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

It is currently 22 Oct 2018, 11:41

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

An automobile tire has two punctures. The first puncture by itself wou

  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: 50042
An automobile tire has two punctures. The first puncture by itself wou  [#permalink]

Show Tags

New post 26 Oct 2017, 02:58
1
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

86% (01:13) correct 14% (00:56) wrong based on 121 sessions

HideShow timer Statistics

An automobile tire has two punctures. The first puncture by itself would make the tire flat in 9 minutes. The second puncture by itself would make the tire flat in 6 minutes. How long will it take for both punctures together to make the tire flat? (Assume the air leaks out at a constant rate.)

(A) 18/5 minutes
(B) 4 minutes
(C) 21/4 minutes
(D) 15/2 minutes
(E) 15 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

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3194
Location: India
GPA: 3.12
Premium Member CAT Tests
An automobile tire has two punctures. The first puncture by itself wou  [#permalink]

Show Tags

New post 26 Oct 2017, 04:18
Bunuel wrote:
An automobile tire has two punctures. The first puncture by itself would make the tire flat in 9 minutes. The second puncture by itself would make the tire flat in 6 minutes. How long will it take for both punctures together to make the tire flat? (Assume the air leaks out at a constant rate.)

(A) 18/5 minutes
(B) 4 minutes
(C) 21/4 minutes
(D) 15/2 minutes
(E) 15 minutes


If we assume the quantity of air that the tire contains to be 54 units,
the first puncture leaks 6 units/minute and the second puncture leaks 9 units/minute.
Together, they would leak 15 units/minute

Hence, we would need \(\frac{54}{15}\) = \(\frac{18}{5}\)minutes to leak the air if both the punctures leak air(Option A)
_________________

You've got what it takes, but it will take everything you've got

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6978
Re: An automobile tire has two punctures. The first puncture by itself wou  [#permalink]

Show Tags

New post 26 Oct 2017, 05:20
pushpitkc wrote:
Bunuel wrote:
An automobile tire has two punctures. The first puncture by itself would make the tire flat in 9 minutes. The second puncture by itself would make the tire flat in 6 minutes. How long will it take for both punctures together to make the tire flat? (Assume the air leaks out at a constant rate.)

(A) 18/5 minutes
(B) 4 minutes
(C) 21/4 minutes
(D) 15/2 minutes
(E) 15 minutes


If we assume the quantity of air that the tire contains to be 54 units,
the first puncture leaks 6 units/minute and the second puncture leaks 9 units/minute.
Together, they would leak 15 units/minute

Hence, we would need \(\frac{54}{15}\) = \(\frac{18}{5}\)minutes to leak the air if both the punctures leak air(Option A)



Hi,

THAT may not be the correct way..
If you had assumed it to be 15 units, ans would be 15/15=1

One releases air in 9 min ; so in 1 min, it will release 1/9
other releases in 6 minutes ; so in 1 min it will release 1/6
so in 1 minute combined they will release \(\frac{1}{9}+\frac{1}{6} = \frac{15}{54}\)...
so entire air will be released in \(\frac{54}{15} = \frac{18}{5}\)
A


otherwise, if one releases in 9 min and second in less than that, ans has to be <9/2
all but A and B remain
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3194
Location: India
GPA: 3.12
Premium Member CAT Tests
Re: An automobile tire has two punctures. The first puncture by itself wou  [#permalink]

Show Tags

New post 26 Oct 2017, 05:58
chetan2u wrote:
pushpitkc wrote:
Bunuel wrote:
An automobile tire has two punctures. The first puncture by itself would make the tire flat in 9 minutes. The second puncture by itself would make the tire flat in 6 minutes. How long will it take for both punctures together to make the tire flat? (Assume the air leaks out at a constant rate.)

(A) 18/5 minutes
(B) 4 minutes
(C) 21/4 minutes
(D) 15/2 minutes
(E) 15 minutes


If we assume the quantity of air that the tire contains to be 54 units,
the first puncture leaks 6 units/minute and the second puncture leaks 9 units/minute.
Together, they would leak 15 units/minute

Hence, we would need \(\frac{54}{15}\) = \(\frac{18}{5}\)minutes to leak the air if both the punctures leak air(Option A)



Hi,

THAT may not be the correct way..
If you had assumed it to be 15 units, ans would be 15/15=1

One releases air in 9 min ; so in 1 min, it will release 1/9
other releases in 6 minutes ; so in 1 min it will release 1/6
so in 1 minute combined they will release \(\frac{1}{9}+\frac{1}{6} = \frac{15}{54}\)...
so entire air will be released in \(\frac{54}{15} = \frac{18}{5}\)
A


otherwise, if one releases in 9 min and second in less than that, ans has to be <9/2
all but A and B remain


If I had assumed 15 units,
the first puncture would have leaked \(\frac{15}{9}\) or \(\frac{5}{3}\) units in a minute
and the second puncture would have leaked \(\frac{15}{6}\) or \(\frac{5}{2}\) units in a minute

Combined they would have released \(\frac{5}{3}+\frac{5}{2} = \frac{10+15}{6} = \frac{25}{6}\) units in a minute.

The time taken to release the air by both the punctures will now be \(\frac{15 * 6}{25} = \frac{90}{25} = \frac{18}{5}\)(Option A)
_________________

You've got what it takes, but it will take everything you've got

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: An automobile tire has two punctures. The first puncture by itself wou  [#permalink]

Show Tags

New post 29 Oct 2017, 07:47
Bunuel wrote:
An automobile tire has two punctures. The first puncture by itself would make the tire flat in 9 minutes. The second puncture by itself would make the tire flat in 6 minutes. How long will it take for both punctures together to make the tire flat? (Assume the air leaks out at a constant rate.)

(A) 18/5 minutes
(B) 4 minutes
(C) 21/4 minutes
(D) 15/2 minutes
(E) 15 minutes


The combined rate of the two punctures is:

1/9 + 1/6 = 2/18 + 3/18 = 5/18

Thus, the time to make a flat with both punctures is 1/(5/18) = 18/5 minutes.

Answer: A
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12694
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: An automobile tire has two punctures. The first puncture by itself wou  [#permalink]

Show Tags

New post 25 Nov 2017, 14:51
Hi All,

This is an example of a "Work Formula" question - when you have two entities working together on a task, you can use the following formula to determine how long it will take the two entities to complete the task:

(A)(B)/(A+B) = time to complete the task (where A and B are the two times it takes the individuals to complete the task when working alone)

We're told that the first puncture would create a flat tire in 9 minutes and the second puncture would make a flat tire in 6 minutes. Plugging in those values, we'd have...

(9)(6)/(9+6) = 54/15 = 18/5 = 3 3/5 minutes to make a flat tire

Final Answer:

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

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/

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

GMAT Club Bot
Re: An automobile tire has two punctures. The first puncture by itself wou &nbs [#permalink] 25 Nov 2017, 14:51
Display posts from previous: Sort by

An automobile tire has two punctures. The first puncture by itself wou

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


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®.