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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

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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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

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).
_________________

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

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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 ?

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.
_________________

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.

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

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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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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.

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

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02 Dec 2016, 23:32

If x = -3.9, then here x>-4 but not in the range of -3<x<9 if 0<x<3, then all the values in this range MUST be in the range -3<x<9 So need to understand why are we not considering D?

If x = -3.9, then here x>-4 but not in the range of -3<x<9 if 0<x<3, then all the values in this range MUST be in the range -3<x<9 So need to understand why are we not considering D?

This is explained couple of times above. Kindly re-read the discussion. Hope it helps.
_________________

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

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03 Dec 2016, 21:17

Bunuel wrote:

niks18 wrote:

If x = -3.9, then here x>-4 but not in the range of -3<x<9 if 0<x<3, then all the values in this range MUST be in the range -3<x<9 So need to understand why are we not considering D?

This is explained couple of times above. Kindly re-read the discussion. Hope it helps.

Hi Bunnel, thanks for the reply

Correct if I am wrong here - The approach for such questions should be to find out the range of values from question stem. In this case -3<x<9 Now test the values within this range against each option. So if x = 8.5 then it eliminates option a, b & d All values in the range -3<x<9 satisfy inequality x>-4, hence must be true.

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

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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? Thanks

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