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If |3-x| < x+5, which of the following

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ajaygaur319
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If |3-x| < x+5, which of the following [#permalink] New post   22 Jun 2020, 04:43
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59% (01:48) correct 41% (01:52) wrong based on 437 sessions
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If |3-x| < x+5, which of the following must be true about x?

I. x > -1
II. x < 2
III. x > 0

A) I only
B) II only
C) III only
D) I and III only
E) I, II, and III
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A
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GMATinsight
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Re: If |3-x| < x+5, which of the following [#permalink] New post   22 Jun 2020, 04:49
Expert Reply
ajaygaur319 wrote:
If |3-x| < x+5, which of the following must be true about x?

I. x > -1
II. x < 2
III. x > 0

A) I only
B) II only
C) III only
D) I and III only
E) I, II, and III


|3-x| < x+5

Let's start with |3-x| = x+5

i.e. x = -1

for |3-x| < x+5
x > -1 so that the absolute value of |3-x| is Less than absolute value of x+5

Hence, I. x > -1 is TRUE

rest may be proves false because we have entire range x > -1

Answer: Option A
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ajaygaur319
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Re: If |3-x| < x+5, which of the following [#permalink] New post   22 Jun 2020, 04:55
GMATinsight wrote:
ajaygaur319 wrote:
If |3-x| < x+5, which of the following must be true about x?

I. x > -1
II. x < 2
III. x > 0

A) I only
B) II only
C) III only
D) I and III only
E) I, II, and III


|3-x| < x+5

Let's start with |3-x| = x+5

i.e. x = -1

for |3-x| < x+5
x > -1 so that the absolute value of |3-x| is Less than absolute value of x+5

Hence, I. x > -1 is TRUE

rest may be proves false because we have entire range x > -1

Answer: Option A


I marked this question wrong because I thought both 1 and 3 are true. Because if x is greater than -1 then x must also be greater than 0. I still cannot get my head around why 3 is not included. Can you please elaborate the statement?
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Re: If |3-x| < x+5, which of the following [#permalink] New post   22 Jun 2020, 05:01
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ajaygaur319 wrote:
GMATinsight wrote:
ajaygaur319 wrote:
If |3-x| < x+5, which of the following must be true about x?

I. x > -1
II. x < 2
III. x > 0

A) I only
B) II only
C) III only
D) I and III only
E) I, II, and III


|3-x| < x+5

Let's start with |3-x| = x+5

i.e. x = -1

for |3-x| < x+5
x > -1 so that the absolute value of |3-x| is Less than absolute value of x+5

Hence, I. x > -1 is TRUE

rest may be proves false because we have entire range x > -1

Answer: Option A


I marked this question wrong because I thought both 1 and 3 are true. Because if x is greater than -1 then x must also be greater than 0. I still cannot get my head around why 3 is not included. Can you please elaborate the statement?


ajaygaur319

Nowhere does the question mention that x is an Integer so x may be -1/2 as well which proves that III is NOT ALWAYS TRUE

+

x may be 0 as well which is not taken care of by III part which says x > 0

Remember: When question uses term "MUST BE TRUE" then our job is to find even one reason and prove that the information is MOT true in that case
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Re: If |3-x| < x+5, which of the following [#permalink] New post   13 Jul 2020, 08:34
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|3-x| < x + 5

Square both the sides

(3-x)^2 < (x+5)^2

x^2 - 6x + 9 < x^2 + 10x + 25

16x + 16 > 0

x+1>0

x>-1

Answer A
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Re: If |3-x| < x+5, which of the following [#permalink] New post   16 Jul 2020, 22:14
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Hi, can you explain why III isn't an option? Even if x is an integer, III says x>0 which means it will be 1/2 not -1/2 which makes the statement true.
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Re: If |3-x| < x+5, which of the following [#permalink] New post   05 Aug 2020, 07:45
III says that x is always positive, but x = -0.5 is also a solution. Hence statement III is not a must condition.

If the question would have been:

Which all can be true?
Then III also holds True.
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Re: If |3-x| < x+5, which of the following [#permalink] New post   07 Aug 2020, 21:40
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ajaygaur319 wrote:
If |3-x| < x+5, which of the following must be true about x?

I. x > -1
II. x < 2
III. x > 0

A) I only
B) II only
C) III only
D) I and III only
E) I, II, and III


|3-x| <x+5
-x-5<3-x<x+5
-x-8<-x<x+2
x+8>x>-x-2

x+8>x 0>-8 not possible

x>-x-2
2x>-2
x>-1
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Re: If |3-x| < x+5, which of the following [#permalink] New post   03 Jul 2023, 04:08
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Re: If |3-x| < x+5, which of the following [#permalink]
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