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Posts: 4
Updated on: 03 Oct 2017, 22:58
Originally posted by gmatdemolisher1234 on 28 Nov 2016, 06:28.
Last edited by Bunuel on 03 Oct 2017, 22:58, edited 2 times in total.
Last edited by Bunuel on 03 Oct 2017, 22:58, edited 2 times in total.
Renamed the topic and edited the question.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Question Stats:
44% (01:36) correct
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wrong
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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
A. x > 0
B. x < 8
C. x > -4
D. 0 < x < 3
E. None of the above
gmatdemolisher1234
|-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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gmatdemolisher1234
|-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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General Discussion
gmatdemolisher1234
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)
praty23
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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Posts: 1
Bunuel
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
girish1991
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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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:
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
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
shashankism
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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Bunuel
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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shashankism
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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KarishmaB
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
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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If |-x/3 + 1| < 2, which of the following must be true?
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Posts: 31
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)
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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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?
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?
lg800
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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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
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
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Posts: 13
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.
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.
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[quote="gmatdemolisher1234"]If |-x/3 + 1| < 2, which of the following must be true?
Case 1: x > 3
x-3 < 6
x<9
3<x<9
Case 2: x<= 3
3-x < 6
x > -3
-3<x<=3
Combining
-3<x<9
x>-4
IMO C
Case 1: x > 3
x-3 < 6
x<9
3<x<9
Case 2: x<= 3
3-x < 6
x > -3
-3<x<=3
Combining
-3<x<9
x>-4
IMO C
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