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# m11 q24

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Manager
Joined: 17 Dec 2008
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08 Feb 2009, 17:33
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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

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions

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SVP
Joined: 29 Aug 2007
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15 Feb 2009, 14:38
2
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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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Manager
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18 Feb 2009, 07:53
Thanks. What a tough question though (to get in 2 min).
Maybe its one to guess and move on

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Manager
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24 Feb 2010, 06:43
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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24 Feb 2010, 07:30
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 2: 07/10/10 - This time it's personal.

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Senior Manager
Joined: 21 Dec 2009
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24 Feb 2010, 11:46
3
KUDOS
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.
_________________

Cheers,
SD

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Manager
Joined: 26 Nov 2009
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27 Feb 2010, 02:02
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by substituting values only ans choice c is valid

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Manager
Joined: 12 Jul 2010
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08 Sep 2010, 02:25
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
Joined: 02 Feb 2011
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01 Mar 2011, 09:18
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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Intern
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02 Mar 2011, 10:41
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
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
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02 Mar 2011, 17:13
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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02 Mar 2012, 15:06
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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02 Mar 2012, 20:32
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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Intern
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05 Mar 2013, 21:56
1
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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 to$$F(-x)$$

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
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06 Mar 2013, 08:31
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 to$$F(-x)$$

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
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06 Mar 2013, 08:32
This is not a level 700-800 question...

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Re: m11 q24   [#permalink] 06 Mar 2013, 08:32
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# m11 q24

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