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If |-x/3 + 1| < 2, which of the following must be true?

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If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post Updated on: 03 Oct 2017, 23:58
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If |-x/3 + 1| < 2, which of the following must be true?

A. x > 0
B. x < 8
C. x > -4
D. 0 < x < 3
E. None of the above

Originally posted by gmatdemolisher1234 on 28 Nov 2016, 07:28.
Last edited by Bunuel on 03 Oct 2017, 23:58, edited 2 times in total.
Renamed the topic and edited the question.
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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post 28 Nov 2016, 09:43
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gmatdemolisher1234 wrote:
If |-x/3 + 1| < 2, which of the following must be true?

a. x>0
b. x<8
c. x>-4
d. 0<x<3
e. None of the above



|-x/3 + 1| < 2
|x/3 - 1| < 2
(1/3) * |x - 3| < 2
|x - 3| < 6

Distance of x from 3 is less than 6 so -3 < x < 9.
So in every case, x will be greater than -4.

Answer (C)
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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post 30 Nov 2016, 22:41
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Here's a little 'thumb rule' that i have noted in my notes to decipher the confusion in these kinda Must be true questions-

You obtain a range for X from the given ineq.: Obtained range
You have 5 options with different ranges: Option ranges

Rule:

For an option to be correct, nothing from the Obtained Range should be omitted in the Option Range! However, If the Option Range covers more than the Obtained Range, its fine.



In this question,
Obtained Range= -3 < x <9
only Option Range = x >-4 covers the complete Obtained Range (and it covers more than the Obtained Range, this is fine). No other Option Range does this.

Hope this will ease up things a bit :)
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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post 28 Nov 2016, 07:36
1
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gmatdemolisher1234 wrote:
If |-x/3 + 1| < 2, which of the following must be true?

a. x>0
b. x<8
c. x>-4
d. 0<x<3
e. None of the above


|-x/3 + 1| < 2

Get rid of the modulus: -2 < -x/3 + 1 < 2

Multiply by -3 and flip the sign: 6 > x - 3 > -6

Add 3 to all parts: 9 > x > -3.

Any number from -3 to 9 will for sure be more than -4.

Answer: C.
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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post 28 Nov 2016, 10:10
gmatdemolisher1234 wrote:
If |-x/3 + 1| < 2, which of the following must be true?

a. x>0
b. x<8
c. x>-4
d. 0<x<3
e. None of the above



I believe the question's answer choices is not apt or its not correctly framed. even D) is also true.

and the question asks which of the following must be true.. MUST be true D) is limiting x to be in a certain range so we are sure of this option.

but C) x>-4 , we can assume x to be -12 as well which won't be the correct choice.

So IMO answer should be D)
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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post 28 Nov 2016, 10:13
praty23 wrote:
gmatdemolisher1234 wrote:
If |-x/3 + 1| < 2, which of the following must be true?

a. x>0
b. x<8
c. x>-4
d. 0<x<3
e. None of the above



I believe the question's answer choices is not apt or its not correctly framed. even D) is also true.

and the question asks which of the following must be true.. MUST be true D) is limiting x to be in a certain range so we are sure of this option.

but C) x>-4 , we can assume x to be -12 as well which won't be the correct choice.

So IMO answer should be D)


It's the other way around. We know that -3 < x < 9 and need to find which of the options must be correct about x. Now, if -3 < x < 9, then x must be more than -4 (any x from -3 to 9 will for sure be more than -4).
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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post 30 Nov 2016, 11:18
Bunuel wrote:
gmatdemolisher1234 wrote:
If |-x/3 + 1| < 2, which of the following must be true?

a. x>0
b. x<8
c. x>-4
d. 0<x<3
e. None of the above


|-x/3 + 1| < 2

Get rid of the modulus: -2 < -x/3 + 1 < 2

Multiply by -3 and flip the sign: 6 > x - 3 > -6

Add 3 to all parts: 9 > x > -3.

Any number from -3 to 9 will for sure be more than -4.

Answer: C.



finding the range x > -3 and x< 9 is correct . But , x> -4 cannot be a valid range because x=-3 is within the range of x>-4 .
If x is substituted with -3 , then the answer in modulus becomes 2 . 2 cannot be lesser than 2 here.
Please let me know if my understanding is incorrect
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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post 30 Nov 2016, 11:21
girish1991 wrote:
Bunuel wrote:
gmatdemolisher1234 wrote:
If |-x/3 + 1| < 2, which of the following must be true?

a. x>0
b. x<8
c. x>-4
d. 0<x<3
e. None of the above


|-x/3 + 1| < 2

Get rid of the modulus: -2 < -x/3 + 1 < 2

Multiply by -3 and flip the sign: 6 > x - 3 > -6

Add 3 to all parts: 9 > x > -3.

