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# Is r < 1?

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Math Expert
Joined: 02 Sep 2009
Posts: 52295

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30 Jul 2016, 02:05
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Difficulty:

25% (medium)

Question Stats:

76% (00:47) correct 24% (00:32) wrong based on 62 sessions

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Is r < 1?

(1) r > 0

(2) r^2 < 1

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Re: Is r < 1?  [#permalink]

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30 Jul 2016, 04:06
Top Contributor
Bunuel wrote:
Is r < 1?

(1) r > 0

(2) r^2 < 1

(1) r>0,so r could be $$\frac{1}{2}$$ or 2,Not Sufficient

(2) $$r^2$$<1 ,here,to hold the inequality true, $$r^2$$ must be a fraction less than 1 thus r<1.Sufficient

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Re: Is r < 1?  [#permalink]

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09 Feb 2018, 09:53
Bunuel wrote:
Is r < 1?

(1) r > 0

(2) r^2 < 1

Statement 1
r > 0 doesnt tell us whether r is between 0 and 1, or equal to 1, or greater than 1. So not sufficient.

Statement 2

r^2 < 1 means that r has to lie between -1 and 1. (then only its square will be less than 1, else not)
All the values between -1 and 1 are definitely less than 1. So this gives us YES as an answer to the question asked. Sufficient.

Re: Is r < 1? &nbs [#permalink] 09 Feb 2018, 09:53
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