What inequality represents the condition 1<x<9 : GMAT Problem Solving (PS)
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# What inequality represents the condition 1<x<9

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What inequality represents the condition 1<x<9 [#permalink]

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21 Oct 2011, 05:06
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What inequality represents the condition 1<x<9?

(A) |x|<3
(B) |x+5|<4
(C) |x-1|<9
(D) |-5+x|<4
(E) |3+x|<5

OPEN DISCUSSION OF THE QUESTION IS HERE: which-of-the-following-represents-1-x-126845.html

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[Reveal] Spoiler: Doubt
The answer to this question is D.
I am confused because even C seems to be satisfying most of the numbers tested on this inequality . The answer is an obvious D, if we solve the algebraic inequality but on testing with numbers both options seem to be right
Am just trying to find a way to use the number plugging method accurately

Any body any idea ? Thanks ..
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Mar 2012, 00:41, edited 2 times in total.
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Re: What inequality represents the condition 1<x<9 [#permalink]

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21 Oct 2011, 05:15
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devinawilliam83 wrote:
What inequality represents the condition 1<x<9?

(A) |x|<3
(B) |x+5|<4
(C) |x-1|<9
(D) |-5+x|<4
(E) |3+x|<5

Remember this:

|x|<k means; -k<x<+k

So,
D) |-5+x|<4
|x-5|<4
-4<x-5<4
-4+5<x-5+5<4+5
1<x<9

Ans: "D"

Please do the same for C.
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Re: What inequality represents the condition 1<x<9 [#permalink]

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21 Oct 2011, 08:18
Quote:
I am confused because even C seems to be satisfying most of the numbers tested on this inequality . The answer is an obvious D, if we solve the algebraic inequality but on testing with numbers both options seem to be right
Am just trying to find a way to use the number plugging method accurately

Any body any idea ? Thanks ..

You need to test both numbers inside and outside the range of 1<x<9 to see if each inequality represents the condition of 1<x<9 and nothing more. The inequality found in answer C satisfies the range 1<x<9 but also includes numbers outside of this range.

You likely only tested numbers inside this range, which resulted in your error.
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Re: What inequality represents the condition 1<x<9 [#permalink]

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03 Mar 2012, 00:27
I honestly just do not understand. I read everyone's reply. But I still don't understand how this makes since. I read where you said outside the range but the way I am understanding it, the answer D doesn't work either. I am just lost. If anyone can explain this more in depth please do. I apologize for being difficult. It's hard for me to understand things like this without someone being right here with me to explain why and how you get the answer.
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Re: What inequality represents the condition 1<x<9 [#permalink]

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03 Mar 2012, 00:38
Mercury14 wrote:
I honestly just do not understand. I read everyone's reply. But I still don't understand how this makes since. I read where you said outside the range but the way I am understanding it, the answer D doesn't work either. I am just lost. If anyone can explain this more in depth please do. I apologize for being difficult. It's hard for me to understand things like this without someone being right here with me to explain why and how you get the answer.

Here is another topic discussing the same question: which-of-the-following-represents-1-x-126845.html There is conceptual approach in Mike's post and plug-in method in my post.

Hope it helps.

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Re: What inequality represents the condition 1<x<9   [#permalink] 03 Mar 2012, 00:38
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# What inequality represents the condition 1<x<9

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