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# Find an integer F

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Find an integer F [#permalink]  21 May 2003, 23:57
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Difficulty:

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Question Stats:

57% (01:41) correct 43% (00:39) wrong based on 201 sessions
Find an integer F.

(1) F = 1/F
(2) |F| = 1/F
[Reveal] Spoiler: OA
Manager
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Re: Find an integer F [#permalink]  06 Jun 2014, 00:41
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]  06 Jun 2014, 01:01
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

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Find an integer F [#permalink]  09 Jul 2015, 01:30
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!
Find an integer F   [#permalink] 09 Jul 2015, 01:30
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