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

It is currently 22 Aug 2014, 05:51

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

For every positive even integer n, the function h(n) is

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 13 Aug 2005
Posts: 26
Location: Israel
Followers: 0

Kudos [?]: 1 [0], given: 0

For every positive even integer n, the function h(n) is [#permalink] New post 27 Aug 2005, 03:55
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

63% (02:04) correct 37% (01:32) wrong based on 81 sessions
For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is

(A) between 2 and 10
(B) between 10 and 20
(C) between 20 and 30
(D) between 30 and 40
(E) greater than 40

OPEN DISCUSSION OF THIS QUESTION IS HERE: for-every-positive-even-integer-n-the-function-h-n-is-126691.html
[Reveal] Spoiler: OA
Kaplan Promo CodeKnewton GMAT Discount CodesManhattan GMAT Discount Codes
Senior Manager
Senior Manager
avatar
Joined: 29 Nov 2004
Posts: 486
Location: Chicago
Followers: 1

Kudos [?]: 5 [0], given: 0

GMAT Tests User
Re: PS - factors (from GmatPrep) [#permalink] New post 27 Aug 2005, 07:56
yaron wrote:
Here is a PS from GmatPrep, Can you explain?

For every positive even integer n, the function f(h) is defined to be the product of all even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is
a. between 2 and 10
b. between 10 and 20
c. between 20 and 30
d. between 30 and 40
e. greater than 40

Thanks, Yaron


First thing I think there are some mistakes in the question I think the bolded parts above should be "function f(n)" and f(100) + 1

Solution

f(100) + 1 = 2(1x2x3...50) + 1

2^50x 50! +1

So the number should be something like xyz....0000001

So the prime factor should be much higher than 40...infact over 1000 probably...

Answer E
_________________

Fear Mediocrity, Respect Ignorance

Director
Director
avatar
Joined: 11 Mar 2005
Posts: 726
Followers: 1

Kudos [?]: 22 [0], given: 0

GMAT Tests User
 [#permalink] New post 29 Aug 2005, 13:49
E is it

f(100) = 2* 4 * 6------100 + 1
or
2^50(1* 2* 3* 4.... *46 * 47 * 48 * 49 * 50) + 1

who knows what will divide this number..
Manager
Manager
avatar
Joined: 06 Aug 2005
Posts: 198
Followers: 3

Kudos [?]: 5 [0], given: 0

GMAT Tests User
 [#permalink] New post 29 Aug 2005, 14:46
We had this question or a very similar one, two weeks ago !
Senior Manager
Senior Manager
avatar
Joined: 13 Jan 2005
Posts: 331
Followers: 1

Kudos [?]: 2 [0], given: 0

GMAT Tests User
 [#permalink] New post 30 Aug 2005, 14:09
f(100) = 2* 4 * 6------100 + 1
or
2^50(1* 2* 3* 4.... *46 * 47 * 48 * 49 * 50) + 1

Why wud it be 2^50? Shudnt it be 2(1.2.3.4...50)+1?
Director
Director
avatar
Joined: 15 Aug 2005
Posts: 804
Location: Singapore
Followers: 2

Kudos [?]: 3 [0], given: 0

GMAT Tests User
PS - Function [#permalink] New post 11 Oct 2005, 23:39
For every positive integer n, the function h(n) is defined to be the product of all even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is

A. Between 0 and 20
B. Between 10 and 20
C. Between 20 and 30
D. Between 30 and 40
E. Greater than 40
_________________

Cheers, Rahul.

