Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 15 Nov 2009
Posts: 39

For every integer n ≥ 3, the function g(n) is defined as the
[#permalink]
Show Tags
26 Aug 2011, 06:23
Question Stats:
80% (01:07) correct 20% (01:18) wrong based on 171 sessions
HideShow timer Statistics
For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(100) – g(99)? A. 0 B. 1 C. 3 D. 99 E. 100
Official Answer and Stats are available only to registered users. Register/ Login.



Intern
Joined: 15 Nov 2009
Posts: 39

Functions
[#permalink]
Show Tags
26 Aug 2011, 07:01
For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(100) – g(99)?
1. 0 2. 1 3. 3 4. 99 5. 100
What's the concept behind this? Can someone please help?
Apologies  I have posted in the wrong forum before.



Manager
Status: Quant 50+?
Joined: 02 Feb 2011
Posts: 100
Concentration: Strategy, Finance

Re: Functions
[#permalink]
Show Tags
26 Aug 2011, 09:43
gsaxena26 wrote: For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(100) – g(99)?
1. 0 2. 1 3. 3 4. 99 5. 100
What's the concept behind this? Can someone please help?
Apologies  I have posted in the wrong forum before. Simple concept, g(100) = g(99) because 100 is not an odd number, thus g(100) is 3X5X7....X99. The 100 does nothing. If you didn't see this right away you could kind of cheat. G(3) = 3, G(5) = 15, G(7) = 105, G(9) = 945.... As you can see there is no real pattern and hence way to hard to actually determine G(99) easily, therefore you will start looking for the trick.



VP
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1489

Re: Functions
[#permalink]
Show Tags
26 Aug 2011, 11:27
The odd integers from 1 to 100, inclusive = the odd integers from 1 to 99, inclusive [because 100 is even] Therefore g(100) = g(99) => g(100)  g(99) = 0 (A)
_________________
GyanOne  Top MBA Rankings and MBA Admissions Blog
Top MBA Admissions Consulting  Top MiM Admissions Consulting
Premium MBA Essay ReviewBest MBA Interview PreparationExclusive GMAT coaching
Get a FREE Detailed MBA Profile Evaluation  Call us now +91 98998 31738



Retired Moderator
Joined: 20 Dec 2010
Posts: 1836

Re: Functions
[#permalink]
Show Tags
26 Aug 2011, 23:42
gsaxena26 wrote: For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(100) – g(99)?
1. 0 2. 1 3. 3 4. 99 5. 100
What's the concept behind this? Can someone please help? Just understanding what stem is trying to convey: for every integer \(n \ge 3\), g(n)=Product of odd integers from 1 to n: g(3): Here, n=3 So, g(3)=1*3(Product of ODD integers from 1 to n i.e. 1 to 3) g(4): Here, n=4 So, g(4)=1*3 (Product of ODD integers from 1 to n i.e. 1 to 4) Likewise, g(99): Here, n=99 So, g(99)=1*3*5*7*....*95*97*99 (Product of ODD integers from 1 to n i.e. 1 to 99) g(100): Here, n=100 So, g(100)=1*3*5*7*....*95*97*99 (Product of ODD integers from 1 to n i.e. 1 to 100) You see g(99) and g(100) are same. Thus the difference must be 0. Ans: "A" ******************************** BTW: you have posted the question in wrong forum. No PS or DS question should be posted in Math forum.
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Current Student
Status: :)
Joined: 29 Jun 2010
Posts: 105
WE: Information Technology (Consulting)

Re: Functions
[#permalink]
Show Tags
27 Aug 2011, 02:37
For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(100) – g(99)? 1. 0 2. 1 3. 3 4. 99 5. 100 g(n) is defined as product of all odd integers from 1 to n. Lets consider a case : let n =7 ;then g(n)=3*5*7 =75 let n =8 ;then g(n)=3*5*7 =75 There is no change in the final value of both the functions .This is because there is no odd number between 7 and 8 and hence the value is same. The same is the case with 99 and 100. i.e. g(100) will be same as g(99) => g(100)g(99) = 0 which is the answer choice A.
_________________
Thanks, GC24
Please click Kudos ,if my post helped you



