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

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Intern
Joined: 16 Jan 2007
Posts: 18

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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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Question Stats:

62% (01:12) correct 38% (01:55) wrong based on 21 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

Kudos [?]: 7 [0], given: 2

Intern
Joined: 16 Jan 2007
Posts: 18

Kudos [?]: 7 [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.

Kudos [?]: 7 [0], given: 2

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Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132619 [0], given: 12326

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

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12 Jul 2010, 15:57
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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Kudos [?]: 132619 [0], given: 12326

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Joined: 25 Feb 2010
Posts: 448

Kudos [?]: 112 [0], given: 10

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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Kudos [?]: 112 [0], given: 10

Senior Manager
Status: Yeah well whatever.
Joined: 18 Sep 2009
Posts: 341

Kudos [?]: 79 [0], given: 17

Location: United States
GMAT 1: 660 Q42 V39
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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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Kudos [?]: 79 [0], given: 17

Re: Inequality is k < –2 ?   [#permalink] 15 Jul 2010, 12:24
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