GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 11 Dec 2019, 21:07

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.

Close

Request Expert Reply

Confirm Cancel

For every positive odd integer n, the function g(n) is defined to be t

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 15 Aug 2013
Posts: 12
WE: Marketing (Energy and Utilities)
GMAT ToolKit User
For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

Show Tags

New post 14 Sep 2014, 07:04
3
26
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

70% (01:46) correct 30% (01:39) wrong based on 326 sessions

HideShow timer Statistics

I came across this question on gmatpill. Now i have seen a similar question for even integer product...how do we approach this one...?

For every positive odd integer n, the function g(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If t is the smallest prime factor of g(99) +1, then t is?


(A) between 2 and 19
(B) between 20 and 39
(C) between 40 and 59
(D) between 60 and 79
(E) 80 or greater

_________________
Someday, everything will make perfect sense :)
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59674
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

Show Tags

New post 14 Sep 2014, 17:14
7
8
TheDelhiDude wrote:
I came across this question on gmatpill. Now i have seen a similar question for even integer product...how do we approach this one...?

For every positive odd integer n, the function g(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If t is the smallest prime factor of g(99) +1, then t is?


(A) between 2 and 19
(B) between 20 and 39
(C) between 40 and 59
(D) between 60 and 79
(E) 80 or greater


g(99) = 1*3*5*..*99 = odd.

g(99) + 1 = odd + 1 = even. The smallest prime factor of any even number is 2 --> t = 2.

Answer: A.
_________________
General Discussion
Manager
Manager
User avatar
Joined: 21 Jul 2014
Posts: 119
GMAT ToolKit User
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

Show Tags

New post 14 Sep 2014, 13:40
1
TheDelhiDude wrote:
I came across this question on gmatpill. Now i have seen a similar question for even integer product...how do we approach this one...?

For every positive odd integer n, the function g(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If t is the smallest prime factor of g(99) +1, then t is?


(A) between 2 and 19
(B) between 20 and 39
(C) between 40 and 59
(D) between 60 and 79
(E) 80 or greater


This question tries to trick you into thinking that you have to find the prime factorization of a very huge number. In fact, you won't have to do that at all.

Consider what g(99) means:
g(99) = 1 * 3 * 5 * 7 * 9 * ... * 97 * 99 = some huge number.

You can already establish that the smallest prime factor of that huge number is 3, since it is defined within what g(x) means.

Since t = smallest prime factor (which will always be 3 when n > 1) + 1, we can conclude that t = 4.

The correct answer is A.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59674
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

Show Tags

New post 14 Sep 2014, 17:15
1
4
Bunuel wrote:
TheDelhiDude wrote:
I came across this question on gmatpill. Now i have seen a similar question for even integer product...how do we approach this one...?

For every positive odd integer n, the function g(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If t is the smallest prime factor of g(99) +1, then t is?


(A) between 2 and 19
(B) between 20 and 39
(C) between 40 and 59
(D) between 60 and 79
(E) 80 or greater


g(99) = 1*3*5*..*99 = odd.

g(99) + 1 = odd + 1 = even. The smallest prime factor of any even number is 2 --> t = 2.

Answer: A.


Similar questions to practice:
for-every-positive-even-integer-n-the-function-h-n-is-126691.html
for-every-positive-even-integer-n-the-function-h-n-149722.html
for-any-integer-p-p-is-equal-to-the-product-of-all-the-int-112494.html
x-is-the-product-of-all-even-numbers-from-2-to-50-inclusive-156545.html
if-a-and-b-are-odd-integers-a-b-represents-the-product-of-144714.html
the-function-f-m-is-defined-for-all-positive-integers-m-as-108309.html
for-every-even-positive-integer-m-f-m-represents-the-produ-168636.html

Check questions about various functions in Special Questions Directory

Operations/functions defining algebraic/arithmetic expressions
Symbols Representing Arithmetic Operation
Rounding Functions
Various Functios
_________________
Intern
Intern
avatar
Joined: 15 Aug 2013
Posts: 12
WE: Marketing (Energy and Utilities)
GMAT ToolKit User
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

Show Tags

New post 14 Sep 2014, 19:03
Thanks Bunuel so its safe to assume if the question involves a product of consecutive odd integers (from any odd no. till any odd no.) and adds 1 to the product, it can be said that the smallest prime factor is 2.

Say if its g(n)=[5x7x9x...any no.]+1 , the smallest prime factor is 2?
_________________
Someday, everything will make perfect sense :)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59674
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

Show Tags

New post 14 Sep 2014, 20:31
1
TheDelhiDude wrote:
Thanks Bunuel so its safe to assume if the question involves a product of consecutive odd integers (from any odd no. till any odd no.) and adds 1 to the product, it can be said that the smallest prime factor is 2.

Say if its g(n)=[5x7x9x...any no.]+1 , the smallest prime factor is 2?


Well, yes. How else?

The product of odd numbers (consecutive or not) is odd. ODD + 1 = EVEN. The smallest prime factor of any even number is 2.
_________________
Manager
Manager
User avatar
Joined: 21 Jul 2014
Posts: 119
GMAT ToolKit User
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

Show Tags

New post 15 Sep 2014, 08:38
Thanks for the clarification Bunuel, but maybe there could be two interpretations of the question?

