Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 13 Feb 2016, 10:29

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# m11 q24

Author Message
Manager
Joined: 17 Dec 2008
Posts: 177
Followers: 2

Kudos [?]: 87 [1] , given: 0

m11 q24 [#permalink]  08 Feb 2009, 16:33
1
KUDOS
4
This post was
BOOKMARKED
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
 Kaplan Promo Code Knewton GMAT Discount Codes GMAT Pill GMAT Discount Codes
SVP
Joined: 29 Aug 2007
Posts: 2492
Followers: 64

Kudos [?]: 634 [2] , given: 19

Re: m11 q24 [#permalink]  15 Feb 2009, 13:38
2
KUDOS
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.
_________________
Manager
Joined: 17 Dec 2008
Posts: 177
Followers: 2

Kudos [?]: 87 [0], given: 0

Re: m11 q24 [#permalink]  18 Feb 2009, 06:53
Thanks. What a tough question though (to get in 2 min).
Maybe its one to guess and move on
Manager
Joined: 14 Aug 2009
Posts: 123
Followers: 2

Kudos [?]: 95 [0], given: 13

Re: m11 q24 [#permalink]  24 Feb 2010, 05:43
I just draw the graph.
_________________

Kudos me if my reply helps!

Manager
Joined: 09 Dec 2009
Posts: 122
Followers: 4

Kudos [?]: 31 [0], given: 19

Re: m11 q24 [#permalink]  24 Feb 2010, 06:30
flyingbunny wrote:
I just draw the graph.

How do you graph this, what does it look like?
_________________

G.T.L. - GMAT, Tanning, Laundry

Round 2: 07/10/10 - This time it's personal.

Senior Manager
Joined: 21 Dec 2009
Posts: 268
Location: India
Followers: 10

Kudos [?]: 149 [3] , given: 25

Re: m11 q24 [#permalink]  24 Feb 2010, 10:46
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

Manager
Joined: 26 Nov 2009
Posts: 176
Followers: 3

Kudos [?]: 55 [1] , given: 5

Re: m11 q24 [#permalink]  27 Feb 2010, 01:02
1
KUDOS
by substituting values only ans choice c is valid
Manager
Joined: 12 Jul 2010
Posts: 67
Followers: 1

Kudos [?]: 2 [0], given: 3

Re: m11 q24 [#permalink]  08 Sep 2010, 01:25
Its C.

f(2) = -1 and f(-2) = -3
Substituting these values in the equations shows that only C hold good.
Intern
Joined: 02 Feb 2011
Posts: 7
Followers: 0

Kudos [?]: 2 [0], given: 2

Re: m11 q24 [#permalink]  01 Mar 2011, 08:18
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.
Intern
Joined: 18 Feb 2011
Posts: 10
Followers: 1

Kudos [?]: 2 [0], given: 22

Re: m11 q24 [#permalink]  02 Mar 2011, 09:41
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.
Director
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 920
Followers: 13

Kudos [?]: 273 [0], given: 123

Re: m11 q24 [#permalink]  02 Mar 2011, 16:13
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.
Manager
Joined: 02 Feb 2012
Posts: 195
Location: United States
Schools: HBS '19
GPA: 3.08
Followers: 1

Kudos [?]: 4 [0], given: 104

Re: m11 q24 [#permalink]  02 Mar 2012, 14:06
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.
Manager
Status: On...
Joined: 16 Jan 2011
Posts: 189
Followers: 3

Kudos [?]: 50 [0], given: 62

Re: m11 q24 [#permalink]  02 Mar 2012, 19:32
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
_________________

Labor cost for typing this post >= Labor cost for pushing the Kudos Button
kudos-what-are-they-and-why-we-have-them-94812.html

Intern
Joined: 10 Aug 2012
Posts: 19
Location: India
Concentration: General Management, Technology
GPA: 3.96
Followers: 0

Kudos [?]: 6 [1] , given: 15

Re: m11 q24 [#permalink]  05 Mar 2013, 20:56
1
KUDOS
$$F(x) = 1 - x$$, 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
Intern
Joined: 27 Feb 2013
Posts: 5
Followers: 0

Kudos [?]: 0 [0], given: 17

Re: m11 q24 [#permalink]  06 Mar 2013, 07:31
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...
Intern
Joined: 27 Feb 2013
Posts: 5
Followers: 0

Kudos [?]: 0 [0], given: 17

Re: m11 q24 [#permalink]  06 Mar 2013, 07:32
This is not a level 700-800 question...
Re: m11 q24   [#permalink] 06 Mar 2013, 07:32
Similar topics Replies Last post
Similar
Topics:
m04q24 1 07 Sep 2009, 11:05
M01Q24 1 06 Sep 2009, 23:27
M01 Q24 2 07 Jul 2009, 06:26
m01-q24 9 16 May 2009, 06:39
14 M24 Q 24 19 12 Mar 2009, 13:54
Display posts from previous: Sort by

# m11 q24

Moderators: WoundedTiger, Bunuel

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.