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Manager
Joined: 17 Dec 2008
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Function F(x) is defined as follows: if x is positive or 0 then F(x) = 1 - x; if x is negative then F(x) = x - 1. Which of the following is true about F(x)? I. F(|x|) = |F(x)|II. F(x) = F(-x)III. |F(x + 1)| = |x|(A) I only (B) II only (C) III only (D) I and III only (E) not I, II, or III Source: GMAT Club Tests - hardest GMAT questions
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CEO
Joined: 29 Aug 2007
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ConkergMat wrote: Function F(x) is defined as follows:
if x is positive or 0 then F(x) = 1 - x;
if x is negative then F(x) = x - 1.
Which of the following is true about F(x)?
I. F(|x|) = |F(x)|
II. F(x) = F(-x)
III. |F(x + 1)| = |x| I. F(|x|) = |F(x)| :- not possible. First, F(|x|) could be -ve, 0 and +ve but |F(x)| is always 0 or +ve. If |x| is greater than 1, F(|x|) = 1 - lxl is -ve fraction or > 1. If |x| is smaller than 1, F(|x|) = 1 - |x| is +ve fraction. If |x| is 0, F(|x|) is 1. But |F(x)| is always 0 or +ve. So not true. II. F(x) = F(-x):- not possible. If x is +ve, -x is -ve and vice versa. If x is 0, F(x) = F(-x) = 1 If x is +ve, F(x) = 1 - x, which could be +ve if x is smaller than 1 or -ve if x is > 1, and F(-x) = -x-1, which could also be -ve if x is >-1 or +ve if x is <-1. Similarly, if x is negative, then F(x) and F(-x) will have +ve or -ve values. They are not equal. not suff. III. |F(x + 1)| = |x|:- is possible. |F(x + 1)| is always |x| whether (x+1) is +ve or -ve. If (x + 1) is +ve, |F(x + 1)| = |1- (x + 1)| = |x|If (x + 1) is -ve, |F(x + 1)| = |(x + 1)-1| = |x|III is true.
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GT
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Manager
Joined: 17 Dec 2008
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Thanks. What a tough question though (to get in 2 min). Maybe its one to guess and move on 
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Manager
Joined: 14 Aug 2009
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I just draw the graph.
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Kudos me if my reply helps!
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Manager
Joined: 09 Dec 2009
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flyingbunny wrote: I just draw the graph. How do you graph this, what does it look like?
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G.T.L. - GMAT, Tanning, Laundry
Round 1: 05/12/10 handling-a-grenade-thesituation-s-official-debrief-94181.html
Round 2: 07/10/10 - This time it's personal.
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Senior Manager
Joined: 21 Dec 2009
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GMAT TIGER's explanation is right but you are not supposed to write Math major test. Just take x=2 and x=-2.
Then apply on the rule. Its time consuming not tough. In fact it is easy. It took 2 min for me to solve this one.
It will take 5-6 min to draw a graph for most of the guys.
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Cheers,
SD
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Manager
Joined: 27 Aug 2009
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Answer is clearly C
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Intern
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hmm, i am an engineer and i got this wrong 
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Manager
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by substituting values only ans choice c is valid
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Manager
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Its C.
f(2) = -1 and f(-2) = -3
Substituting these values in the equations shows that only C hold good.
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Intern
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just by looking at the functions you can tell that 1 & 2 are not valid because they are saying that the value of X is the same, before and after the function which we know is untrue as depending on the value of X it will either be subtracted from 1 or 1 will be added to it.
for answer 3, if you subtract 1 and then add 1 back, you will have your original number in absolute terms. if you subtract your original number from 1 and then add 1 back, you will have your number in absolute terms. therefore answer is C.
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Manager
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C , tough one though
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Intern
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It seems as if it's time consuming and then you begin to panic and want to guess so you can do it in under 2 minutes, but if you do as silasaaa2 suggests and just substitute. Pick a positive and negative number and substitute for each. You WILL find the answer in less than 2 minutes.
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Director
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F(0) = 1
F(1) = 0
F(-1) = -2
Statement I is false. F(1) != F(-1) a, d gone
Statement II is false. F(1) != F(-1) b gone
Statement III is true. x = 0 = F(1), e gone. C it is.
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Manager
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I just took two values for x and tested them all. It took me about 2 minutes and 30 seconds to get the answer. A bit slow but it worked.
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Manager
Status: On...
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30 seconds to substitute and confirm C. Do not solve these type of questions unless of course this is your 37th question and you have 15 mns spare time. Even then, I would prefer not to solve, but substitute for this question
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Manager
Status: I will not stop until i realise my goal which is my dream too
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ConkergMat wrote: Function F(x) is defined as follows: if x is positive or 0 then F(x) = 1 - x; if x is negative then F(x) = x - 1. Which of the following is true about F(x)? I. F(|x|) = |F(x)|II. F(x) = F(-x)III. |F(x + 1)| = |x|(A) I only (B) II only (C) III only (D) I and III only (E) not I, II, or III Source: GMAT Club Tests - hardest GMAT questions followed substitution method and the answer is C
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Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat 
Satyameva Jayate - Truth alone triumphs
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Intern
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F(x) = 1 - x, for x greater than equal to zero.....condition 1
F(x) = x -1 , for x less than zero.....condition 2
I- F(|x|) = 1- |x| and |F(x)| = | 1 - x |.....condition 1
and F(|x|) = |x| -1 and |F(x)| = | x - 1 |.....condition 2
F(|x|) not equal to F(|x|)
II-F(-x) = 1- (-x) = 1+ x.....condition 1
and F(-x) = (-x) -1 = -( x + 1).....condition 2
F(x) not equal toF(-x)
III-|F(x +1)| = |1- (x+1)| = |x|.....condition 1
and |F(x +1)| = |(x + 1) - 1| = |x|.....condition 2
Hence, III is correct answer and C is the correct choice
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Intern
Joined: 27 Feb 2013
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vipinktyagi wrote: F(x) = 1 - x, for x greater than equal to zero.....condition 1
F(x) = x -1 , for x less than zero.....condition 2
I- F(|x|) = 1- |x| and |F(x)| = | 1 - x |.....condition 1
and F(|x|) = |x| -1 and |F(x)| = | x - 1 |.....condition 2
F(|x|) not equal to F(|x|)
II-F(-x) = 1- (-x) = 1+ x.....condition 1
and F(-x) = (-x) -1 = -( x + 1).....condition 2
F(x) not equal toF(-x)
III-|F(x +1)| = |1- (x+1)| = |x|.....condition 1
and |F(x +1)| = |(x + 1) - 1| = |x|.....condition 2
Hence, III is correct answer and C is the correct choice This question doesn't look like hardest category question....indeed good detailed explanation...
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Intern
Joined: 27 Feb 2013
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This is not a level 700-800 question...
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close
