Which of the following inequalities... : GMAT Problem Solving (PS)
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# Which of the following inequalities...

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Intern
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Which of the following inequalities... [#permalink]

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02 May 2010, 20:39
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Which of the following inequalities has a solution set that when graphed on the number line is a single line segment of finite lenght?

a)x^4 >=1
b)x^3<=27
c)x^2>=16
d)2<= /x/<=5
e) 2 <= 3x+4 <=6

I came across this question when taking a CAT, it was apparent that a,b and c were not the right answer, but I had a hard time deciding between d and e.
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Re: Which of the following inequalities... [#permalink]

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03 May 2010, 03:38
perseverant wrote:
Which of the following inequalities has a solution set that when graphed on the number line is a single line segment of finite lenght?

a)x^4 >=1
b)x^3<=27
c)x^2>=16
d)2<= /x/<=5
e) 2 <= 3x+4 <=6

I came across this question when taking a CAT, it was apparent that a,b and c were not the right answer, but I had a hard time deciding between d and e.

Its clearly E.

Just plug values for d -3, 3 satisfies but -1 does not. And -1 comes between -3 and 3
=> Its not a single line segment.

But the best way is to use algebra.
take cases |x| <=5 => -5<= x <= 5
|x| >=2 => -2 >= x >= 2 .

Now just draw it,its not single line segment.
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Re: Which of the following inequalities... [#permalink]

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03 May 2010, 10:00
perseverant wrote:
Which of the following inequalities has a solution set that when graphed on the number line is a single line segment of finite lenght?

a)x^4 >=1
b)x^3<=27
c)x^2>=16
d)2<= /x/<=5
e) 2 <= 3x+4 <=6

I came across this question when taking a CAT, it was apparent that a,b and c were not the right answer, but I had a hard time deciding between d and e.

e should be the answer as the slope lies within finite boundaries. The solution for d is -infinity to -2 and 5 to infinity
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Re: Which of the following inequalities... [#permalink]

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03 May 2010, 10:15
perseverant wrote:
Which of the following inequalities has a solution set that when graphed on the number line is a single line segment of finite lenght?

a)x^4 >=1
b)x^3<=27
c)x^2>=16
d)2<= /x/<=5
e) 2 <= 3x+4 <=6

I came across this question when taking a CAT, it was apparent that a,b and c were not the right answer, but I had a hard time deciding between d and e.

Its E , you can use POE in this one, you don't even have to calculate to get the answer. Options 1,2 and 3 are clearly out.

Between D and E if you see the equation in D it's |x| which means X has 2 values +X and -X and hence it will form 2 equations 2<= -x <= 5 and 2<= +x <= 5 which means it will form 2 lines .. !

I hope this help .!
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Re: Which of the following inequalities... [#permalink]

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04 May 2010, 01:40
Thank you all! it has now become obvious why the answer is E.
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Re: Which of the following inequalities... [#permalink]

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05 May 2010, 04:07
I could not understand the question .......can anyone explain in more details
Thanks
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Re: Which of the following inequalities... [#permalink]

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05 May 2010, 04:39
hardnstrong wrote:
I could not understand the question .......can anyone explain in more details
Thanks

Basically the question is asking which inequality when graphed is a line with a defined start and end point. Options a,b, and c are inmediately out because you only have one point and you dont know where the line ends, so it would be a infinite line and not finite like the question is asking.
Option D, would give 2 lines because of the absolute value, because x could be positive or negative.
Then the only option left is d which gives a defined range for x (start and end point), which is a one finite line.
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Re: Which of the following inequalities... [#permalink]

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05 May 2010, 04:41
perseverant wrote:
hardnstrong wrote:
I could not understand the question .......can anyone explain in more details
Thanks

Basically the question is asking which inequality when graphed is a line with a defined start and end point. Options a,b, and c are inmediately out because you only have one point and you dont know where the line ends, so it would be a infinite line and not finite like the question is asking.
Option D, would give 2 lines because of the absolute value, because x could be positive or negative.
Then the only option left is E which gives a defined range for x (start and end point), which is a one finite line.

Correction I meant the only option left is E.
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Re: Which of the following inequalities... [#permalink]

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06 May 2010, 23:17
perseverant wrote:
hardnstrong wrote:
I could not understand the question .......can anyone explain in more details
Thanks

Basically the question is asking which inequality when graphed is a line with a defined start and end point. Options a,b, and c are inmediately out because you only have one point and you dont know where the line ends, so it would be a infinite line and not finite like the question is asking.
Option D, would give 2 lines because of the absolute value, because x could be positive or negative.
Then the only option left is d which gives a defined range for x (start and end point), which is a one finite line.

this is the confusing part for me

1st option says x^4=1
(so x can be 1 or -1) 2 points

same is the case with option 3
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Re: Which of the following inequalities... [#permalink]

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07 May 2010, 06:55
hardnstrong wrote:
perseverant wrote:
hardnstrong wrote:
I could not understand the question .......can anyone explain in more details
Thanks

Basically the question is asking which inequality when graphed is a line with a defined start and end point. Options a,b, and c are inmediately out because you only have one point and you dont know where the line ends, so it would be a infinite line and not finite like the question is asking.
Option D, would give 2 lines because of the absolute value, because x could be positive or negative.
Then the only option left is d which gives a defined range for x (start and end point), which is a one finite line.

this is the confusing part for me

1st option says x^4=1
(so x can be 1 or -1) 2 points

same is the case with option 3

for the 1st option, the key is that x can be 1 OR -1, not AND which would give you 2 infinite lines because in both cases you have a start points, not end points. The same happens with option 3.
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Re: Which of the following inequalities... [#permalink]

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08 May 2010, 00:31
Got it now .....THANKS
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Re: Which of the following inequalities... [#permalink]

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12 Aug 2010, 10:51
For option E, i got

e) $$2 <= 3x+4 <=6$$

$$-2/3 <= x <= -2$$ and

$$-10/3 <= x <= 2/3$$

How do the above equations suggest that it is a finite line. I am sorry but I still dont understand....
Re: Which of the following inequalities...   [#permalink] 12 Aug 2010, 10:51
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