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

It is currently 21 Oct 2014, 14:24

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The function f is defined for all positive integers n > 4 as

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Senior Manager
Senior Manager
User avatar
Status: Final Lap
Joined: 25 Oct 2012
Posts: 294
Concentration: General Management, Entrepreneurship
GPA: 3.54
WE: Project Management (Retail Banking)
Followers: 2

Kudos [?]: 104 [2] , given: 85

The function f is defined for all positive integers n > 4 as [#permalink] New post 15 Jan 2014, 11:00
2
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

41% (03:01) correct 59% (01:50) wrong based on 111 sessions
The function f is defined for all positive integers n > 4 as f(n) = 3n – 9 if n is odd and f(n) = 2n – 7 if n is even. What is the value of the positive integer a?

(1) f(f(a)) = a

(2) f(f(f(a))) is odd.
[Reveal] Spoiler: OA

_________________

KUDOS is the good manner to help the entire community.

"If you don't change your life, your life will change you"

Expert Post
8 KUDOS received
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 2142
Followers: 539

Kudos [?]: 2264 [8] , given: 31

Re: The function f is defined for all positive integers n > 4 as [#permalink] New post 15 Jan 2014, 17:09
8
This post received
KUDOS
Expert's post
Rock750 wrote:
The function f is defined for all positive integers n > 4 as f(n) = 3n – 9 if n is odd and f(n) = 2n – 7 if n is even. What is the value of the positive integer a?

(1) f(f(a)) = a

(2) f(f(f(a))) is odd.

I'm happy to help. :-) As usual, this is a spectacularly clever problem from those folks at MGMAT.

Here's a blog you may find helpful on function notation:
http://magoosh.com/gmat/2012/function-n ... -the-gmat/

Notice that for this particular function, when f(n) has an even input, it yields an odd output, and vice versa: when it has an odd input, it yield an even output.

Statement #1:
Well, if a is even, then f(a) = 2a - 7, which will be odd, and f(f(a)) = 3(2a - 7) - 9 = 6a - 30.
Then, if f(f(a)) = a, we have
6a - 30 = a
5a = 30
a = 6
That's one possible value.
If a is odd, then f(a) = 3a - 9, which will be even, and f(f(a)) = 2(3a - 9) - 7 = 6a - 25
Then, if f(f(a)) = a, we have
6a - 25 = a
5a = 25
a = 5
That's also one possible value.
This statement yields two possible values, so no definitive answer to the prompt. This statement, alone and by itself, is insufficient.

Statement #2:
If f(f(f(a))) is odd,
then f(f(a)) is even,
and f(a) is odd,
and a is even.
This tells us that a is even, but a could be any even number.
This statement yields no definitive answer to the prompt. This statement, alone and by itself, is insufficient.

Combined
We have two values from statement #1. From statement #2, we know a must be even. This means that a = 6. Now, we can give a definitive answer to the prompt question. Combined, the statements are sufficient.
Answer = (C)

Does all this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Manager
Manager
avatar
Joined: 25 Oct 2013
Posts: 173
Followers: 0

Kudos [?]: 25 [0], given: 56

Re: The function f is defined for all positive integers n > 4 as [#permalink] New post 01 Feb 2014, 05:58
Stmt1: f(f(a))=a

If a is odd f(a) = 3a-9 this is even.
f(f(a))=2(3a-9)-7 = a (given)
solving a = 5.

If a is even f(a) is odd.
solving f(f(a))=a
gives us a=6.

Since 2 values of a are possible, stmt 1 is INSUFF.

Stmt2: f(f(f(a))) is odd
then f(f(a)) is even
f(a) is odd
a is even. Clearly INSUFF

Stmt1+stmt2: a=5 or 6 and a is even. a can only be 6. Hence C.
_________________

Click on Kudos if you liked the post!

Practice makes Perfect.

Senior Manager
Senior Manager
avatar
Joined: 15 Aug 2013
Posts: 284
Followers: 0

Kudos [?]: 16 [0], given: 23

Re: The function f is defined for all positive integers n > 4 as [#permalink] New post 11 May 2014, 13:59
mikemcgarry wrote:
Rock750 wrote:
The function f is defined for all positive integers n > 4 as f(n) = 3n – 9 if n is odd and f(n) = 2n – 7 if n is even. What is the value of the positive integer a?

(1) f(f(a)) = a

(2) f(f(f(a))) is odd.

I'm happy to help. :-) As usual, this is a spectacularly clever problem from those folks at MGMAT.

