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Let k and p be nonzero integers. Is k - 1/p >= 1/p?

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Joined: 02 Sep 2009
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Let k and p be nonzero integers. Is k - 1/p >= 1/p? [#permalink]

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New post 21 Mar 2017, 05:46
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A
B
C
D
E

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Question Stats:

38% (01:06) correct 62% (00:47) wrong based on 16 sessions

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Re: Let k and p be nonzero integers. Is k - 1/p >= 1/p? [#permalink]

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New post 21 Mar 2017, 06:11
1
Bunuel wrote:
Let k and p be nonzero integers. Is \(k - \frac{1}{p} \geq \frac{1}{p}\)?

(1) k and p are distinct and positive.
(2) k = 1 and |p|>1.


On simplying the equation we get is k>= (2/p) ?

(1) k and p are distinct and positive. - Sufficient

k=1 and p=2. Is k>= (2/p) ? - Yes
k=3 and p=1. Is k>= (2/p) ? - Yes

Note : The condition fails only for k=p=1. This cannot be the case as the numbers are distinct.

(2) k = 1 and |p|>1 - Sufficient

1>= (2/p). p can vary from [- infinity, 2] and [2, infinity]. Substituting the limits we can see this statement is also sufficient.

Hence D.

Cheers!
Re: Let k and p be nonzero integers. Is k - 1/p >= 1/p?   [#permalink] 21 Mar 2017, 06:11
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Let k and p be nonzero integers. Is k - 1/p >= 1/p?

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