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

It is currently 21 Mar 2019, 07:09

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

M01-07

  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: 53768
M01-07  [#permalink]

Show Tags

New post 16 Sep 2014, 00:14
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

74% (02:11) correct 27% (02:23) wrong based on 200 sessions

HideShow timer Statistics

A ship is transporting several cats and a crew (sailors, a cook, and a one-legged captain) to a nearby port. If these passengers combined have 15 heads and 41 legs, then how many cats is the ship transporting?

A. 3
B. 5
C. 6
D. 7
E. 8

_________________

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53768
Re M01-07  [#permalink]

Show Tags

New post 16 Sep 2014, 00:14
1
3
Official Solution:

A ship is transporting several cats and a crew (sailors, a cook, and a one-legged captain) to a nearby port. If these passengers combined have 15 heads and 41 legs, then how many cats is the ship transporting?

A. 3
B. 5
C. 6
D. 7
E. 8


Step 1: Simplify. The captain and the cook together have 2 heads and 3 legs; therefore, all cats and all sailors together have 13 heads and 38 legs.

Step 2: Express the remaining information in mathematical equations, where \(S\) is the number of sailors and \(C\) is the number of cats. Multiply \(S\) and \(C\) by the number of legs each has, and set the equation equal to the remaining number of legs. The second equation represents the number of remaining heads:
\(4C + 2S = 38\)
\(C + S = 13\)

Solve the second equation for \(S\), plug the answer into the first equation, and solve for \(C\).
\(4C + 2(13-C) = 38\)
\(2C = 38 - 26 = 12\)
\(C = 6\)

Therefore, the ship has 6 cats on board.

Another approach is to backsolve. For example, if you choose Answer (B): 5 cats would mean 5 heads and 20 legs, add 2 heads and 3 legs for the captain and the cook, and the remaining 8 heads belong to the sailors who would then have 18 legs, because \(41 - (20 + 3) = 18\). 18 legs for 8 sailors would mean that each sailor has 2.25 legs, which is not reasonable. Continue backsolving until you find the correct answer.


Answer: C
_________________

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

Intern
Intern
avatar
Joined: 12 Nov 2014
Posts: 3
Concentration: Finance, Real Estate
WE: Investment Banking (Investment Banking)
Re: M01-07  [#permalink]

Show Tags

New post 29 Jan 2015, 15:10
Hi Bunuel,

Could you explain why you chose to take
Quote:
The captain and the cook together have 2 heads and 3 legs
rather than just the captain? I solved by removing only the captain (1 head and 1 leg) and got the answer C.
Intern
Intern
avatar
Joined: 19 Dec 2014
Posts: 1
Re: M01-07  [#permalink]

Show Tags

New post 31 Jan 2015, 15:29
adgrossb,

The problem says that the captain has 1 leg. Thus, it is safe to assume that the cook (and sailors) has two legs, unless otherwise stated. So, the captain and the cook together have 2 heads and 3 legs.
Intern
Intern
avatar
Joined: 19 Sep 2014
Posts: 22
GPA: 3.96
GMAT ToolKit User Reviews Badge
Re M01-07  [#permalink]

Show Tags

New post 16 Aug 2015, 06:10
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Kindly explain the second equation 4C+2S=38.How come 4C and 2S is in the equation.Please explain.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53768
Re: M01-07  [#permalink]

Show Tags

New post 17 Aug 2015, 04:13
1
schak2rhyme wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Kindly explain the second equation 4C+2S=38.How come 4C and 2S is in the equation.Please explain.


The captain and the cook together have 2 heads and 3 legs; therefore, all cats and all sailors together have 13 heads and 38 legs. Each cat has 4 legs and each sailor has 2 legs, thus 4C + 2S = 38.
_________________

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

Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2562
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: M01-07  [#permalink]

Show Tags

New post 31 Oct 2015, 20:32
i solved this way:
captain - 1 head 1 leg
remains 14 heads 40 legs
-1 human - 13 heads 38 legs
-1 human 12 heads 36 legs
-1 human 11 heads 34 legs
-1 human 10 heads 32 legs
-1 human 9 heads 30 legs
-1 human 8 heads 28 legs
-1 human 7 heads 26 legs
-1 human 6 heads 24 legs
now 24 is divisible by 6.
if we continue to remove heads/legs as if there were more humans, we would get to numbers that are not divisible by 4 when we have a specific number of heads..therefore, there must be 6 cats.

for the sake of making sure:
5 heads 22 legs
4 heads 20 legs
3 heads 18 legs
2 heads 16 legs
1 head 14 legs (mutant cat) :)

C is the answer :)
Senior Manager
Senior Manager
User avatar
Joined: 31 Mar 2016
Posts: 383
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)
GMAT ToolKit User Premium Member
Re M01-07  [#permalink]

Show Tags

New post 26 Jul 2016, 10:58
I think this is a high-quality question and I agree with explanation. Great! terrific trap
Intern
Intern
avatar
B
Joined: 28 Apr 2016
Posts: 19
Re: M01-07  [#permalink]

Show Tags

New post 26 Mar 2017, 04:54
I just left the one-leg person of of both equations and still get the answer. It doesnt matter whether you include captain and cook or not because the question asks about cats.

Cats: C
People: P
1 Leg person: X

Without one-leg person there are 40 legs.
4C+2P: 40

Without one leg person there are 14 heads
C+P: 14

Thus C=6
Manager
Manager
avatar
B
Status: Turning my handicaps into assets
Joined: 09 Apr 2017
Posts: 123
CAT Tests
Re: M01-07  [#permalink]

Show Tags

New post 15 May 2018, 05:37
I think the best way to solve this question under time pressure is to check the answer choices.
_________________

If time was on my side, I'd still have none to waste......

VP
VP
User avatar
P
Joined: 31 Oct 2013
Posts: 1272
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
M01-07  [#permalink]

Show Tags

New post 25 Feb 2019, 04:02
Bunuel wrote:
A ship is transporting several cats and a crew (sailors, a cook, and a one-legged captain) to a nearby port. If these passengers combined have 15 heads and 41 legs, then how many cats is the ship transporting?

A. 3
B. 5
C. 6
D. 7
E. 8



Back solve the question.

Option C)

cats = 6

legs = 6*4 = 24.

remaining head = 9

remaining legs = 17.

we must have 9*2 = 18 legs. but our captain is one-leg one.

9*2 = 18

but we have 17 legs.

Matched.

In this ways , other options can also be verified.

Max 1 min will be needed.

C is the correct answer.
Intern
Intern
avatar
Joined: 04 Feb 2018
Posts: 3
Re: M01-07  [#permalink]

Show Tags

New post 25 Feb 2019, 16:31
Cook & one-legged captain have 2 heads and 3 legs.
Therefore 13 heads and 38 legs are remaining for cats and sailors.
No of Sailors No of Cats Total Number of legs
0 13 52
1 12 50
2 11 48
3 10 46
4 9 44
5 8 42
6 7 40
7 6 38 (correct answer).
As can be observed, the only option that results in 38 legs is the option where we have 7 sailors and 6 cats. Therefore there are 6 cats in the ship.
GMAT Club Bot
Re: M01-07   [#permalink] 25 Feb 2019, 16:31
Display posts from previous: Sort by

M01-07

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

Moderators: chetan2u, Bunuel



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®.