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# M01-07

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Math Expert
Joined: 02 Sep 2009
Posts: 58325

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16 Sep 2014, 00:14
00:00

Difficulty:

35% (medium)

Question Stats:

74% (02:06) correct 26% (02:23) wrong based on 223 sessions

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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

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Posts: 58325

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16 Sep 2014, 00:14
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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.

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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.
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Joined: 19 Dec 2014
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31 Jan 2015, 15:29

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.
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Joined: 19 Sep 2014
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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.
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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.
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31 Oct 2015, 20:32
i solved this way:
captain - 1 head 1 leg
-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:
1 head 14 legs (mutant cat)

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26 Jul 2016, 10:58
I think this is a high-quality question and I agree with explanation. Great! terrific trap
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Joined: 28 Apr 2016
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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
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15 May 2018, 05:37
I think the best way to solve this question under time pressure is to check the answer choices.
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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 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.

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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
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.
Re: M01-07   [#permalink] 25 Feb 2019, 16:31
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# M01-07

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