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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

The function f is defined for all positive integers n > 4 as [#permalink]
15 Jan 2014, 11:00

2

This post received KUDOS

5

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

40% (03:07) correct
60% (01:51) wrong based on 186 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?

Re: The function f is defined for all positive integers n > 4 as [#permalink]
15 Jan 2014, 17:09

12

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.

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)

Re: The function f is defined for all positive integers n > 4 as [#permalink]
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.

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?

Re: The function f is defined for all positive integers n > 4 as [#permalink]
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.

Re: The function f is defined for all positive integers n > 4 as [#permalink]
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.

Re: The function f is defined for all positive integers n > 4 as [#permalink]
11 Jun 2015, 03:55

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Low GPA MBA Acceptance Rate Analysis Many applicants worry about applying to business school if they have a low GPA. I analyzed the low GPA MBA acceptance rate at...

In out-of-the-way places of the heart, Where your thoughts never think to wander, This beginning has been quietly forming, Waiting until you were ready to emerge. For a long...