Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 09 Feb 2013
Posts: 121

There are three different hoses used to fill a pool: hose [#permalink]
Show Tags
11 Jun 2013, 04:31
12
This post was BOOKMARKED
Question Stats:
52% (02:40) correct
48% (01:36) wrong based on 396 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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Kudos will encourage many others, like me. Good Questions also deserve few KUDOS.



Math Expert
Joined: 02 Sep 2009
Posts: 39662

Re: There are three different hoses used to fill a pool: hose [#permalink]
Show Tags
11 Jun 2013, 04:59
1
This post received KUDOS
Expert's post
2
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 coldwater and the hotwater fixtures leak. The coldwater leak alone would fill an empty bucket in c hours and the hotwater 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 Discussed here: inacertainbathtubboththecoldwaterandthehotwater127878.html
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics



Verbal Forum Moderator
Joined: 16 Jun 2012
Posts: 1127
Location: United States

Re: There are three different hoses used to fill a pool: hose [#permalink]
Show Tags
11 Jun 2013, 23:30
3
This post received KUDOS
1
This post was BOOKMARKED
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."
Chris Bangle  Former BMW Chief of Design.



Intern
Joined: 29 Jan 2013
Posts: 1
GPA: 3.5

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: \((ab+bc+ca) < 3ab\) I tried to solve it but was unsuccesful Here is where I got stuck: \(\frac{c}{3} < d = \frac{abc}{ab+ac+cb}\) \(c^2b + abc + ac^2 < 3 abc\) \(c (b+a) < 2ab\) ???
_________________
Just do it!



Verbal Forum Moderator
Joined: 16 Jun 2012
Posts: 1127
Location: United States

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: \((ab+bc+ca) < 3ab\) I tried to solve it but was unsuccesful Here is where I got stuck: \(\frac{c}{3} < d = \frac{abc}{ab+ac+cb}\) \(c^2b + abc + ac^2 < 3 abc\) \(c (b+a) < 2ab\) ??? Hi szDave Because a > b > cSo: (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."
Chris Bangle  Former BMW Chief of Design.



Intern
Joined: 05 Jun 2011
Posts: 15
Schools: Kellog, Stern, Stanford, Booth,HBS, Wharton

Re: There are three different hoses used to fill a pool: hose [#permalink]
Show Tags
26 Sep 2013, 09:32
1
This post received KUDOS
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.



Current Student
Joined: 06 Sep 2013
Posts: 1997
Concentration: Finance

Re: There are three different hoses used to fill a pool: hose [#permalink]
Show Tags
31 Mar 2014, 09:24
1
This post was BOOKMARKED
Stolen question from GMAT Prep again. Prep companies need to start getting more creative Express solution Statement 1 is correct because the three hoses together fill faster than one hose does ALWAYS. Now, the second statement is NOT always true because 'd' may be less than or greater than 'b', it depends on the values of 'a' and 'c'. Third condition is ALWAYS true, 3 times the average must always be between the extremes. Therefore C is correct Hope this helps Cheers J



VP
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1250
GRE 1: 1540 Q800 V740

Re: There are three different hoses used to fill a pool: hose [#permalink]
Show Tags
31 Mar 2014, 11:48
1
This post was BOOKMARKED
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. (C) it is.
_________________
GyanOne  Top MBA Rankings and MBA Admissions Blog
Top MBA Admissions Consulting  Top MiM Admissions Consulting
Premium MBA Essay ReviewBest MBA Interview PreparationExclusive GMAT coaching
Get a FREE Detailed MBA Profile Evaluation  Call us now +91 98998 31738



Manager
Joined: 10 May 2014
Posts: 141

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!
What would you do if you weren´t afraid?



CEO
Joined: 17 Jul 2014
Posts: 2524
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

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.



CEO
Joined: 17 Jul 2014
Posts: 2524
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

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.



Manager
Joined: 14 Oct 2012
Posts: 126

Re: There are three different hoses used to fill a pool: hose [#permalink]
Show Tags
08 Dec 2016, 13:06
Hello friends, my 2 cents a>b>c>d => 3>2>1>d abc/(ab+bc+ca) = 6/(6+2+3) = 6/11 ~ 0.6 ~> 3>2>1>0.6 (iii) c/3 = 1/3 = 0.33 & a/3 = 3/3 = 1 => 0.33 < 0.6 < 1 => c/3 < d < a/3




Re: There are three different hoses used to fill a pool: hose
[#permalink]
08 Dec 2016, 13:06







