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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

There are three different hoses used to fill a pool: hose [#permalink]

Show Tags

11 Jun 2013, 04:31

6

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

85% (hard)

Question Stats:

49% (02:37) correct
51% (01:39) wrong based on 277 sessions

HideShow timer Statistics

There are three different hoses used to fill a pool: hose x, hose y, and hose z. Hose x can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true? I. d<c II. d>b III. c/3<d<a/3

A) I only B) III only C) I and III only D) II only E) I, II and III

Re: There are three different hoses used to fill a pool: hose [#permalink]

Show Tags

11 Jun 2013, 04:59

Expert's post

1

This post was BOOKMARKED

emmak wrote:

There are three different hoses used to fill a pool: hose x, hose y, and hose z. Hose x can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true? I. d<c II. d>b III. c/3<d<a/3

A) I only B) III only C) I and III only D) II only E) I, II and III

"Stolen" question from GMAT Prep:

Quote:

In a certain bathtub, both the cold-water and the hot-water fixtures leak. The cold-water leak alone would fill an empty bucket in c hours and the hot-water leak alone would fill the same bucket in h hours, where c<h. If both fixtures began to leak at the same time into the empty bucket at their respective constant rates and consequently it took t hours to fill the bucket, which of the following must be true?

I. 0 < t < h II. c < t < h III. c/2 < t < h/2

A. I only B. II only C. III only D. I and II E. I and III

Re: There are three different hoses used to fill a pool: hose [#permalink]

Show Tags

11 Jun 2013, 23:30

2

This post received KUDOS

Name T = full pool X fills a pool in a days ==> 1 day X fills: T/a Y fills a pool in b days ==> 1 day Y fills: T/b Z fills a pool in c days ==> 1 day Z fills: T/c

1 day (X+Y+Z) together fill: T(1/a + 1/b + 1/c) d days (X+Y+Z) together fill: T

==> d = Tx1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca) ==> d = abc/(ab+bc+ca)

Statement 1: d < c ==> Correct because three hoses together fill faster than one hose does

Statement 2: d > b ==> Wrong because d may be less than or greater than b. Please note that the question is MUST BE TRUE.

Statement 3: c/3 < d < a/3 ==> Correct

* Because (ab+bc+ca) < 3ab. [Please note that a > b > c] ==> d = abc/(ab+bc+ca) > abc/3ab ==> d > c/3

* Because (ab+bc+ca) > 3bc [ab > bc; bc = bc; ac > bc ==> ab+bc+ca > 3bc] ==> d = abc/(ab+bc+ca) < abc/3bc ==> d < a/3

Hence, C is correct. _________________

Please +1 KUDO if my post helps. Thank you.

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Re: There are three different hoses used to fill a pool: hose [#permalink]

Show Tags

20 Jun 2013, 06:32

1

This post was BOOKMARKED

pqhai wrote:

Name T = full pool X fills a pool in a days ==> 1 day X fills: T/a Y fills a pool in b days ==> 1 day Y fills: T/b Z fills a pool in c days ==> 1 day Z fills: T/c

1 day (X+Y+Z) together fill: T(1/a + 1/b + 1/c) d days (X+Y+Z) together fill: T

==> d = Tx1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca) ==> d = abc/(ab+bc+ca)

Statement 1: d < c ==> Correct because three hoses together fill faster than one hose does

Statement 2: d > b ==> Wrong because d may be less than or greater than b. Please note that the question is MUST BE TRUE.

Statement 3: c/3 < d < a/3 ==> Correct

* Because (ab+bc+ca) < 3ab. [Please note that a > b > c] ==> d = abc/(ab+bc+ca) > abc/3ab ==> d > c/3

* Because (ab+bc+ca) > 3bc [ab > bc; bc = bc; ac > bc ==> ab+bc+ca > 3bc] ==> d = abc/(ab+bc+ca) < abc/3bc ==> d < a/3

Hence, C is correct.

