpful to anyone
GMAT Club Bot
Re: Question of the Week- 24 (Three pipes, A, B , C can fill a tank in...)   [#permalink] 11 Jan 2019, 20:59
Display posts from previous: Sort by

Question of the Week- 24 (Three pipes, A, B , C can fill a tank in...)

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





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