Which of the following represents 1

Question

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.

mikemcgarry · Accepted Answer

Hi, I'm happy to help with this.

Fundamentally, absolute value is about distance . That is something many folks fail to grasp. |x| is the distance of x from the origin on the number line. |x - 5| is the distance of x from the point 5 on the number line. |x + 3| is the distance of x from the point -3 on the number line. (That's because x + 3 = x - (-3)) So, we want to write 1 |x - 5| Step #2: how far can we get from 5? Well, up to almost 9, or down to almost 1 -- that is, almost 4. Thus: distance from 5 < 4 |x - 5| < 4 Once you understand the distance-interpretation of absolute value, you need not spend much time at all on questions like this. Does that make sense? Please let me know if I can clarify anything here or if you have any more questions. Here's a challenging absolute value question for practice. https://gmat.magoosh.com/questions/964 Once you submit your answer, that question should be followed by a video explanation of the answer. Mike

eaakbari · Answer

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

Bunuel · Answer

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 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 Hope it helps.

mbaiseasy · Answer

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 "<"

ANsweR: |x-5| < 4

muralilawson · Answer

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

ydmuley · Answer

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.

Bunuel · Answer

FYI, bb and Bunuel , are two different people.

ydmuley · Answer

Ha Ha.... You caught that..... How can i even think of crediting Maths answers to anyone else other than Bunuel :-D

I was reading some articles of bb and hence jotted down bb instead og Bunuel .... Sorry!

susheelh · Answer

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

AkshdeepS · Answer

Such approach makes life easier and smoother while preparing for GMAT. Hopefully, I get this kind of solution for every question.

JeffTargetTestPrep · Answer

By looking at the choices, we can make an educated guess that the answer is going to be either choice B or choice D since only 4 and 5 can sum to 9 (when added) and make 1 (when subtracted). Let’s check choice B first.

If (x + 5) is positive:

x + 5 < 4

x < -1

We can stop here since this doesn’t match the given inequality 1 < x < 9.

Now let’s check choice D.

If (-5 + x) is positive:

-5 + x < 4

x < 9

If (-5 + x) is negative:

-(-5 + x) < 4

5 - x < 4

1 < x

Thus we see that 1 < x < 9.

Answer: D

EMPOWERgmatRichC · Answer

Hi All,

We're told that 1 < X < 9. We're asked which of the absolute value inequalities properly 'matches.' This question can be solved rather easily by TESTing VALUES. We're going to test numbers against the prompt and the answers to find the correct answer:

Answer A: doesn't include certain numbers (3 - 8.99999) = eliminate 
Answer B: doesn't include any of the numbers = eliminate 
Answer C: Includes the above range BUT ALSO includes numbers NOT in that range (1, 0, -1, etc.) = SUSPICIOUS ANSWER 
Answer D: Includes ALL numbers from that range = LOOKS GOOD 
Answer E: doesn't include certain numbers (2 - 8.9999) = eliminate

Final answer:  D

GMAT assassins aren't born, they're made, 
Rich

vrsthe1 · Answer

|-5+x|<4 => -(-5+x)<4 or (-5+x)<4 => -5+x>-4 or -5+x<4 => x>1 or x<9 => 1

Schachfreizeit · Answer

I understand everything until you list the steps. Why we can conclude from 1<x<9 to |x-5| ?

zaidi1212 · Answer

Clearly |-5+x|<4 is true because positive Case: -5+x <4 —> x< 9 Negative case : 5-x < 4 —> x> 1 Posted from my mobile device

Schachfreizeit · Answer

I did not doubt if it is correct, I just wonder how you get to step 1 and 2

zaidi1212 · Answer

Both positive and negative values are possible for value inside mod || which is -5+x 1) For -5+x to be positive, |-5+x| < 4 --> -5+x < 4 --> x < 9 2) For (-5+x) to be negative, |-5+x| < 4 --> -(-5+x) < 4 --> 5-x < 4 --> 5 < 4+x --> x > 1 A. |x|<3 --> Not possible as positive case : x<3, negative case: -x < 3 or x > -3 B. |x+5|<4 --> Not possible as positive case: x+5 < 4 --> x < -1 C. |x-1|<9 --> Not possible, as positive case: x-1 < 9 --> x < 10, negative case : -x+1 < 9 --> x > -8 E. |3+x|<5 --> Not possible, as positive case: 3+x < 5 --> x < 2

TheBipedalHorse · Answer

This might be helpful: |x| < constant basically means (-constant) < x < (+constant) ~~ |x|> constant basically means x>constant or x<-constant ~~ And now for how to solve such questions easily without having to go through evaluating all choices - One look at the answer choices and all of them are of the form "|expression| 1-5

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Which of the following represents 1 < x < 9?

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Which of the following represents 1 < x < 9?

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