M01-07

Question

A ship is carrying several cats, along with a crew consisting of sailors, a cook, and a one-legged captain, to a nearby port. If the crew and cats collectively have 15 heads and 41 legs, how many cats are on the ship?

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

Show Answer

Official Answer

C

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

Bunuel · Accepted Answer

Official Solution:

A ship is carrying several cats, along with a crew consisting of sailors, a cook, and a one-legged captain, to a nearby port. If the crew and cats collectively have 15 heads and 41 legs, how many cats are on the ship?

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

Show Answer

Official Answer

C

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

Excluding the cook, the remaining passengers — cats, sailors, and the one-legged captain — collectively have 14 heads and 39 legs.
 
Excluding the one-legged captain, the remaining passengers — cats and sailors — collectively have 13 heads and 38 legs.
 
Let's assume there are  x  cats and  13 - x  sailors. Consequently, we can set up the equation  4*x + 2*(13 - x) = 38 , which gives  x=6 .
 
Another way to solve this question is via Backsolving:
 
1. We know that we have 1 cook and 1-legged captain, removing them from the totals, leaves us with 38 legs (out of 41 starting legs) and 13 heads (out of 15 starting heads). Things are a bit clearer now. 
 
 2. Now we can pick 7 cats and try if this makes the puzzle work - that would be 7 heads and 28 legs, plus 5 sailors (38-28 legs gives us that) But the heads do not match, we need 13 heads but 7+5 is only 12. Thus likely need a smaller number of cats, which they have a 2:1 relationship with humans, so removing 1 cat will give us 2 sailors. 
 
 3. Picking 6 cats, give us 24 legs, and then 38-24 = 14 sailor legs or 7 sailors with 7 heads. This means 13 heads, which matches our totals.

Answer: C

iantGMAT · Answer

I find using simultaneous equations more intuitive:

Let C = no. of cats, S = no. of sailors
  No. of Legs  
4C + 2S + 2 + 1 = 41
4C + 2S = 38 ( Equation 1 )
  No. of Heads  
C + S + 1 + 1 = 15
C + S = 13
2C + 2S = 26 ( Equation 2 )

Equation 1  -  Equation 2 
2C = 12
C = 2

Senthil7 · Answer

I think this is a  high-quality  question and I agree with explanation. Great! terrific trap

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

abini · Answer

Cn you please explain the 3rd line on how did you set up the equation?

Bunuel · Answer

The equation is set up by considering that each cat has 4 legs and each sailor has 2 legs. With x cats and 13 - x sailors, the total number of legs is 4x + 2(13 - x) = 38, which represents the total legs for both.

sachingc · Answer

I like the solution - it’s helpful.

Deepannita_ · Answer

I like the solution - it’s helpful.

Mahuettm · Answer

I like the solution - it’s helpful.

Emi4016 · Answer

I like the solution - it’s helpful.

godinero · Answer

I like the solution - it’s helpful.

Vishnupriyasundar · Answer

I like the solution - it’s helpful.

Bixy34 · Answer

I like the solution - it’s helpful.

coala · Answer

I did not quite understand the solution. how did you get 13-x sailors?

Bunuel · Answer

The total number of heads for cats and sailors is 13. Since each has one head, the number of cats is x, so the number of sailors must be 13 - x to keep the total head count at 13.

That’s why we write it as x cats and 13 - x sailors.

lekhaabra · Answer

I like the solution - it’s helpful.

agabdulina · Answer

I like the solution - it’s helpful.

shaliny · Answer

I like the solution - it’s helpful.

veltenetur · Answer

I don’t quite agree with the solution. Why is cook not a passenger?

M01-07

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