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

It is currently 06 Dec 2019, 08:22

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 an integer n, the function f(n) is defined as the product of all

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

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
G
Joined: 07 Jun 2017
Posts: 160
Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
GMAT ToolKit User Reviews Badge
For an integer n, the function f(n) is defined as the product of all  [#permalink]

Show Tags

New post 30 Oct 2017, 22:14
2
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

47% (01:34) correct 53% (01:36) wrong based on 134 sessions

HideShow timer Statistics

For an integer n, the function f(n) is defined as the product of all integers from 1 to n, where n is greater than 10. Which of the following is NOT a factor of f(n)+1?

I. 2
II. 3
III. 10


A. None
B. II only
C. I and II only
D. I and III only
E. I, II and III
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59586
Re: For an integer n, the function f(n) is defined as the product of all  [#permalink]

Show Tags

New post 30 Oct 2017, 23:08
nkmungila wrote:
For an integer n, the function f(n) is defined as the product of all integers from 1 to n, where n is greater than 10. Which of the following is NOT a factor of f(n)+1?

I. 2
II. 3
III. 10


A. None
B. II only
C. I and II only
D. I and III only
E. I, II and III


f(n) = n!, where n > 10. So, f(n) is even, a multiple of 3 and a multiple of 10.

Therefore, f(n) + 1 is odd, 1 more than a multiple of 3 and 1 more than a multiple of 10, which means that f(n) + 1 is not divisible by 2, 3, or 10.

Answer: E.
_________________
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59586
Re: For an integer n, the function f(n) is defined as the product of all  [#permalink]

Show Tags

New post 30 Oct 2017, 23:10
Bunuel wrote:
nkmungila wrote:
For an integer n, the function f(n) is defined as the product of all integers from 1 to n, where n is greater than 10. Which of the following is NOT a factor of f(n)+1?

I. 2
II. 3
III. 10


A. None
B. II only
C. I and II only
D. I and III only
E. I, II and III


f(n) = n!, where n > 10. So, f(n) is even, a multiple of 3 and a multiple of 10.

Therefore, f(n) + 1 is odd, 1 more than a multiple of 3 and 1 more than a multiple of 10, which means that f(n) + 1 is not divisible by 2, 3, or 10.

Answer: E.


Similar questions to practice:
http://gmatclub.com/forum/for-every-pos ... 26691.html
http://gmatclub.com/forum/for-every-pos ... 49722.html
http://gmatclub.com/forum/x-is-the-prod ... 56545.html
http://gmatclub.com/forum/if-n-is-a-pos ... 44553.html
http://gmatclub.com/forum/for-every-eve ... 68636.html
http://gmatclub.com/forum/for-any-integ ... 12494.html
http://gmatclub.com/forum/if-a-and-b-ar ... 44714.html
http://gmatclub.com/forum/the-function- ... 08309.html
http://gmatclub.com/forum/for-every-pos ... 81815.html
http://gmatclub.com/forum/for-any-integ ... 31701.html
http://gmatclub.com/forum/let-p-be-the- ... 32329.html
http://gmatclub.com/forum/does-the-inte ... 26735.html
http://gmatclub.com/forum/if-x-is-an-in ... 00670.html

Hope it helps.
_________________
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8281
Re: For the integer n, the function f(n) is defined as the product of all  [#permalink]

Show Tags

New post 12 Sep 2018, 05:01
2
1
pushpitkc wrote:
For the integer n, the function f(n) is defined as the product of all integers from 1 to n,
where n is greater than 10. Which of the following is NOT a factor of f(n) + 1?

I. 2
II. 3
III. 10

A. None
B. II only
C. I and II only
D. I and III only
E. I, II, and III

Source: Experts Global


F(n)=1*2*3*...n where n>10
So f(n)=1*2*3*....*10*..*n
Thus f(n) is product of all numbers till n and at least till 1
f(n) and f(n)+1 are co-prime, as they are consecutive terms.

Therefore f(n)+1 will not have any common factor that f(n) has..
So all numbers till 10 will NOT be factors

E
_________________
Senior Manager
Senior Manager
avatar
P
Joined: 15 Oct 2017
Posts: 295
GMAT 1: 560 Q42 V25
GMAT 2: 570 Q43 V27
GMAT 3: 710 Q49 V39
Reviews Badge
Re: For the integer n, the function f(n) is defined as the product of all  [#permalink]

Show Tags

New post 12 Sep 2018, 09:16
f(n) can be expressed as n! hence n! + 1 will be a prime integer and none of the integers smaller than n can be a factor of the same. Hence, E.
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8281
Re: For the integer n, the function f(n) is defined as the product of all  [#permalink]

Show Tags

New post 12 Sep 2018, 09:27
urvashis09 wrote:
f(n) can be expressed as n! hence n! + 1 will be a prime integer and none of the integers smaller than n can be a factor of the same. Hence, E.


Although the second part that none of the integers smaller than n can be a factor of n!+1 is correct..

But that n!+1 will be prime integer may not be correct every time..
Example 3!+1=6+1=7 yes..
4!+1=24+1=25....Not a prime
5!+1=120+1=121=11^2... Again not aprime integer..

So the point is that n!+1 will not be a multiple of any prime number <n
_________________
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8619
Location: United States (CA)
Re: For the integer n, the function f(n) is defined as the product of all  [#permalink]

Show Tags

New post 14 Sep 2018, 17:40
pushpitkc wrote:
For the integer n, the function f(n) is defined as the product of all integers from 1 to n,
where n is greater than 10. Which of the following is NOT a factor of f(n) + 1?

I. 2
II. 3
III. 10

A. None
B. II only
C. I and II only
D. I and III only
E. I, II, and III


Notice that f(n) = n!. Since two consecutive integers cannot share any of the same prime factors, f(n) and f(n) + 1 cannot share any of the same prime factors. Since f(n) is greater than 10!, and 10! has prime factors of 2, 3, 5, and 7, we see that 2, 3, and 2 x 5 = 10 cannot be primes of f(n) + 1.

Answer: E
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8619
Location: United States (CA)
Re: For an integer n, the function f(n) is defined as the product of all  [#permalink]

Show Tags

New post 06 Feb 2019, 19:38
nkmungila wrote:
For an integer n, the function f(n) is defined as the product of all integers from 1 to n, where n is greater than 10. Which of the following is NOT a factor of f(n)+1?

I. 2
II. 3
III. 10


A. None
B. II only
C. I and II only
D. I and III only
E. I, II and III


We must remember that f(n) and f(n) + 1 WON’T SHARE ANY OF THE SAME PRIME FACTORS because they are consecutive integers.

So, since n is greater than 10, we see that f(n) will have prime factors of at least 2, 3, 5, and 7. Thus, 2, 3, and 10 won’t be factors of f(n) + 1.

Answer: E
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Manager
User avatar
B
Joined: 24 Jul 2019
Posts: 151
Location: Austria
GPA: 3.9
CAT Tests
Re: For an integer n, the function f(n) is defined as the product of all  [#permalink]

Show Tags

New post 08 Sep 2019, 22:39
US09 wrote:
f(n) can be expressed as n! hence n! + 1 will be a prime integer and none of the integers smaller than n can be a factor of the same. Hence, E.


Is this a applicable rule for other problems or just "made up" for this problem?
Because if I try it wih 4! => 4*3*2*1 = 24 + 1 will result in 25 which is not a prime integer.
_________________
Let's get some
GMAT Club Bot
Re: For an integer n, the function f(n) is defined as the product of all   [#permalink] 08 Sep 2019, 22:39
Display posts from previous: Sort by

For an integer n, the function f(n) is defined as the product of all

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





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