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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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VP
Joined: 23 Feb 2015
Posts: 1255
Is x>25? 1) |x-22|+|24-x|+|25-x|>4 2) |21-x|+|22-x|+|24-x|<4  [#permalink]

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10 Apr 2019, 10:58
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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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Math Expert
Joined: 02 Aug 2009
Posts: 7958
Is x>25? 1) |x-22|+|24-x|+|25-x|>4 2) |21-x|+|22-x|+|24-x|<4  [#permalink]

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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..

B
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Joined: 03 Jan 2019
Posts: 9
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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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
Intern
Joined: 07 Apr 2018
Posts: 2
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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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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