If |-x/3 + 1|

Question

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

KarishmaB · Accepted Answer

|-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)

Bunuel · Answer

|-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.

praty23 · Answer

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)

Bunuel · Answer

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).

girish1991 · Answer

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

Bunuel · Answer

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).

arhumsid · Answer

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

Bunuel · Answer

shashankism · Answer

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.

Bunuel · Answer

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

PTibrewal · Answer

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.

KarishmaB · Answer

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.

MBAHOUSE · Answer

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

gmattyfatty · Answer

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)

lg800 · Answer

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.

Answer: C.[/quote]

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?

Bunuel · Answer

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.

BinodBhai · Answer

I see a lot of confusion with regards to the answer... till the point we need to find the range, its all good. Range is -3<x<9

What if the value of x is 4 or 6.. then (D) falls apart and hence it is not always true...

However, option (C) x > -4 will always be true for whatever x's value may be from the given range above. Be it -2, 0, 6,8 etc... these will always be greater than -4

Other options
A. x > 0 - what if x is -2? this option falls apart
B. x < 8 - what if x = 8, this option falls apart

sanatakesGMAT · Answer

Hi experts, I had a doubt here.

we get the final equation as 9>x>-3

however the answer here is C. x>-4

which doesn???t make sense to me since if x>-4, then -3 could also be a possible solution for x, which according to our solution is wrong (x must be greater then -3)

Please let me know if im missing some logic here.

Kinshook · Answer

If |-x/3 + 1| < 2, which of the following must be true? Case 1: x > 3 x-3 < 6 x<9 3 -3 -3-4 IMO C

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

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