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m04q36 Fish that had a 60 foot long head [#permalink]
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09 Feb 2009, 16:23
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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? (A) 120 (B) 200 (C) 240 (D) 400 (E) 480 Source: GMAT Club Tests  hardest GMAT questions I feel that the second sentence is ambiguous. Any comments will be appreciated



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Re: M4  36 ambiguous sentence? [#permalink]
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09 Feb 2009, 23:49
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Making equations out of the sentences, we have head=60 > A body=(1/2)whole > B 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
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Re: M04  36 ambiguous sentence? [#permalink]
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07 Oct 2010, 05:06
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Here's how I solved it (let H stand for Head, B for Body, and T for Tail):
"One fisherman was telling his friends that he caught a fish that had a 60 foot long head" => Equation 1: H = 60 ft.
"It also had a tail that was as long as the fish's head and a half of its body." => Equation 2: T = 60ft. + 0.5*B
"Finally, the body was half the size of the whole fish. What is the length of this fish?" => Equation 3: B = 0.5*(60ft. + T + B)
Solve Equation 3 for B => B = 60ft. + T Plug result into Equation 2 to get T = 180ft. Based on T = 180ft. => B = 240ft.
The total length of the fish is H + B + T = 60ft. + 240ft. + 180ft. = 480ft. Hence, solution E is correct.



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Re: M04  36 ambiguous sentence? [#permalink]
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07 Oct 2010, 05:46
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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



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Re: M04  36 ambiguous sentence? [#permalink]
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07 Oct 2010, 06:50
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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 RJ



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Re: M04  36 ambiguous sentence? [#permalink]
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07 Oct 2010, 09:40
Got it wrong .But after seeing the answer and reading it once more, solved it correctly.A very good question.Thanks.KUDOS for this.



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Re: M04  36 ambiguous sentence? [#permalink]
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07 Oct 2010, 11:55
not that ambiguous. just started writing down the equations...
h = 60 t = h + 1/2b b = 1/2f
f = h + t + b = 60 + 60 + 1/2b + b = 120 + 1.5b = 120 + 0.75f
0.25f = 120 ==> f = 480  E
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Re: M04  36 ambiguous sentence? [#permalink]
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07 Oct 2010, 15:00
Easy one. Given: h=60, t=60+b/2, b=(h+b+t)/2 => b=h+b b=h+b b=60+60+b/2=> b=240 and hence t=180. Now h+b+t = 60+240+180=> 480 (E).
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Re: M04  36 ambiguous sentence? [#permalink]
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10 Oct 2010, 08:12
F = 2B F = 60 + B + 0,5B + 60 F = 120 + 1,5B  2B = 120+1,5B B= 240 F = 480
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Re: Problem Solving 700+ [#permalink]
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12 Sep 2011, 20:59
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.
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Re: Problem Solving 700+ [#permalink]
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12 Sep 2011, 21:32
Given, Head = 60 Let body = x => from the problem, Tail = 60 + (x/2) Total Length of fish = 60 + x + 60 + (x/2) = 240 + (3x/2) Also it is given that x = half of total length of fish => 2x = 240 + (3x/2) Solving for x, x=240 Total length of fish = 1/2 (240 + 3(240)) = 480
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Re: Problem Solving 700+ [#permalink]
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12 Sep 2011, 23:43
Let the length of whole fish be X and since head=60,then Body =1/2x Tail =60+1/2*body=60 +1/2*1/2*x=60+1/4*x so the length of whole fish= (60+1/4*x)+1/2*x+60 = x x=480 p.s.is it really 700+??
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Re: m04q36 Fish that had a 60 foot long head [#permalink]
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11 Oct 2011, 22:29
let the length of body x. x = [(60)+x+(60+{x/2})] / 2 x= 240 total length = [(60)+x+(60+{x/2})] = 480
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Re: m04q36 Fish that had a 60 foot long head [#permalink]
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14 Oct 2011, 08:07
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...



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Re: m04q36 Fish that had a 60 foot long head [#permalink]
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11 Oct 2012, 05:27
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? (A) 120 (B) 200 (C) 240 (D) 400 (E) 480 Source: GMAT Club Tests  hardest GMAT questions 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: \(head+body+tail=total \ length\) > \(60+b+(60+0.5b)=2b\) > \(b=240\) > \(total \ length=2b=480\). Answer: E.
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Re: m04q36 Fish that had a 60 foot long head [#permalink]
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11 Oct 2012, 05:49
H+B+T = X H= 60 B= x/2 T=60 + B/2 = 60 + x/4 So formula is 60 + x/2 + 60 + x/4 = X So X = 480
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Re: m04q36 Fish that had a 60 foot long head [#permalink]
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11 Oct 2012, 10:14
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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.



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Re: m04q36 Fish that had a 60 foot long head [#permalink]
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11 Oct 2012, 21:15
Full Fish(f)= 60+body(b)+(60+body/2) 2f=120+2b+120+b Also given that f=2b So... 4b=240+3b b=240 f=2*240=480



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Re: m04q36 Fish that had a 60 foot long head [#permalink]
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17 Dec 2012, 11:44
Make a table man! The easiest and simplest way.Head Body Tail = Fish60 foot + 2x + 60 + x = 60 + 2x + 60 + x I assumed the body to be 2x, so that I could go make the tail 60 + x, that saves some time. Then they tell you the second statement, that the body of the fish is half the size of the fish. Which implies, 2x = {60 + 2x + (60 + x)}/2 Multiplying both sides by 2, we have 4x = 60 + 2x + 60 + x 4x = (60+60) + (2x+x) 4x = 120 +3x Subtracting 3x from both sides, we have, 4x  3x = 120 x = 120. Plug, this back in the table. And don't forget that the body is 2x and not x. Head Body Tail = Fish60 foot + 2x + 60 + x = 60 + 2x + 60 + x 60 foot + 2(120) = 240 60+120=180 = 60 + 240 + 180 = 480Sorry but I am posting to the forum for the first time! how do we make a table while posting.
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Re: m04q36 Fish that had a 60 foot long head [#permalink]
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10 Oct 2013, 05:51
E.
This is a big ol' fish.
Let X = the entire length of the fish.
So, from the given information:
Head = 60. Body = \(\frac{x}{2}\) Tail = 60 + \(\frac{x}{4}\)
Now you have all the pieces of the fish in terms of x.
So the entire length of the fish is:
x = 60 + \(\frac{x}{4}\) + \(\frac{x}{2}\) + 60 x = 480




Re: m04q36 Fish that had a 60 foot long head
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