SVP
SVP
User avatar
Joined: 24 Sep 2005
Posts: 1902
Followers: 10

Kudos [?]: 99 [0], given: 0

GMAT Tests User
Re: PS - Function [#permalink] New post 12 Oct 2005, 02:47
rahulraao wrote:
For every positive integer n, the function h(n) is defined to be the product of all even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is

A. Between 0 and 20
B. Between 10 and 20
C. Between 20 and 30
D. Between 30 and 40
E. Greater than 40


h(100)+1= 2.4.6.8......100 + 1
for every prime factor from 2, 3, to 47 (47 is the largest prime factor here coz 47*2=94<100. Remember all numbers here are even so to find the prime factor we have to, at least, devide each of them by 2). As we see the product contains prime factor from 2 to 47 ----> these prime numbers can't be factors of h(100)+1!. Thus the possible smallest prime factor of h(100)+1 must be greater than 47. E is correct.
Senior Manager
Senior Manager
avatar
Joined: 07 Jul 2005
Posts: 405
Followers: 3

Kudos [?]: 10 [0], given: 0

GMAT Tests User
GMATPrep - Prime [#permalink] New post 23 Oct 2005, 17:11
For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is

a) between 2 and 10
b) between 10 and 20
c) between 20 and 30
d) between 30 and 40
e) greater than 40
2 KUDOS received
SVP
SVP
User avatar
Joined: 24 Sep 2005
Posts: 1902
Followers: 10

Kudos [?]: 99 [2] , given: 0

GMAT Tests User
Re: GMATPrep - Prime [#permalink] New post 23 Oct 2005, 19:23
2
This post received
KUDOS
rigger wrote:
For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is

a) between 2 and 10
b) between 10 and 20
c) between 20 and 30
d) between 30 and 40
e) greater than 40



h(100)= 2*4*6*.....*100 = (2*1)*(2*2)*(2*3) .....*(2*47)*(2*48)*(2*49)*(2*50)
As we observe h(100) is divisible by primes like 2,3,5......,47 ---> h(100)+1 is not divisible by these primes, in other words, these primes can't be factor of h(100)+1. Thus, the smallest prime factor of h(100)+1 must be greater than 47 . E is my choice.
Manager
Manager
avatar
Joined: 04 Jan 2006
Posts: 51
Followers: 1

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

PS. Please explain your answer [#permalink] New post 26 Jan 2006, 18:27
For every positive even integer n, the function h(n) is defined to be the product of all even integers from 2 to n, inclusive. If P is the smallest prime factor of h(100) +1, then p is

1. Between 2 and 10
2. Between 10 and 20
3. Between 20 and 30
4. Between 30 and 40
5. Greater than 40
SVP
SVP
User avatar
Joined: 16 Oct 2003
Posts: 1816
Followers: 4

Kudos [?]: 32 [0], given: 0

GMAT Tests User
 [#permalink] New post 26 Jan 2006, 18:48
2 * 4 * 6 * 8........94....* 100

2*1 *2*2 *2*3....2*47 *2*50

In this list 47 is the biggest prime which does not divide h(100) + 1. So the prime must be bigger than 47. E.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jul 2004
Posts: 5097
Location: Singapore
Followers: 17

Kudos [?]: 136 [0], given: 0

GMAT Tests User
 [#permalink] New post 26 Jan 2006, 19:12
h(100)= 2(1*2*3*4*5...*50) -> Largest prime number 47
h(100)+1 should result in another prime number, which I guess will not be lower than 47..

Going with E
Intern
Intern
User avatar
Joined: 06 Jan 2006
Posts: 23
Location: New York
Followers: 0

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

 [#permalink] New post 27 Jan 2006, 12:36
I don't agree. 47 is not a factor of h(100)+1 but of h(100).

I don't know thw answer though.
Intern
Intern
User avatar
Joined: 06 Jan 2006
Posts: 23
Location: New York
Followers: 0

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

 [#permalink] New post 27 Jan 2006, 12:40
Also, the question asks for the smallest and not the largest prime factor...
Intern
Intern
User avatar
Joined: 06 Jan 2006
Posts: 23
Location: New York
Followers: 0

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

 [#permalink] New post 27 Jan 2006, 15:05
mbadownunder, could you please indicate what is the correct answer, even if we don't have the correst reasoning ? It may help us find the solution...