Thanks for the explanation, however, I don't understand how you get this inequality: \((ab+bc+ca) < 3ab\)

Re: There are three different hoses used to fill a pool: hose [#permalink]

Show Tags

20 Jun 2013, 12:00

2

This post received KUDOS

szDave wrote:

pqhai wrote:

Name T = full pool X fills a pool in a days ==> 1 day X fills: T/a Y fills a pool in b days ==> 1 day Y fills: T/b Z fills a pool in c days ==> 1 day Z fills: T/c

1 day (X+Y+Z) together fill: T(1/a + 1/b + 1/c) d days (X+Y+Z) together fill: T

==> d = Tx1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca) ==> d = abc/(ab+bc+ca)

Statement 1: d < c ==> Correct because three hoses together fill faster than one hose does

Statement 2: d > b ==> Wrong because d may be less than or greater than b. Please note that the question is MUST BE TRUE.

Statement 3: c/3 < d < a/3 ==> Correct

* Because (ab+bc+ca) < 3ab. [Please note that a > b > c] ==> d = abc/(ab+bc+ca) > abc/3ab ==> d > c/3

* Because (ab+bc+ca) > 3bc [ab > bc; bc = bc; ac > bc ==> ab+bc+ca > 3bc] ==> d = abc/(ab+bc+ca) < abc/3bc ==> d < a/3

Hence, C is correct.

Thanks for the explanation, however, I don't understand how you get this inequality: \((ab+bc+ca) < 3ab\)

Hi szDave Because a > b > c So: (1) ab = ab (2) ab > bc (because a > c ==> a*b > c*b) (3) ab > ca (because b > c ==> b*a > c*a)

(1) + (2) + (3) = 3ab > ab + bc + ca This is the key for this question.

Hope it helps.

Regards. _________________

Please +1 KUDO if my post helps. Thank you.

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Re: There are three different hoses used to fill a pool: hose [#permalink]

Show Tags

26 Sep 2013, 09:32

Quote:

There are three different hoses used to fill a pool: hose x, hose y, and hose z. Hose x can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true? I. d<c II. d>b III. c/3<d<a/3

A) I only B) III only C) I and III only D) II only E) I, II and III

I used a conceptual PLUS VIC ( variables in choices MGMAT) approach.

I. d<c - We KNOW this is True because 3 hoses working together MUST BE faster than one hose by itself! B&D out!! II. d>b - This is conceptual as well because we can think of many instances where combining 3 hoses/machines etc. would be faster than ANY individual machine, that's kinda the benefit of combining your rates to increase efficiency so....D & E are out!!

Now we have a 50/50 chance between A & C! better than 20% eh?

III. c/3<d<a/3 - With this option I knew I could try it algebraically but it's very easy to get tangled up in "alphabet soup" (for me), so I went with VIC! **Plus the thing about MUST BE TRUE options is that all you have to do is find 1 option that is to the contrary and you are good to go!** I plugged in 10, 8, and 6, but you can plug in any values and you will see that the principal holds.

Re: There are three different hoses used to fill a pool: hose [#permalink]

Show Tags

31 Mar 2014, 11:48

This question can be answered without really resorting to any calculations at all.

I. d<c. This has to be true, because the three hoses working together will take less time to fill the pool than hose z working alone. CORRECT. II. d>b. This has to be false, because the time taken by the three hoses working together cannot be more than the time taken by hose y working alone. INCORRECT. III. c/3<d<a/3. If all three hoses worked at the rate of the slowest (i.e. hose x which takes a days), then the time taken to fill the pool would be a/3. Since the other two hoses (y and z) are faster than x, the time taken has to be less than a/3. So d<a/3. If all three hoses worked at the rate of the fastest (i.e. hose z which takes c days), then the time taken to fill the pool would be c/3. As the other two hoses (x and y) are slower than z, the time taken has to be more than c/3. So d>c/3. CORRECT.

Re: There are three different hoses used to fill a pool: hose [#permalink]

Show Tags

22 Aug 2015, 19:56

IvanW wrote:

Quote:

There are three different hoses used to fill a pool: hose x, hose y, and hose z. Hose x can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true? I. d<c II. d>b III. c/3<d<a/3

A) I only B) III only C) I and III only D) II only E) I, II and III

I used a conceptual PLUS VIC ( variables in choices MGMAT) approach.

