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Which of the following CANNOT be the value of x - |x| ?

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Bunuel
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Which of the following CANNOT be the value of x - |x| ? [#permalink] New post   08 Feb 2021, 06:45
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A
B
C
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E

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57% (01:19) correct 43% (01:05) wrong based on 242 sessions
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Which of the following CANNOT be the value of x - |x| ?

A. 0
B. 2x
C. Value greater than x
D. Value smaller than x
E. x
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C
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Vivor
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Re: Which of the following CANNOT be the value of x - |x| ? [#permalink] New post   08 Feb 2021, 06:56
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A. At x=0, x - |x| = 0. Possible
B. At x=-2, x - |x| = -4 = 2x. Possible
C. Value greater than x
D. Same example shown above in B. Possible
E. Same example as shown above in A. Possible

Ans is C IMO
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Re: Which of the following CANNOT be the value of x - |x| ? [#permalink] New post   09 Feb 2021, 01:24
x - |x|
Critical value approach
Two scenarios for the modulus: x<0; 0≤x

When x<0 the modulus will become -(x)
x--(x)=x+x=2x

When 0≤x the modulus will become (x)
x-(x)=0

A. 0 (X) Answer to the second scenario
B. 2x (X) Answer to the first scenario
C. Value greater than x (0) if x is positive then x<2x. BUT we only got 2x when x is negative. When x is positive we get 0. 0<x.
D. Value smaller than x (X) If x is positive then 0<x
E. x (X) when x=0 then 0=0 and 2x=0
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Re: Which of the following CANNOT be the value of x - |x| ? [#permalink] New post   02 Mar 2021, 07:06
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I have a query

Why cannot C be correct e.g.
if we take option B that itself says 2x this means x - |x| = 2x this also implies that 2x > x

Assume x = 2
case 1: x - x => 2 - 2 = 0
case 2: x + x => 2 + 2 = 4

Thus 4 is greater than 2. Am I missing something?
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Re: Which of the following CANNOT be the value of x - |x| ? [#permalink] New post   02 Mar 2021, 07:46
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mandeepscheema wrote:
I have a query

Why cannot C be correct e.g.
if we take option B that itself says 2x this means x - |x| = 2x this also implies that 2x > x

Assume x = 2
case 1: x - x => 2 - 2 = 0
case 2: x + x => 2 + 2 = 4

Thus 4 is greater than 2. Am I missing something?


In case 2, it would be 2-2
If X=2,

If X=-2
It would be -2-2=-4
And -4<-2
So C is correct in any scenario.
I hope I was able to explain correctly.

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Re: Which of the following CANNOT be the value of x - |x| ? [#permalink] New post   18 Apr 2024, 04:50
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↧↧↧ Detailed Video Solution to the Problem ↧↧↧





As we have |x| in the equation so we will have two cases
-Case 1: x ≥ 0
=> |x| = x
=> x - |x| = x - x = 0 => A is POSSIBLE
If x = 0 then x-|x| = 0 = x
=> E is POSSIBLE		-Case 2: x < 0
=> |x| = -x
=> x - |x| = x - (-x) = x + x = 2x => B is POSSIBLE
If x = -1
=> x - |x| = 2x = -2 < -1  => D is POSSIBLE


So, Answer will be C
Hope it helps!

Watch the following video to MASTER Absolute Values

­
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Re: Which of the following CANNOT be the value of x - |x| ? [#permalink]
18 Apr 2024, 04:50
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