Here's a blog you may find helpful on function notation:
http://magoosh.com/gmat/2012/function-n ... -the-gmat/

Notice that for this particular function, when f(n) has an even input, it yields an odd output, and vice versa: when it has an odd input, it yield an even output.

Statement #1:
Well, if a is even, then f(a) = 2a - 7, which will be odd, and f(f(a)) = 3(2a - 7) - 9 = 6a - 30.
Then, if f(f(a)) = a, we have
6a - 30 = a
5a = 30
a = 6
That's one possible value.
If a is odd, then f(a) = 3a - 9, which will be even, and f(f(a)) = 2(3a - 9) - 7 = 6a - 25
Then, if f(f(a)) = a, we have
6a - 25 = a
5a = 25
a = 5
That's also one possible value.
This statement yields two possible values, so no definitive answer to the prompt. This statement, alone and by itself, is insufficient.

Statement #2:
If f(f(f(a))) is odd,
then f(f(a)) is even,
and f(a) is odd,
and a is even.
This tells us that a is even, but a could be any even number.
This statement yields no definitive answer to the prompt. This statement, alone and by itself, is insufficient.

Combined
We have two values from statement #1. From statement #2, we know a must be even. This means that a = 6. Now, we can give a definitive answer to the prompt question. Combined, the statements are sufficient.
Answer = (C)

Does all this make sense?
Mike :-)


Hi Mike,

is there a reason why choosing numbers here doesn't work or isn't optimal?

I tried use 5,6 and 7,8 and my values are all over?

Thanks
Expert Post
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 2142
Followers: 539

Kudos [?]: 2264 [0], given: 31

Re: The function f is defined for all positive integers n > 4 as [#permalink] New post 11 May 2014, 21:27
Expert's post
russ9 wrote:
Hi Mike,

is there a reason why choosing numbers here doesn't work or isn't optimal?

I tried use 5, 6 and 7, 8 and my values are all over?

Thanks

Dear russ9
Think about the prompt question, "What is the value of a?" It may be that a has just one value, or more than one. If you find one value, that's absolutely no guarantee that there aren't other values that also work. Suppose, for the sake of argument, that the two values that worked were a = 6 and a = 50 --- plugging in numbers for some single digit cases would never tell you that there's more than one answer. Do you see what I mean?

Remember, GMAT DS is NOT about "find the answer" --- it's more about "is it possible to find a unique and sensible answer?" If you were looking for one and only one answer, then plugging in numbers would make sense --- that might not be so bad on GMAT PS. But on GMAT DS, that misses the point in a problem such as this.

Does this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Senior Manager
Senior Manager
avatar
Joined: 15 Aug 2013
Posts: 284
Followers: 0

Kudos [?]: 16 [0], given: 23

Re: The function f is defined for all positive integers n > 4 as [#permalink] New post 15 May 2014, 16:22
mikemcgarry wrote:
russ9 wrote:
Hi Mike,

is there a reason why choosing numbers here doesn't work or isn't optimal?

I tried use 5, 6 and 7, 8 and my values are all over?

Thanks

Dear russ9
Think about the prompt question, "What is the value of a?" It may be that a has just one value, or more than one. If you find one value, that's absolutely no guarantee that there aren't other values that also work. Suppose, for the sake of argument, that the two values that worked were a = 6 and a = 50 --- plugging in numbers for some single digit cases would never tell you that there's more than one answer. Do you see what I mean?

Remember, GMAT DS is NOT about "find the answer" --- it's more about "is it possible to find a unique and sensible answer?" If you were looking for one and only one answer, then plugging in numbers would make sense --- that might not be so bad on GMAT PS. But on GMAT DS, that misses the point in a problem such as this.

Does this make sense?
Mike :-)


Makes total sense. Thanks, Mike!
Re: The function f is defined for all positive integers n > 4 as   [#permalink] 15 May 2014, 16:22
    Similar topics Author Replies Last post
Similar
Topics:
The function f is defined for all positive integers n by the ipc302 12 06 May 2006, 13:24
The function f is defined for all positive integers n by the dinesh8 7 28 Apr 2006, 22:05
The function f is defined by all positive integers n by the jodeci 1 09 Apr 2006, 03:23
The function f is define for all positive integers n by the myc2004 4 26 Feb 2006, 15:51
The function f is defined for all positive integers n by the Avis 5 20 Feb 2006, 16:39
Display posts from previous: Sort by

The function f is defined for all positive integers n > 4 as

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.