Thanks.
Manager
Manager
avatar
Joined: 12 Jul 2006
Posts: 67
Location: Boston
Followers: 1

Kudos [?]: 3 [0], given: 0

PS: Prime factor (from GMAT Prep) [#permalink] New post 16 Jul 2006, 11:05
Could you please help me with this problem.

For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is

a) between 2 and 10
b) between 10 and 20
c) between 20 and 30
d) between 30 and 40
e) greater than 40

Thanks
_________________

Good is the greatest enemy of great.

Manager
Manager
avatar
Joined: 04 Jul 2006
Posts: 57
Followers: 1

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 16 Jul 2006, 11:18
E.

(1) Note first:Let x, y be two pos. integers then xy+1 is not divisible by x or y.
(2) Therefore H(100)+1 = 2*4*6*....*96*98*100 + 1 cannot be divisible by any odd number k smaller than 50 (because k*2 is a factor of H(100)).
Manager
Manager
avatar
Joined: 12 Jul 2006
Posts: 67
Location: Boston
Followers: 1

Kudos [?]: 3 [0], given: 0

 [#permalink] New post 16 Jul 2006, 11:33
Thanks game over. That is the correct answer. Initially I did not follow your line number 2, but I think I follow now.

Is your reasoning that if K*2 can divide the number n, then it cannot possiblly divide the number n + 1.
_________________

Good is the greatest enemy of great.

Manager
Manager
avatar
Joined: 04 Jul 2006
Posts: 57
Followers: 1

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 16 Jul 2006, 11:48
Quote:
Is your reasoning that if K*2 can divide the number n, then it cannot possiblly divide the number n + 1


[If your statement is correct, then 30 cannot be divisible by 6, because it is divisible by 5]

Example for (1)

Since 30 = 5*6 is divisible by 5 and 6, 30+1= 31 cannot be divisible by 5 and 6.

Example for (2):

Is H(100)+1 divisible by 37?

We know that H(100) = 2*4*6* .... * 74 * ... * 92*96*98*100.
Hence H(100) is divisible by 74 and therefore divisible by 37.

Using (1), we know that H(100)+1 cannot be divisible by 37.
Intern
Intern
avatar
Joined: 17 Jul 2006
Posts: 26
Followers: 0

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 17 Jul 2006, 12:40
H(100) + 1 = 2 * 4 * 6 * 8 * 10 * 12 ..* 100 + 1

Note that n is not the number of terms, the function is defined as the product of all even integer up to n.

Therefore, h(100) + 1 = (taking 2 as the common factor) 2^50 * ( 1 * 2 * 3 * 4 * …* 50) + 1

Note also that the problem is not asking for a value of P, it is only asking you what might be P.

Note that a number divisible by 2, can be written as 2k where k is an integer, similarly, a number divisible by 3 can be written as 3i, where i is an integer.

Note also that h(100) is divisible by all the numbers 2,3,4,5,6,7,...50.

Hence, when h(100) + 1 is divided by the numbers 2,3,4,5,6,7,..50, the remainder is 1.

Hence, Note that h(100) cannot be divisible by any number that is less than or equal to 50. Hence, the smallest number that is a factor of h(100) is 51. Answer E.

-mathguru
http://www.askmathguru.com
_________________

http://www.askmathguru.com

  [#permalink] 17 Jul 2006, 12:40
    Similar topics Author Replies Last post
Similar
Topics:
7 1) For every positive even integer n, function h(n) is g1m2a3t406 6 24 Nov 2006, 13:25
For every positive even integer, n, the function h(n) is ffgmat 1 22 May 2006, 03:56
For every positive even integer n, the function hn) is john2005 5 07 May 2006, 13:17
6 For every positive even integer n, the function h(n) is jlui4477 7 17 Apr 2006, 00:48
For every positive even integer n, the function h(n) is jodeci 1 01 Apr 2006, 21:31
Display posts from previous: Sort by

For every positive even integer n, the function h(n) is

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2   3   4   5   6   7   8   9   10   11  ...  14    Next  [ 273 posts ] 



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®.