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

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

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

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)

|-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

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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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.

|-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

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.

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?