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8385
Location: Pune, India

Re: Functions
[#permalink]
Show Tags
27 Aug 2011, 08:07
gsaxena26 wrote: For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(100) – g(99)?
1. 0 2. 1 3. 3 4. 99 5. 100
What's the concept behind this? Can someone please help? @gsaxena26: As per your request, here is my solution. First, we will first try and understand what the function g(n) is. g(n) is product of all odd integers upto and including n. Let me take some examples to understand this. g(3) = 1*3 (Odd integers upto and including 3) g(4) = 1*3 (Odd integers upto and including 4) g(5) = 1*3*5 (Odd integers upto and including 5) g(6) = 1*3*5 (Odd integers upto and including 6) etc Ok. Now we have to deal with g(99) and g(100). Let's get a sense of what they are. g(99) = 1*3*5*7*9*...*99 g(100) = 1*3*5*7*9*...*99 They are going to be the same. Hence their difference will be 0. Takeaway: If it is hard to understand what the question is saying, try and take some examples to understand it. Here, we tried to figure out what g(n) is using g(3), g(4) etc
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Director
Joined: 01 Feb 2011
Posts: 668

Re: Functions
[#permalink]
Show Tags
27 Aug 2011, 15:23
for n>=3 , g(n) = product of all odd integers 1 to n.
g(100) = 1*3*5.....99
g(99) = 1*3*5*.....99
=> g(100)g(99) = 0
Answer is A.



Manager
Joined: 12 May 2013
Posts: 67

Re: For every integer n ≥ 3, the function g(n) is defined as the
[#permalink]
Show Tags
20 Dec 2014, 03:46
VeritasPrepKarishma wrote: gsaxena26 wrote: For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(100) – g(99)?
1. 0 2. 1 3. 3 4. 99 5. 100
What's the concept behind this? Can someone please help? gsaxena26: As per your request, here is my solution. First, we will first try and understand what the function g(n) is. g(n) is product of all odd integers upto and including n. Let me take some examples to understand this. g(3) = 1*3 (Odd integers upto and including 3) g(4) = 1*3 (Odd integers upto and including 4) g(5) = 1*3*5 (Odd integers upto and including 5) g(6) = 1*3*5 (Odd integers upto and including 6) etc Ok. Now we have to deal with g(99) and g(100). Let's get a sense of what they are. g(99) = 1*3*5*7*9*...*99 g(100) = 1*3*5*7*9*...*99 They are going to be the same. Hence their difference will be 0. Takeaway: If it is hard to understand what the question is saying, try and take some examples to understand it. Here, we tried to figure out what g(n) is using g(3), g(4) etc Hey Karishma, i got this question correct. But i am curious to know what if the question were g(102) – g(99) ? how would you solve the question ?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8385
Location: Pune, India

Re: For every integer n ≥ 3, the function g(n) is defined as the
[#permalink]
Show Tags
21 Dec 2014, 21:25
adymehta29 wrote: VeritasPrepKarishma wrote: gsaxena26 wrote: For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(100) – g(99)?
1. 0 2. 1 3. 3 4. 99 5. 100
What's the concept behind this? Can someone please help? gsaxena26: As per your request, here is my solution. First, we will first try and understand what the function g(n) is. g(n) is product of all odd integers upto and including n. Let me take some examples to understand this. g(3) = 1*3 (Odd integers upto and including 3) g(4) = 1*3 (Odd integers upto and including 4) g(5) = 1*3*5 (Odd integers upto and including 5) g(6) = 1*3*5 (Odd integers upto and including 6) etc Ok. Now we have to deal with g(99) and g(100). Let's get a sense of what they are. g(99) = 1*3*5*7*9*...*99 g(100) = 1*3*5*7*9*...*99 They are going to be the same. Hence their difference will be 0. Takeaway: If it is hard to understand what the question is saying, try and take some examples to understand it. Here, we tried to figure out what g(n) is using g(3), g(4) etc Hey Karishma, i got this question correct. But i am curious to know what if the question were g(102) – g(99) ? how would you solve the question ? The logic remains the same: g(102) = 1*3*5*7*9*...*99*101 g(99) = 1*3*5*7*9*...*99 g(102)  g(99) = 1*3*5*7*9*...*99*101  1*3*5*7*9*...*99 = 1*3*5*7*9*...*99*(101  1) = 1*3*5*7*9*...*99*100
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



NonHuman User
Joined: 09 Sep 2013
Posts: 8423

Re: For every integer n ≥ 3, the function g(n) is defined as the
[#permalink]
Show Tags
17 Apr 2018, 00:24
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: For every integer n ≥ 3, the function g(n) is defined as the &nbs
[#permalink]
17 Apr 2018, 00:24