My understanding was that the question was defining t = [smallest prime factor of g(99)] + 1, rather than t = smallest prime factor of (g(99)+1).

I thought that because answer choice A did not clarify "between 2 and 19 INCLUSIVE" (which the GMAT typically does, right?).

Either way, the answer choice is A.
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 384
Location: India
GMAT 1: 760 Q50 V44
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

Show Tags

New post 27 Nov 2015, 09:15
2
1
TheDelhiDude wrote:
For every positive odd integer n, the function g(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If t is the smallest prime factor of g(99) +1, then t is?


(A) between 2 and 19
(B) between 20 and 39
(C) between 40 and 59
(D) between 60 and 79
(E) 80 or greater


The key here is not to get intimidated by the huge number g(99)

g(99) = 1*3*5* ...*97*99
We need to find the smallest prime factor of g(99) + 1

We know that:
Odd*Odd = Odd
Odd*Even = Even
Even*Even = Even

Hence g(99) = 1*3*5* ...*97*99 will always be an odd number

We also know that
Odd + Odd = Even
Even + Even = Even
Odd + Even = Odd


Therefore g(99) + 1 has to be an even number
The smallest prime factor of any even number = 2
Hence Option A
Manager
Manager
avatar
Joined: 10 Feb 2014
Posts: 81
GMAT 1: 690 Q50 V33
GMAT ToolKit User
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

Show Tags

New post 28 Nov 2015, 04:31
TheDelhiDude wrote:
I came across this question on gmatpill. Now i have seen a similar question for even integer product...how do we approach this one...?

For every positive odd integer n, the function g(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If t is the smallest prime factor of g(99) +1, then t is?


(A) between 2 and 19
(B) between 20 and 39
(C) between 40 and 59
(D) between 60 and 79
(E) 80 or greater



Bunuel: One doubt?

What if the question were reworded to find the largest prime number of g(99)+1?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59674
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

Show Tags

New post 28 Nov 2015, 08:23
itzmyzone911 wrote:
TheDelhiDude wrote:
I came across this question on gmatpill. Now i have seen a similar question for even integer product...how do we approach this one...?

For every positive odd integer n, the function g(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If t is the smallest prime factor of g(99) +1, then t is?


(A) between 2 and 19
(B) between 20 and 39
(C) between 40 and 59
(D) between 60 and 79
(E) 80 or greater



Bunuel: One doubt?

What if the question were reworded to find the largest prime number of g(99)+1?


GMAT would never ask such question because the largest prime of g(99) +1 is 7728802419974390867942174885150693176068821337346448420812666105479729917, which is not that easy to find.
_________________
Manager
Manager
avatar
Joined: 10 Feb 2014
Posts: 81
GMAT 1: 690 Q50 V33
GMAT ToolKit User
For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

Show Tags

New post 28 Nov 2015, 10:13
Bunuel wrote:
itzmyzone911 wrote:
TheDelhiDude wrote:
I came across this question on gmatpill. Now i have seen a similar question for even integer product...how do we approach this one...?

For every positive odd integer n, the function g(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If t is the smallest prime factor of g(99) +1, then t is?


(A) between 2 and 19
(B) between 20 and 39
(C) between 40 and 59
(D) between 60 and 79
(E) 80 or greater



Bunuel: One doubt?

What if the question were reworded to find the largest prime number of g(99)+1?


GMAT would never ask such question because the largest prime of g(99) +1 is 7728802419974390867942174885150693176068821337346448420812666105479729917, which is not that easy to find.


Wow what a number! :roll:

Just for curiosity, Bunuel is this a symbolic representation (fictitious) of the prime factor or you actually calculated it. Can you explain how you arrived at this no?...and in any case if the options were kept the same, option E would have been the correct answer?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59674
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

Show Tags

New post 28 Nov 2015, 10:20
itzmyzone911 wrote:
Bunuel wrote:
itzmyzone911 wrote:
GMAT would never ask such question because the largest prime of g(99) +1 is 7728802419974390867942174885150693176068821337346448420812666105479729917, which is not that easy to find.


Wow what a number! :roll:

Just for curiosity, Bunuel is this a symbolic representation (fictitious) of the prime factor or you actually calculated it. Can you explain how you arrived at this no?...and in any case if the options were kept the same, option E would have been the correct answer?


This is the largest prime of g(99) + 1. I used special calculator to get it.
_________________
Manager
Manager
avatar
Joined: 10 Feb 2014
Posts: 81
GMAT 1: 690 Q50 V33
GMAT ToolKit User
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

Show Tags

New post 28 Nov 2015, 10:53
Ok...thanks Bunuel :-D
Intern
Intern
avatar
Joined: 03 Jul 2015
Posts: 5
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

Show Tags

New post 18 Apr 2016, 13:34
I agree that t=2, but the answer choice A reads: 2 < t < 19. Doesn't that make t=2 the wrong answer, since t={3,4,...,18}?
Can you please clarify?
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13744
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

Show Tags

New post 05 Oct 2019, 05:51
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 Club Bot
Re: For every positive odd integer n, the function g(n) is defined to be t   [#permalink] 05 Oct 2019, 05:51
Display posts from previous: Sort by

For every positive odd integer n, the function g(n) is defined to be t

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne