If 8 < k < 8, is k < 2 ? S1 K^2 - 7k - 18 > 0 S2 : GMAT Data Sufficiency (DS)
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# If 8 < k < 8, is k < 2 ? S1 K^2 - 7k - 18 > 0 S2

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If 8 < k < 8, is k < 2 ? S1 K^2 - 7k - 18 > 0 S2 [#permalink]

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21 Dec 2010, 15:33
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If –8 < k < 8, is k < –2 ?

S1 K^2 - 7k - 18 > 0

S2 1/k > 1/2

can some one explain S2 for me in the OA
[Reveal] Spoiler: OA

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Re: inequalities DS [#permalink]

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21 Dec 2010, 16:00
rxs0005 wrote:
If –8 < k < 8, is k < –2 ?

S1 K^2 - 7k - 18 > 0

S2 1/k > 1/2

can some one explain S2 for me in the OA

Not a good question.
If -8<k<8, is k<-2?

(1) k^2-7k-18>0 --> $$(y+2)(y-9)>0$$ --> $$y<-2$$ or $$y>9$$ --> as also given that $$-8<k<8$$ then $$-8<k<-2$$, so the answer to the question "is $$k<-2$$" will be YES. Sufficient.

(2) 1/k>1/2 --> you can directly tell that $$k$$ must be positive in order this inequality to hold true, thus in any case $$k$$ won't be less than -2, so the answer to the question "is $$k<-2$$" will be NO. Sufficient.

The exact range for $$k$$ in order $$\frac{1}{k}>\frac{1}{2}$$ to hold true will be $$0<k<2$$: $$k$$ must be positive and also it must be less than 2 so that LHS to be more than RHS OR rewrite as $$\frac{2-k}{2k}>0$$ --> $$0<k<2$$.

Now, technically answer would be D, as EACH statement ALONE is sufficient to answer the question.

But even though formal answer to the question is D (EACH statement ALONE is sufficient), this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

So we can not have answer YES from statement (1) and answer NO from statement (2), as in this case statements would contradict each other.

Guess statement (1) should read: k^2-7k-18<0. If it were so then $$(y+2)(y-9)<0$$ --> $$-2<y<9$$ --> as also given that $$-8<k<8$$ then $$-2<k<8$$, so the answer to the question "is $$k<-2$$" will be NO. Sufficient.

So in this case answer would be D and statements wouldn't contradict each other.

Hope it's clear.
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Re: inequalities DS [#permalink]

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24 Dec 2010, 05:16
Bunnel
what my process of thought was as follows:
S1 K^2 - 7k - 18 > 0
therefore (k+2)(k+9)>0
hence can also be written k>-2 or K>9, is it? so answer to question if K<-2 ? Answer is NO, therefore it is sufficient.

S2 1/k > 1/2
or it could be written as 0<K<2 so it is sufficient.
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Re: inequalities DS [#permalink]

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24 Dec 2010, 05:46
tirupatibalaji wrote:
Bunnel
what my process of thought was as follows:
S1 K^2 - 7k - 18 > 0
therefore (k+2)(k+9)>0
hence can also be written k>-2 or K>9, is it? so answer to question if K<-2 ? Answer is NO, therefore it is sufficient.

S2 1/k > 1/2
or it could be written as 0<K<2 so it is sufficient.

The red part is not correct: $$(y+2)(y-9)>0$$ --> $$y<-2$$ or $$y>9$$ --> as also given that $$-8<k<8$$ then $$-8<k<-2$$, so the answer to the question "is $$k<-2$$" will be YES. Sufficient.

Check this x2-4x-94661.html#p731476
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Re: inequalities DS [#permalink]

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24 Dec 2010, 05:56
Thanks Brunnel. this has cleared my doubts. cheers!!
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Re: inequalities DS   [#permalink] 24 Dec 2010, 05:56
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# If 8 < k < 8, is k < 2 ? S1 K^2 - 7k - 18 > 0 S2

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