If |3-x|

Question

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

surjin · Accepted Answer

|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

GMATinsight · Answer

|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

ajaygaur319 · Answer

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?

GMATinsight · Answer

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

BrushMyQuant · Answer

|3-x| < x+5, which of the following must be true about x?

As we have \|3 - x\| in the equation so we will have two cases
-Case 1: 3 - x ≥ 0 => x ≤ 3 => \|3 - x\| = 3 - x => 3 - x < x + 5 => 2x > -2 => x > -1 But condition was x ≤ 3 and x > 3 is in the same range => -1 < x ≤ 3 is the SOLUTION	-Case 2: 3 - x ≤ 0 => x ≥ 3 => \|3 - x\| = -(3 - x) = x - 3 => x - 3 < x + 5 => 8 > 0 => Which is TRUE ALWAYS But condition was x ≥ 3 and it is TRUE ALWAYS => x ≥ 3 is the SOLUTION

=> Combined solution is -1 < x ≤ 3 and x ≥ 3
=> x > -1

(I) x > -1
=> ALWAYS TRUE

(II) x < 2
=> NOT TRUE for values of x ≤ -1

(III) x > 0
=> NOT TRUE for values of -1 < x ≤ 0

So, Answer will be A
Hope it helps!

Watch the following video to MASTER Absolute Values

Aarjav112004 · Answer

Still I am really confused as option III is the subset of I so it is also a true statement. They did not mention that we had to find the solution, the question just states which is true.

Bunuel · Answer

As explained above, |3 - x| < x + 5 implies x > -1. The question asks to find options which must be true, so which are always true for any possible values of x. Now let's check the options: I. x > -1. This statement is always true. II. x < 2. This statement is NOT always true because x could be 10, which would violate it. III. x > 0. This statement is NOT always true because x could be -1/2, which would violate it. Answer: A.

adroitpensador · Answer

Bunuel  I have a doubt in st 3.

Just by solving the inequalities incorporating the Mod, we get the equation satisfies for all x > -1

If something is true for x > -1, then it must be true for x > 0 (subset of broader condition). I see in x > 0, we'll ignore values such as -1/2 that satisfies the equation but EVERY number within x > 0 region SATISFIES (must be true) for the given equation.

Help me align my thinking.

Bunuel · Answer

Yes, if something is true for x > -1, it must also be true for x > 0. However, if x > -1 is true, it’s not necessary for x > 0 to be true. For example, x can be -1/2, which is greater than -1 and satisfies the original inequality but is not greater than 0. To reiterate, the question does not ask if the original inequality will be true for x > 0 (which it is); it asks if x > 0 is necessarily true considering the original inequality.

I'd suggest referring to similar questions from the link:  Trickiest Inequality Questions Type: Confusing Ranges . This should help clarify any confusion.

adroitpensador · Answer

Nirvana moment: 'it asks if x > 0 is necessarily true considering the original inequality'. Thanks. Let me go through the recommended questions.

SomeOneUnique · Answer

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

Still I am really confused as option III is the subset of I so it is also a true statement. They did not mention that we had to find the solution, the question just states which is true.

bumpbot · Answer

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

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