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How many weeks was the Carnival open last year? (1) The

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Hades
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How many weeks was the Carnival open last year? (1) The [#permalink] New post   02 Jun 2009, 23:15
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B
C
D
E

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How many weeks was the Carnival open last year?

(1) The ratio between the number of weeks it was open and closed last year is \(1:3\).

(2) The multiple of the number of weeks the Carnival was open and the number of weeks the Carnival was closed is \(507\).



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Re: How many weeks was the Carnival open last year? (1) The [#permalink] New post   03 Jun 2009, 09:30
1
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\(X\) - # of weeks open
\(Y\) - # of weeks closed

\(X + Y = 52\) (inferred)

Question:\((X?)\)

(1) \(X/Y = 1/3\)

2 linear equations, 2 variables \(\longrightarrow SUFFICIENT\) .

(2) \(XY = 507\)

Rearrange inferred equation to \(Y = 52-X\) and substitute into above

\(X(52-X) = 507\)
\(52X - X^{2} = 507\)
\(X^{2} - 52X + 507 = 0\)
\(X^{2} - 13X - 39X + 507 = 0\)
\(X(X - 13) - 39(X - 13) = 0\)
\((X - 13)(X - 39) = 0\)

\(\longrightarrow X=13\) or \(X=39\)
\(\longrightarrow INSUFFICIENT\).



Final Answer, \(A\).

\(\surd\)
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Re: How many weeks was the Carnival open last year? (1) The [#permalink] New post   02 Jun 2009, 23:50
the answer is C,

1, insuffucient X/y = 1/3 =>3X = Y but no idea of the x,y
2, insufficient.. x*y*k = 507 = 3*13*13

when k = 1, x=3 and y = 39 or x = 39 or y = 3

combining 1 and 2 ,

3x^2 K = 507
x^2 K = 169..

when k = 1, X = 13, y = 39/...

Whats the OA ?
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Re: How many weeks was the Carnival open last year? (1) The [#permalink] New post   02 Jun 2009, 23:52
Hades wrote:
How many weeks was the Carnival open last year?

(1) The ratio between the number of weeks it was open and closed last year is \(1:3\).

(2) The multiple of the number of weeks the Carnival was open and the number of weeks the Carnival was closed is \(507\).


C

x=open
y=closed
x/y=1/3
xy=507
3x^2=507
x=13
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Re: How many weeks was the Carnival open last year? (1) The [#permalink] New post   02 Jun 2009, 23:55
Good attempts 8-)
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Re: How many weeks was the Carnival open last year? (1) The [#permalink] New post   03 Jun 2009, 00:08
Hades wrote:
Good attempts 8-)


must be E..there are only 52 weeks in a year

52 factors to 13*2*2...no combo will give you 1/3 so cant be A
507 factors to 13*13*3 ...no sum adds to 52, cant be B

did you make this question up?
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Re: How many weeks was the Carnival open last year? (1) The [#permalink] New post   03 Jun 2009, 09:07
How many weeks was the Carnival open last year?

(1) The ratio between the number of weeks it was open and closed last year is .

(2) The multiple of the number of weeks the Carnival was open and the number of weeks the Carnival was closed is 507.


Answer D
1 - one year -52 weeks
the ratio ==> x:3x

4x=52
x=52/4 =13

2.507=3x13x13
we can derive from B also. Number of weeks when open + number of weeks when closed should be 52 and change the multiples.

As 507 is a multiple 0f 13 and 52 is a multiple of 13, we can solve from stat 2.
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Re: How many weeks was the Carnival open last year? (1) The [#permalink] New post   03 Jun 2009, 15:57
Thanks amolsk.

And yes bigtreezl, I actually did. My questions are sneaky MF'ers.
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Re: How many weeks was the Carnival open last year? (1) The [#permalink] New post   03 Jun 2009, 23:04
i am sure i am gonna leave out such ones..

Hades, What is the source of such brilliant questions ..?
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Re: How many weeks was the Carnival open last year? (1) The [#permalink] New post   04 Jun 2009, 00:00
Neochronic wrote:
i am sure i am gonna leave out such ones..

Hades, What is the source of such brilliant questions ..?


My brain my friend, :)



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Re: How many weeks was the Carnival open last year? (1) The [#permalink]
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