I. d<c - We KNOW this is True because 3 hoses working together MUST BE faster than one hose by itself! B&D out!! II. d>b - This is conceptual as well because we can think of many instances where combining 3 hoses/machines etc. would be faster than ANY individual machine, that's kinda the benefit of combining your rates to increase efficiency so....D & E are out!!

Now we have a 50/50 chance between A & C! better than 20% eh?

III. c/3<d<a/3 - With this option I knew I could try it algebraically but it's very easy to get tangled up in "alphabet soup" (for me), so I went with VIC! **Plus the thing about MUST BE TRUE options is that all you have to do is find 1 option that is to the contrary and you are good to go!** I plugged in 10, 8, and 6, but you can plug in any values and you will see that the principal holds.

Hi there, I´m sorry but I don`t quite understand the III statement.

- In the question stem we are given that: d < c < b < a - In III statement we are given that c/3 < d < a/3. Therefore, c < 3d < a

How is it that when you plugged in d = 6, c = 8, and a = 10, the principle held true?

Can you please show me where I am worng? _________________

Consider giving me Kudos if I helped, but don´t take them away if I didn´t!

Re: There are three different hoses used to fill a pool: hose [#permalink]

Show Tags

11 Jan 2016, 19:05

emmak wrote:

There are three different hoses used to fill a pool: hose x, hose y, and hose z. Hose x can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true? I. d<c II. d>b III. c/3<d<a/3

A) I only B) III only C) I and III only D) II only E) I, II and III

all together work faster than each individually, thus I is always true, and we can eliminate B and D. II - same thing as said before, but d can never be greater than individual rate. thus, II is not correct, and we can eliminate E. III - I used some testing: a=4, b=2, c=1. 1/4+1/2+1/1 = 1+2+4/4 = 7/4 or d=4/7 c/3 = 1/3 d=4/7 a/3 = 4/3

c/3 < d < a/3 true. thus, we can eliminate A and select C.

Re: There are three different hoses used to fill a pool: hose [#permalink]

Show Tags

11 Jan 2016, 19:09

minwoswoh wrote:

IvanW wrote:

Quote:

There are three different hoses used to fill a pool: hose x, hose y, and hose z. Hose x can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true? I. d<c II. d>b III. c/3<d<a/3

A) I only B) III only C) I and III only D) II only E) I, II and III

I used a conceptual PLUS VIC ( variables in choices MGMAT) approach.

I. d<c - We KNOW this is True because 3 hoses working together MUST BE faster than one hose by itself! B&D out!! II. d>b - This is conceptual as well because we can think of many instances where combining 3 hoses/machines etc. would be faster than ANY individual machine, that's kinda the benefit of combining your rates to increase efficiency so....D & E are out!!

Now we have a 50/50 chance between A & C! better than 20% eh?

III. c/3<d<a/3 - With this option I knew I could try it algebraically but it's very easy to get tangled up in "alphabet soup" (for me), so I went with VIC! **Plus the thing about MUST BE TRUE options is that all you have to do is find 1 option that is to the contrary and you are good to go!** I plugged in 10, 8, and 6, but you can plug in any values and you will see that the principal holds.

Hi there, I´m sorry but I don`t quite understand the III statement.

- In the question stem we are given that: d < c < b < a - In III statement we are given that c/3 < d < a/3. Therefore, c < 3d < a

How is it that when you plugged in d = 6, c = 8, and a = 10, the principle held true?

Can you please show me where I am worng?

I don't think you quite understand the concept...you can plug in a, b, and C. D is deducted from a,b,and C. you cannot just plug in value for D.

gmatclubot

Re: There are three different hoses used to fill a pool: hose
[#permalink]
11 Jan 2016, 19:09

Last year when I attended a session of Chicago’s Booth Live , I felt pretty out of place. I was surrounded by professionals from all over the world from major...

I recently returned from attending the London Business School Admits Weekend held last week. Let me just say upfront - for those who are planning to apply for the...