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17 Aug 2011, 05:36
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
53% (02:29) correct
48%
(01:47)
wrong
based on 80
sessions
History
Date
Time
Result
Not Attempted Yet
Is |x-1| < 1?
(1) (x-1)^2 <= 1
(2) x^2 - 1 > 0
OPEN DISCUSSION OF THIS QUESTION IS HERE: is-x-127462.html
(1) (x-1)^2 <= 1
(2) x^2 - 1 > 0
Hi someone help solve this, shouldnt be very difficult.
I know how to evaluate statement 1 and statement 2, looking to just understand how do we test a combined statement i,e C when we have multiple inequality equations. Do we test 4 values...
Maybe somebody could explain while solving this question..
Once again how do we evaluate c- statement combined together..is my main concern
Thanks
Kaps
I know how to evaluate statement 1 and statement 2, looking to just understand how do we test a combined statement i,e C when we have multiple inequality equations. Do we test 4 values...
Maybe somebody could explain while solving this question..
Once again how do we evaluate c- statement combined together..is my main concern
Thanks
Kaps
OPEN DISCUSSION OF THIS QUESTION IS HERE: is-x-127462.html
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Updated on: 17 Aug 2011, 11:06
Originally posted by anordinaryguy on 17 Aug 2011, 10:24.
Last edited by anordinaryguy on 17 Aug 2011, 11:06, edited 1 time in total.
Last edited by anordinaryguy on 17 Aug 2011, 11:06, edited 1 time in total.
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First I did calculation partially and got the answer C, but than when I was trying to type solution for you, I get more insight into the question.
We need to prove
Is |x-1| < 1? => -1<(x-1)<1 => 0<x<2 ?
(1) (x-1)^2 <= 1
=> 0 <= X <= 2 (Correction in earlier calculation)
=> Doesn't prove 0<x<2, Not Sufficient
(2) x^2 - 1 > 0
=> (x > -1 and x > 1) OR (x < -1 and x < 1)
=> x > 1 or x < -1
=> Doesn't prove 0<x<2, Not Sufficient
Combining these two we get
1 < X <= 2
=> Doesn't prove 0<x<2, because x = 2 is a possible solution in combined equality.
So E is the answer
We need to prove
Is |x-1| < 1? => -1<(x-1)<1 => 0<x<2 ?
(1) (x-1)^2 <= 1
=> 0 <= X <= 2 (Correction in earlier calculation)
=> Doesn't prove 0<x<2, Not Sufficient
(2) x^2 - 1 > 0
=> (x > -1 and x > 1) OR (x < -1 and x < 1)
=> x > 1 or x < -1
=> Doesn't prove 0<x<2, Not Sufficient
Combining these two we get
1 < X <= 2
=> Doesn't prove 0<x<2, because x = 2 is a possible solution in combined equality.
So E is the answer
17 Aug 2011, 10:33
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mokap25
Is |x-1| < 1?
(1) (x-1)^2 <= 1
(2) x^2 - 1 > 0
(1) (x-1)^2 <= 1
(2) x^2 - 1 > 0
From statement 1: If (x-1)^2 <= 1, the value of x varies from 0 to 2 i.e. x is non-negative.
(x-1)^2 <= 1
(x-1) (x-1) <= 1
i) x-1 <= 1
x-1 <= 1
x <= 2
If x is 2, |x-1| = |2-1| = 1 ..........No.
If x is 1.5, |x-1| = |1.5-1| = 0.5.. Yes.
ii) x-1 => 1
x => 0
If x is 0, |x-1| = |0-1| = 1 ..........No.
If x is 0.5, |x-1| = |0.5-1| = 0.5.. Yes.
Not sufficient......
From statement 2: x^2 - 1 > 0
x^2 > 1
i) either, x > 1
ii) or x < -1
If x is 1.1, |x-1| = |1.1-1| = 0.1 .......... yes.
If x is -1.1, |x-1| = |-1.1-1| = -2.1. No.
From 1 and 2: the value of x varies from 0 to 2 but still insufficient.
E.