Any number from -3 to 9 will for sure be more than -4.

Answer: C.



finding the range x > -3 and x< 9 is correct . But , x> -4 cannot be a valid range because x=-3 is within the range of x>-4 .
If x is substituted with -3 , then the answer in modulus becomes 2 . 2 cannot be lesser than 2 here.
Please let me know if my understanding is incorrect


Yes, your understanding is not correct. You see it's the other way around. The question asks: if 9 > x > -3, then which of the options must be correct. Now, if -3 < x < 9, then x must be more than -4 (any x from -3 to 9 will for sure be more than -4).
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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post 30 Nov 2016, 12:07
Yes, your understanding is not correct. You see it's the other way around. The question asks: if 9 > x > -3, then which of the options must be correct. Now, if -3 < x < 9, then x must be more than -4 (any x from -3 to 9 will for sure be more than -4).[/quote]

In that case x<8 is also a possible contender right ? any number from -3 to 9 will be lesser than 8 .
On what basis option (b ) is incorrect ?
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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post 30 Nov 2016, 12:12
girish1991 wrote:
Yes, your understanding is not correct. You see it's the other way around. The question asks: if 9 > x > -3, then which of the options must be correct. Now, if -3 < x < 9, then x must be more than -4 (any x from -3 to 9 will for sure be more than -4).


In that case x<8 is also a possible contender right ? any number from -3 to 9 will be lesser than 8 .
On what basis option (b ) is incorrect ?[/quote]

Since 9 > x > -3, then x can be say 8.5, which makes x < 8 not true.
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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post 30 Nov 2016, 15:52
VeritasPrepKarishma wrote:
gmatdemolisher1234 wrote:
If |-x/3 + 1| < 2, which of the following must be true?

a. x>0
b. x<8
c. x>-4
d. 0<x<3
e. None of the above



|-x/3 + 1| < 2
|x/3 - 1| < 2
(1/3) * |x - 3| < 2
|x - 3| < 6

Distance of x from 3 is less than 6 so -3 < x < 9.
So in every case, x will be greater than -4.

Answer (C)



Hi Karishma , I'm confused on must be true questions. In this case option C says it must be true that x >-4 , but if we take X = 30 , in this case LHS will be 9 which is more than 2.
Can you please explain.
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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post 01 Dec 2016, 00:01
rakaisraka wrote:
VeritasPrepKarishma wrote:
gmatdemolisher1234 wrote:
If |-x/3 + 1| < 2, which of the following must be true?

a. x>0
b. x<8
c. x>-4
d. 0<x<3
e. None of the above



|-x/3 + 1| < 2
|x/3 - 1| < 2
(1/3) * |x - 3| < 2
|x - 3| < 6

Distance of x from 3 is less than 6 so -3 < x < 9.
So in every case, x will be greater than -4.

Answer (C)



Hi Karishma , I'm confused on must be true questions. In this case option C says it must be true that x >-4 , but if we take X = 30 , in this case LHS will be 9 which is more than 2.
Can you please explain.


Notice what is given and what is asked.

Given that: |-x/3 + 1| < 2
So we KNOW that -3 < x < 9. x takes values only in this range. x cannot be 30.

For all values in this range, every value is greater than -4.

So answer (C)
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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post 08 Aug 2017, 09:36
explanation is clear, for the range 9 > x > -3 which of the choices satisfy more the solution range.
It easier to understand if we try to visualize each of them,e.g for the right response (C)

-------------(-4)-------(-3)------------------------------(9)--------->
so the range 9 > x > -3 is totally covered by the inequality x>-4, the rest choices cover the solution range just partially.

But should we expect to have such kind of question on the real GMAT?
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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post 03 Oct 2017, 21:57
Bunuel wrote:
gmatdemolisher1234 wrote:
If |-x/3 + 1| < 2, which of the following must be true?

a. x>0
b. x<8
c. x>-4
d. 0<x<3
e. None of the above


|-x/3 + 1| < 2

Get rid of the modulus: -2 < -x/3 + 1 < 2

Multiply by -3 and flip the sign: 6 > x - 3 > -6

Add 3 to all parts: 9 > x > -3.

Any number from -3 to 9 will for sure be more than -4.

