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Find an integer F

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stolyar
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Find an integer F [#permalink] Find an integer F   22 May 2003, 00:57
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A
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64% (00:54) correct 36% (01:00) wrong based on 507 sessions
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Find an integer F.

(1) F = 1/F
(2) |F| = 1/F
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B
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madn800
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Re: Find an integer F [#permalink] Find an integer F   06 Jun 2014, 01:41
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S1
After looking at the equations that this equations con only hold true for 1, -1.
S1 holds true for both.

S2
This equation is true only when F=1.

So, the integer that we are looking for is 1.

Hence, B.
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Re: Find an integer F [#permalink] Find an integer F   06 Jun 2014, 02:01
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stolyar wrote:
Find an integer F.

(1) F = 1/F
(2) |F| = 1/F


St:1 F=1/F or F- 1/F =0

F^2- 1/F=0, Now F cannot be equal to 0
So F^2-1= 0 or F =+1 or -1
Not sufficient

St 2 |F|=1/F

Now LHS is mod value and hence always non-negative. Therefore \(|F|\geq{0}\) or \(1/F\geq{0}\)
Note that F cannot be equal to zero as otherwise the expression becomes undefined.

Therefore |F| >0 or 1/F >0 -----Thus F>0

Since F>0 So we have F= 1/F or F^2=1 and F =1 as F >0
Ans is B

C is Trap answer here
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noTh1ng
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Find an integer F [#permalink] Find an integer F   09 Jul 2015, 02:30
For statement 2) I would try both cases:

I:
\(F = \frac{1}{F}\)
\(F^2 = 1\)
\(F = 1\)


II:
\(- F = \frac{1}{F}\)
\(- F^2 = 1\)
\(F^2 = -1\)


Root of a negative number is not possible, i.e. this one does not work. Leaves the first option -> sufficient to answer the question!
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Re: Find an integer F [#permalink] Find an integer F   31 Oct 2021, 06:39
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Re: Find an integer F [#permalink]
31 Oct 2021, 06:39
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