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

How to do this quickly? The way I m doing it ( i.e. solving each statement possibilities ) takes 3-4 min.

I'd probably use the distance concept for this question the same way as Mike well explained above. Though one can also use plug-in method:

Given: 1<x<9. Now, try two numbers, one from this range and one out of this range. Correct answer choice must be true for the first number and false for the another. Let's try: x=8 and x=0. So, the correct answer choice must be true for x=8 and false for x=0.

A. |x|<3 --> false for x=8, so no need to try another number. Discard; B. |x+5|<4 --> false for x=8, so no need to try another number. Discard; C. |x-1|<9 --> true for x=8, but also true for x=0. Discard; D. |-5+x|<4 --> true for x=8, and false for x=0. Correct; E. |3+x|<5 --> false for x=8, so no need to try another number. Discard.

Only one answer choice D works.

Answer: D.

Note that for plug-in method it might happen that for some particular numbers more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.

You can also check Absolute Value chapter of Math Book, where Walker discusses the same exact question using the distance concept: math-absolute-value-modulus-86462.html

Re: Which of the following represents 1<x<9? [#permalink]

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04 Dec 2012, 02:10

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1<x<9

1) Get the center of the range CENTER = (9 + 1)/2 = 10/2 = 5 2) Flip the sign and append the variable x |x - 5| 3) Get the distance of the CENTER from one of the END DISTANCE = 9 - 5 = 4 4) Decide the inequality sign. WE know that x is within the range so choose "<"

A. |x|<3 => -3<x<3 => no need to go further its wrong B. |x+5|<4 => -4<x+5<4 => -9<x..... no need to go further its wrong C. |x-1|<9 => -9<x+1<9 => -10<x..... no need to go further its wrong D. |-5+x|<4 => -4<x-5<4 => 1<x<9 - BINGO E. |3+x|<5 => -5<x+3<5 => -8<x..... no need to go further its wrong

Re: Which of the following represents 1<x<9? [#permalink]

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19 Dec 2012, 22:21

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docabuzar wrote:

Which of the following represents 1<x<9?

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

How to do this quickly? The way I m doing it ( i.e. solving each statement possibilities ) takes 3-4 min.

The below is my approach for any modulus qtn in GMAT. Please read thru the complete explanation to understand the modulus concept.

Remember. The meaning of |x-y| is "On the number line, the distance between X and +Y" The meaning of |x+y| is "On the number line, the distance between X and -Y" The meaning of |x| is "On the number line, the distance between X and 0".

On the # line, Left to 0 are all the -ve #s and right to 0 are all +ve #s

original qtn: is x between 1 and 9 ==> .....................0..1....................9..... ==> is X in the highlighted area

A) |x| < 3 ---- wrong on the number line, the distance of x from 0 is < 3 ==> ......-3........0........3....

B) |x+5|<4 --- wrong on the number line, the distance of x from -5 is < 4 ==> ............-9............-5...........1...0.......3....

C)|x-1|<9 --- wrong on the number line, the distance of x from 1 is < 9 ==> ..................-8..............................0....1.......................9...10....

D) |-5+x|<4 on the number line, the distance of x from +5 is < 4 ==> ............0..1..............5...............9 ---- This is what is asked in the question, hence, correct answer E. |3+x|<5

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09 Jan 2014, 13:16

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Re: Which of the following represents 1<x<9? [#permalink]

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24 May 2016, 08:17

Hello from the GMAT Club BumpBot!

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Re: Which of the following represents 1<x<9? [#permalink]

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19 Jun 2017, 15:19

Though mikemcgarry and bb explained well - I ended up solving this by solving the mods in the answer choices. And as a result took few secs extra may be.

I liked the value substitution by bb and I will try with other questions.
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Kudos - I hope you liked the post, if you have liked the post, please do not hesitate to show your appreciation and support with a simple click on Kudos, it will make me happy and encourage me to support more people.

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Though mikemcgarry and bb explained well - I ended up solving this by solving the mods in the answer choices. And as a result took few secs extra may be.

I liked the value substitution by bb and I will try with other questions.

FYI, bb and Bunuel, are two different people.
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Re: Which of the following represents 1<x<9? [#permalink]

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19 Jun 2017, 22:10

Bunuel wrote:

ydmuley wrote:

Though mikemcgarry and bb explained well - I ended up solving this by solving the mods in the answer choices. And as a result took few secs extra may be.

I liked the value substitution by bb and I will try with other questions.

Ha Ha.... You caught that..... How can i even think of crediting Maths answers to anyone else other than Bunuel I was reading some articles of bb and hence jotted down bb instead ogBunuel.... Sorry!
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Kudos - I hope you liked the post, if you have liked the post, please do not hesitate to show your appreciation and support with a simple click on Kudos, it will make me happy and encourage me to support more people.

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Re: Which of the following represents 1<x<9? [#permalink]

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21 Jun 2017, 03:36

By far the best response from Bunuel !! There can be only one Legend

Bunuel wrote:

ydmuley wrote:

Though mikemcgarry and bb explained well - I ended up solving this by solving the mods in the answer choices. And as a result took few secs extra may be.

I liked the value substitution by bb and I will try with other questions.

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