Answer: C.


when we remove modulus are we not suppose to take only the +ve value? so -x should not be only +ve?
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If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post Updated on: 04 Oct 2017, 00:54
gmatdemolisher1234 wrote:
If |-x/3 + 1| < 2, which of the following must be true?

a. x>0
b. x<8
c. x>-4
d. 0<x<3
e. None of the above


Though this question seems ambiguous, but the question is very clear and answer will be x>-4 as it covers the whole domain of x which is -3<x<9 .. as explained by Bunuel and VeritasPrepKarishma
Lets not get confused by the different options. A really good question which can cost you marks in the GMAT exam. So, try to understand this question and follow the right approach as provided by the experts..
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Originally posted by shashankism on 03 Oct 2017, 22:28.
Last edited by shashankism on 04 Oct 2017, 00:54, edited 2 times in total.
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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post Updated on: 03 Oct 2017, 23:39
cbh wrote:
explanation is clear, for the range 9 > x > -3 which of the choices satisfy more the solution range.
It easier to understand if we try to visualize each of them,e.g for the right response (C)

-------------(-4)-------(-3)------------------------------(9)--------->
so the range 9 > x > -3 is totally covered by the inequality x>-4, the rest choices cover the solution range just partially.

But should we expect to have such kind of question on the real GMAT?
Thanks


The interpretation seems correct... If you find a question like this in GMAT OG, yes there are high chances that you are going to get such question in the real GMAT. So, try to understand and follow GMAT expert's : VeritasPrepKarishma & Bunuel 's Solution..
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Originally posted by shashankism on 03 Oct 2017, 22:44.
Last edited by shashankism on 03 Oct 2017, 23:39, edited 2 times in total.
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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post 03 Oct 2017, 23:20
1
1
shashankism wrote:
gmatdemolisher1234 wrote:
If |-x/3 + 1| < 2, which of the following must be true?

a. x>0
b. x<8
c. x>-4
d. 0<x<3
e. None of the above


I still believe that the question is ambiguous and can't be framed like this. We are here to solve the quantitative problem and not to decipher what the author from Jamboree believes. It is really ridiculous that people are justifying the answer C. If the question itself creates confusion it is supposed to be a garbage in the GMAT and that's why GMAT adopts the practice of testing the question and removing the useless confusing questions.

0<x<3 clearly true in one way and we can also say x>-4 may be true when we interpret the other way. But if the author believes that the question should have an answer x>-4 , he should not place the options like 0<x<3 and none of these. And if the author believes the 0<x<3 is correct, the author should not have placed the options like x>-4 and none of these.

Anyhow this is not in any case 700 level question. A 700 level questions shows its difficulty without any ambiguity. The 700 level question is so charming that after solving it a person feels the pleasure of achievement not the state of confusion as this question throws upon us..

So, I go with the answer 0<x<3. Others those who feel that answer is 0<x<3, lets not discuss more. Lets solve other better questions friends and don't have confusion. GMAT will not ask such ambiguous questions.


This is totally wrong! You are confused and are confusing others with wrong approach.

The question is not at all ambiguous and the correct answer is C. It's explained couple of times above. Every mathematician or GMAT tutor will tell yo that the answer is C.

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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post 03 Oct 2017, 23:24
3
shashankism wrote:
cbh wrote:
explanation is clear, for the range 9 > x > -3 which of the choices satisfy more the solution range.
It easier to understand if we try to visualize each of them,e.g for the right response (C)

-------------(-4)-------(-3)------------------------------(9)--------->
so the range 9 > x > -3 is totally covered by the inequality x>-4, the rest choices cover the solution range just partially.

But should we expect to have such kind of question on the real GMAT?
Thanks


The question says which must be true.. and not "which of the choices satisfy more the solution range."... These interpretations are not correct anyway..
We should always follow the natural flow of the question and not our interpretations.

I have found a few questions in this forum where wrong answers has been justified by even experts like anything..


I wouldn't say that every expert is always right - experts could make mistakes too. But if multiple experts are taking the pains to explain why a particular answer is correct, you might want to keep an open mind and delve a but deeper in the concept to understand what they are trying to explain.
Anyway, the choice is always yours.
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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post 03 Oct 2017, 23:30
Bunuel wrote:


Bunuel Since you have provided lot many questions with similar approach , I believe that what you are saying is correct and I will edit my post .. so as not to confuse others.
But I will really like to search such question in GMAT OG.
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Re: If |-x/3 + 1| < 2, which of the following must be true?  [#permalink]

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New post 03 Oct 2017, 23:35
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shashankism wrote:
Bunuel wrote:


Bunuel Since you have provided lot many questions with similar approach , I believe that what you are saying is correct and I will edit my post .. so as not to confuse others.
But I will really like to search such question in GMAT OG.


GMAT Prep: https://gmatclub.com/forum/if-it-is-tru ... 29093.html
OG: https://gmatclub.com/forum/if-4-7-x-3-w ... 68681.html

Theory:
3 FORMATS FOR GMAT INEQUALITIES QUESTIONS YOU NEED TO KNOW
HOW TO QUICKLY INTERPRET RANGES OF VARIABLES IN GMAT QUESTIONS
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Re: If |-x/3 + 1| < 2, which of the following must be true? &nbs [#permalink] 03 Oct 2017, 23:35
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