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by Brent@GMATPrepNow » Fri Oct 10, 2014 7:31 pm
Which inequality solution set, when graphed on the number line, is a single line segment of finite length?

A) x� ≥ 1
B) x³ ≤ 27
C) x² ≥ 16
D) 2 ≤ |x| ≤ 5
E) 2 ≤ 3x + 4 ≤ 6
This is one of those questions that require us to check/test the answer choices. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top. For more on this strategy, see my article: https://www.beatthegmat.com/mba/2014/09/ ... -questions

E) 2 ≤ 3x + 4 ≤ 6
Subtract 4 from all sides to get: -2 ≤ 3x ≤ 2
Divide all sides by 3 to get: -2/3 ≤ x ≤ 2/3
So, x can have any value from -2/3 to 2/3
So, if we were to graph the possible values of x, the line segment would have a FINITE length.

Answer: E

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Last edited by Brent@GMATPrepNow on Fri Oct 10, 2014 8:06 pm, edited 1 time in total.
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by kamalakarthi » Fri Oct 10, 2014 7:58 pm
Thank you Brent for your fast reply. I have a doubt on choice D.

2 ≤ |x| ≤ 5 , In this choice I took a positive value of X and thought that value of x will be less than or = 5 and x is <= 2 so I thought the definite value are between 2 and 5 and concluded this is a correct answer. Can you please help me understand on what is wrong in this choice.
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by Brent@GMATPrepNow » Fri Oct 10, 2014 8:05 pm
kamalakarthi wrote:Thank you Brent for your fast reply. I have a doubt on choice D.

2 ≤ |x| ≤ 5 , In this choice I took a positive value of X and thought that value of x will be less than or = 5 and x is <= 2 so I thought the definite value are between 2 and 5 and concluded this is a correct answer. Can you please help me understand on what is wrong in this choice.
The solution here consists of 2 line segments, and the question is looking for a solution consisting of ONE line segment.
The full solution is 2 ≤ x ≤ 5 or -5 ≤ x ≤ -2

Cheers,
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Last edited by Brent@GMATPrepNow on Sat Oct 11, 2014 10:31 am, edited 1 time in total.
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by Matt@VeritasPrep » Sat Oct 11, 2014 10:16 am
kamalakarthi wrote:Thank you Brent for your fast reply. I have a doubt on choice D.

2 ≤ |x| ≤ 5 , In this choice I took a positive value of X and thought that value of x will be less than or = 5 and x is <= 2 so I thought the definite value are between 2 and 5 and concluded this is a correct answer. Can you please help me understand on what is wrong in this choice.
One important thing here: 2 ≤ |x| ≤ 5 implies that 2 ≤ x ≤ 5 OR -5 ≤ x ≤ -2, so the conclusion is slightly more specific than that. You're correct that this does give a segment of finite length, but unfortunately (for us) it gives two of them. (This is the rare case where two is not better than one!)
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by Brent@GMATPrepNow » Sat Oct 11, 2014 10:32 am
Good catch, Matt.
I edited my response accordingly.

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by shahfahad » Fri Nov 13, 2015 3:45 am
I was going through the questions in GMAT Prep Now course and found this question. I just want to ask that if option D would have been " 2 <= x <= 5 " rather than " 2 <= |x| <= 5 ". Then option D WOULD be correct? It is the ABSOLUTE SIGN that creates 2 line segments rather than 1? Because if it had been " 2 <= x <= 5 " then the line segment would be 1? But as it is "|x|", it could be either positive or negative creating two line segments?
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by Jim@StratusPrep » Fri Nov 13, 2015 1:26 pm
All you really need to know if that exponents will always add a 'curve' to the plot and absolute value will always create an 'angle'.
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by Matt@VeritasPrep » Fri Nov 13, 2015 2:46 pm
shahfahad wrote:I was going through the questions in GMAT Prep Now course and found this question. I just want to ask that if option D would have been " 2 <= x <= 5 " rather than " 2 <= |x| <= 5 ". Then option D WOULD be correct? It is the ABSOLUTE SIGN that creates 2 line segments rather than 1? Because if it had been " 2 <= x <= 5 " then the line segment would be 1? But as it is "|x|", it could be either positive or negative creating two line segments?
Yup, you're on the right track: 2 ≤ x ≤ 5 means that x is a single segment of finite length.

That said, if you had |x| ≤ 1, you'd also have a single segment of finite length, so be careful!
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by shahfahad » Sat Nov 14, 2015 2:07 am
Jim@StratusPrep: Could not really understand this part "absolute value will always create an 'angle'"

Matt@VeritasPrep: Because |x| ≤ 1 would be -1 <= x <= 1 therefore creating one line segment?
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by vishalwin » Sat Nov 14, 2015 8:01 am
Hi shahfahad,


Jim is saying if you plot |x|= 0

It will be like a V shaped curve centered at origin.

and if we include modulus || with inequalities that gives a range of numbers and hence a straight line like you said

|x| <= 1 this is equal to x lies between -1 and 1


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Last edited by vishalwin on Sat Nov 14, 2015 8:18 am, edited 1 time in total.
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by vishalwin » Sat Nov 14, 2015 8:07 am
Hi shahfahad,


Jim is saying if you plot |x|= 0

It will be like a V shaped curve centered at origin.

and if we include modulus || with inequalities that gives a range of numbers and hence a straight line like you said

|x| <= 1 this is equal to x lies between -1 and 1


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