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

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

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]
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]
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.

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]
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.

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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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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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.

You can check similar questions below:

https://gmatclub.com/forum/if-it-is-tru ... 81702.html
https://gmatclub.com/forum/if-xy-0-and- ... 39194.html
https://gmatclub.com/forum/if-it-is-true ... 29093.html
https://gmatclub.com/forum/if-it-is-tru ... 66196.html
https://gmatclub.com/forum/if-4x-12-x-9- ... 01732.html
https://gmatclub.com/forum/if-4-7-x-3-w ... 68681.html
https://gmatclub.com/forum/if-5-x-0-whi ... 31556.html
https://gmatclub.com/forum/if-it-is-tru ... -9602.html
https://gmatclub.com/forum/if-m-0-which ... 54150.html
https://gmatclub.com/forum/if-x-0-which ... 76331.html
https://gmatclub.com/forum/if-x-3-1-2-w ... 29673.html
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Re: If |-x/3 + 1| < 2, which of the following must be true? [#permalink]
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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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? [#permalink]
KarishmaB 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.

Hi Karishma

Even I was able to calculate the range, but got confused because the question does not mention that x is an integer. What if x=-3.57, it does not fall within the range but still x>-3? Please help.
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If |-x/3 + 1| < 2, which of the following must be true? [#permalink]
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PTibrewal wrote:
KarishmaB 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.

Hi Karishma

Even I was able to calculate the range, but got confused because the question does not mention that x is an integer. What if x=-3.57, it does not fall within the range but still x>-3? Please help.

PTibrewal

The point here is "what is given" and "what is asked".

What is given: |-x/3 + 1| < 2
What does this tell us? This tells us that x lies between -3 and 9 exclusive. So x can be -2.99, -1.24, 0.38, 4 etc.
So we are given that x cannot be -3 or less than that.

So what must be true? It is true that whatever value x may take, it will certainly be more than -4. It doesn't mean that x can be - 3.57. The point is that whatever x will be, it will be greater than -4.
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Re: If |-x/3 + 1| < 2, which of the following must be true? [#permalink]
If |-x/3 + 1| < 2, which of the following must be true?
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Re: If |-x/3 + 1| < 2, which of the following must be true? [#permalink]
I was very confused about this question until I read it a bit differently, and then realized it's a disconnect with how I was phrasing the question linguistically.

We all agree that the stem is saying
"x is definitely -3 < x < 9"

Therefore, which of the following must be the value of x?
1) x has to be greater than 0: wrong. it doesnt have to be because it can be -3 -> 0
2) x has to be less than 8: wrong. it doesnt have it be because it can be 8 -> 9 for example
3) x has to be greater than -4: yes, it 100% has to be, because according to the stem, x is definitely between -3 and 9. so it literally has to be greater than -4
4) x has to be between 0 and 3: wrong. it doesnt have to be because it can be -4 -> 0 for example

I got this question wrong because I was reading the option as "0 < x < 3 is a definite possibility of x". This is true. However thats not what these "must true" questions are asking. They are basically telling you to pick which one HAS to be true as a result of the stem. In other words.

- stem says x is required to be 3 < x < 9. Therefore, x is also required to be _______? (C would be the only correct answer)
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Re: If |-x/3 + 1| < 2, which of the following must be true? [#permalink]
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[/quote]

|-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.

Hi Bunuel, in order to that be true you are assuming that x must be an integer? For instance, as per the answer choice, x could be -3.5.[/quote]

^ I have the same question. How is this true if X could be -3.5 or any number between -3 and -4?
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If |-x/3 + 1| < 2, which of the following must be true? [#permalink]
lg800 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 have the same question. How is this true if X could be -3.5 or any number between -3 and -4?

We are given that 9 > x > -3. Any x from this range will be more than -4.

I recommend two steps to improve your understanding of the OA, which is 100% correct. Firstly, carefully review and study the previous discussion of this thread. Secondly, explore similar questions from Trickiest Inequality Questions Type: Confusing Ranges (part of our Special Questions Directory). This should help clarify any confusion.
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Re: If |-x/3 + 1| < 2, which of the following must be true? [#permalink]
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