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# If 8 < k < 8, is k < 2 ?

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Intern
Joined: 16 Jan 2007
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If 8 < k < 8, is k < 2 ? [#permalink]

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12 Jul 2010, 14:33
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Difficulty:

55% (hard)

Question Stats:

61% (02:26) correct 39% (02:00) wrong based on 18 sessions

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If –8 < k < 8, is k < –2 ?

(1) k^2 – 7k – 18 > 0
(2) 1/k > 1/2
[Reveal] Spoiler: OA
Intern
Joined: 16 Jan 2007
Posts: 18
Followers: 0

Kudos [?]: 5 [0], given: 2

Re: Inequality is k < –2 ? [#permalink]

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12 Jul 2010, 14:47
K is between -8 to 8 range (excluding 8 & -8)

1) (k-9)(k+2)>0 => a) k>9 or k>-2 b) k< 9 or k < -2 which means (by combining a & b) the solution set is k>9 and k < -2. Since it is given k < 8 we can deduce that k < -2. Hence suff

2) 1/k > 1/2 => 1/k-1/2 > 0 => k > 0 and k < 2. Hence suff.

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Re: Inequality is k < –2 ? [#permalink]

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12 Jul 2010, 15:57
Expert's post
paam0101 wrote:
K is between -8 to 8 range (excluding 8 & -8)

1) (k-9)(k+2)>0 => a) k>9 or k>-2 b) k< 9 or k < -2 which means (by combining a & b) the solution set is k>9 and k < -2. Since it is given k < 8 we can deduce that k < -2. Hence suff

2) 1/k > 1/2 => 1/k-1/2 > 0 => k > 0 and k < 2. Hence suff.

Your solution is correct, but the question itself is not good:

(1) $$(k-9)(k+2)>0$$ --> $$k<-2$$ or $$k>9$$, but as given that $$-8<k<8$$, then the final range is $$-8<k<-2$$ and the answer to the question "is $$k<-2$$" is YES, hence sufficient.

(2) $$\frac{1}{k}>\frac{1}{2}$$ --> $$0<k<2$$ and the answer to the question "is $$k<-2$$" is NO, hence sufficient.

Here comes the problematic part: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other but in our case we have that statement (1) gives the answer "YES" to the question and statement (2) gives the answer "NO" to the question, so statements contradict each other. This will never occur on real GMAT.

Hope it helps.
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Re: Inequality is k < –2 ? [#permalink]

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13 Jul 2010, 07:04
paam0101 wrote:
K is between -8 to 8 range (excluding 8 & -8)

1) (k-9)(k+2)>0 => a) k>9 or k>-2 b) k< 9 or k < -2 which means (by combining a & b) the solution set is k>9 and k < -2. Since it is given k < 8 we can deduce that k < -2. Hence suff

2) 1/k > 1/2 => 1/k-1/2 > 0 => k > 0 and k < 2. Hence suff.

You posted this and you're the one who solved this ...
waooooo

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Re: Inequality is k < –2 ? [#permalink]

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15 Jul 2010, 12:24
yeah. you confused me with the contradicting stems, paam0101
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Re: Inequality is k < –2 ?   [#permalink] 15 Jul 2010, 12:24
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