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Is x>25? 1) |x-22|+|24-x|+|25-x|>4 2) |21-x|+|22-x|+|24-x|<4

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Is x>25? 1) |x-22|+|24-x|+|25-x|>4 2) |21-x|+|22-x|+|24-x|<4  [#permalink]

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New post 10 Apr 2019, 10:58
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A
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Difficulty:

  65% (hard)

Question Stats:

46% (02:14) correct 54% (02:11) wrong based on 37 sessions

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Is \(x>25?\)
1) \(|x-22|+|24-x|+|25-x|>4\)
2) \(|21-x|+|22-x|+|24-x|<4\)

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Is x>25? 1) |x-22|+|24-x|+|25-x|>4 2) |21-x|+|22-x|+|24-x|<4  [#permalink]

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New post 14 Apr 2019, 19:58
1
Is \(x>25?\)

1) \(|x-22|+|24-x|+|25-x|>4\)
X can be 0 or any negative number to fit in.
Rather take any value of x and it will fit in..
Insufficient

2) \(|21-x|+|22-x|+|24-x|<4\)
All values of X between 21 and 24 will give you 4, otherwise it will be more than 4..
Sufficient..
The inequality should be \(|21-x|+|22-x|+|24-x|\leq{4}\), there is no value of x otherwise that will give you <4..

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Re: Is x>25? 1) |x-22|+|24-x|+|25-x|>4 2) |21-x|+|22-x|+|24-x|<4  [#permalink]

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New post 15 Apr 2019, 20:33
chetan2u wrote:
Is \(x>25?\)

1) \(|x-22|+|24-x|+|25-x|>4\)
X can be 0 or any negative number to fit in.
Rather take any value of x and it will fit in..
Insufficient

2) \(|21-x|+|22-x|+|24-x|<4\)
All values of X between 21 and 24 will give you 4, otherwise it will be more than 4..
Sufficient..
The inequality should be \(|21-x|+|22-x|+|24-x|\leq{4}\), there is no value of x otherwise that will give you <4..

B


Can you please give a more detailed explanation? I tried the 3 step method but got confused
Have you used some kind of innate logic which I may have overlooked?chetan2u
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Re: Is x>25? 1) |x-22|+|24-x|+|25-x|>4 2) |21-x|+|22-x|+|24-x|<4  [#permalink]

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New post 23 Apr 2019, 11:04
Small query. For b, at x = 22, isn't the value 3?

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Re: Is x>25? 1) |x-22|+|24-x|+|25-x|>4 2) |21-x|+|22-x|+|24-x|<4   [#permalink] 23 Apr 2019, 11:04
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