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m04q36- Fish that had a 60 foot long head

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

[Reveal] Spoiler: OA
E

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I feel that the second sentence is ambiguous. Any comments will be appreciated :)
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Re: M04 - 36 ambiguous sentence? [#permalink] New post 07 Oct 2010, 05:50
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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

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Re: m04q36- Fish that had a 60 foot long head [#permalink] New post 11 Oct 2012, 09:14
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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: M4 - 36 ambiguous sentence? [#permalink] New post 09 Feb 2009, 22:49
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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. :-D

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!


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Re: M04 - 36 ambiguous sentence? [#permalink] New post 07 Oct 2010, 04:06
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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] New post 07 Oct 2010, 04:46
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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] New post 07 Oct 2010, 08:40
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] New post 07 Oct 2010, 10:55
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] New post 07 Oct 2010, 14:00
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] New post 10 Oct 2010, 07:12
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] New post 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.
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Re: Problem Solving 700+ [#permalink] New post 12 Sep 2011, 20:32
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] New post 12 Sep 2011, 22:43
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] New post 11 Oct 2011, 21:29
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] New post 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...
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Re: m04q36- Fish that had a 60 foot long head [#permalink] New post 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?

(A) 120
(B) 200
(C) 240
(D) 400
(E) 480

[Reveal] Spoiler: OA
E

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] New post 11 Oct 2012, 04:49
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] New post 11 Oct 2012, 20:15
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] New post 17 Dec 2012, 10:44
    Make a table man! The easiest and simplest way.

    Head Body Tail = Fish
    60 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 = Fish
    60 foot + 2x + 60 + x = 60 + 2x + 60 + x
    60 foot + 2(120) = 240 60+120=180 = 60 + 240 + 180 = 480

      Sorry 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] New post 10 Oct 2013, 04:51
    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   [#permalink] 10 Oct 2013, 04:51
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