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m04q36- Fish that had a 60 foot long head [#permalink]
09 Feb 2009, 15:23

7

This post received KUDOS

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This post was BOOKMARKED

One fisherman was telling his friends that he caught a fish that had a 60 foot long head. It also had a tail that was as long as the fish's head and a half of its body. Finally, the body was half the size of the whole fish. What is the length of this fish?

Should be E. Solved it this way - let H,B, T represent the the Head, Body, Tail respectively of the fish. and let X be the entire length of the fish. Given: H=60 T=60 + B/2 B=X/2 Rewriting T=60 + X/4, now since all the equations on the RHS comprise only of numbers and a SINGLE variable X, we apply the following Equation -

H+B+T = X Therefore, (60) + (X/2) + (60 + X/4) = X Solving, X=480... Voila!! Therefore option E

Re: m04q36- Fish that had a 60 foot long head [#permalink]
11 Oct 2012, 09:14

2

This post received KUDOS

People getting 240 are confused by the statement "It also had a tail that was as long as the fish's head and a half of its body", assuming that the tail is as long as the fish head AND that the tail is also as long as half of its body. The statement should have read "It also had a tail that was as long as the fish's head PLUS a half of its body".

I guess it's just a matter of wording the question better so as not to confuse people.

Confusing part: Case 1) tail=60 ---> C or tail=(1/2)body ---> D

OR

Case 2) tail=60 + (1/2)body ---> E

Sol:- ------------------------------------ If we proceed taking Case 1), we have

whole = 2 * body ---> (from B) = 2 * (2*tail) ---> (from D) = 2 * (2*60) ---> (from C) = 240 ------------------------------------ Now if we consider Case 2), Let us first rearrange equation E, body = 2 * (tail - 60) ---> F

From B, we have whole = 2 * body = 2 * { 2 * (tail - 60) } ---> Using F

Now we have nowhere to go. ------------------------------------

I agree that the sentence is a bit confusing, and so we have to consider both the scenarios. It's good that the second case is not leading us to any solution or to better say, it's not leading as to any of the other answer option.

I think, it'll be better that we keep such sentence structure in mind and pray to God not to pose such questions again. Amen!

HTH _________________

+++ Believe me, it doesn't take much of an effort to underline SC questions. Just try it out. +++ +++ Please tell me why other options are wrong. +++

~~~ The only way to get smarter is to play a smarter opponent. ~~~

let us represent head , body and tail with H , B and T respectively and total length of fish be L According to question, H=60 ft T=60 + 1/2 B B=1/2 L Now, H+T+B=L =>60+ 60+ L/4 + L/2 = L 120 + 3L/4=L L/4=120 L=120 x 4 L=480 Ans E

Re: Problem Solving 700+ [#permalink]
12 Sep 2011, 19:59

gokoli wrote:

One fisherman was telling his friends that he caught a fish that had a 60 foot long head. It also had a tail that was as long as the fish's head and a half of its body. If the body was half the size of the whole fish, what is the length of the fish?

120 200 240 400 480

Our fish has three parts, the head, body and tail. Say the length of the body is b. Then the length of the fish is 2b, since the body is half of the fish. We also know that the tail is 60 + 0.5b (it's equal to the length of the head plus half the length of the body). Adding the lengths of the three parts (head = 60, body = b, tail = 60 + 0.5b), we must get 2b, the total length:

60 + b + 60 + 0.5b = 2b 120 + 1.5b = 2b 120 = 0.5b 240 = b

So the length of the body is 240, and the length of the fish, which is 2b, is 480. _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Re: m04q36- Fish that had a 60 foot long head [#permalink]
14 Oct 2011, 07:07

one can simply get the ans....putting each option nd checking we can get the ans... we know the head of the fish is 60 foot long... for moment assume the total length of fish be 480 then its tail length=60+480 divided by 2=260 260+60=320 a/q, his body was half the size of whole fish so 320/2=160 320+160=480 ans...

Re: m04q36- Fish that had a 60 foot long head [#permalink]
11 Oct 2012, 04:27

Expert's post

seofah wrote:

One fisherman was telling his friends that he caught a fish that had a 60 foot long head. It also had a tail that was as long as the fish's head and a half of its body. Finally, the body was half the size of the whole fish. What is the length of this fish?

I feel that the second sentence is ambiguous. Any comments will be appreciated

One fisherman was telling his friends that he caught a fish that had a 60 feet long head and a tail which was equal to the length of the head plus half the length of the body. If the body was half the length of the whole fish, what is the length of the fish?

A. 120 B. 200 C. 240 D. 400 E. 480

The fish has three parts: the head, body and tail: \(head+body+tail=total \ length\);

Say the length of the body is \(b\).

Now, since the body was half the size of the whole fish, then \(total \ length=2b\);

Next, since its tail equals to the length of the head plus half the length of the body then \(tail=60+0.5b\);

So we have that: \(head+body+tail=total \ length\) --> \(60+b+(60+0.5b)=2b\) --> \(b=240\) --> \(total \ length=2b=480\).