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:

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

h(n) = 2*(n/2)!
h(100) = 2*(50)!

since h(100) is divisible by every number from 1 to 50, h(100) wont be divisible by any those numbers (i think), so E would be the answer.

someone please correct me if i am wrong about the assumption i made here..

1) 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

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

For every positive interger n, the function h(n) is def. 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 bet. 2 and 10
b. bet. 10-20
c. bet. 20-30
d. bet 30-40
e. greater than 40

I'm not quite sure how to approach this question and I'm not sure what they're asking. Any help is appreciated. OA will follow.
TIA

For every positive interger n, the function h(n) is def. 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 bet. 2 and 10 b. bet. 10-20 c. bet. 20-30 d. bet 30-40 e. greater than 40

I'm not quite sure how to approach this question and I'm not sure what they're asking. Any help is appreciated. OA will follow. TIA

I am taking a shot. Others can chime in

H(100) = 2 x 4 x 6 x ... x 100
= 2(1 x 2 x 3 x ... x 50)

so H(100) + 1 = 2(1 x 2 x 3 x ... x 50) + 1

Now any divisor of the above expression must divide both terms. Any prime factor below 50 will always divide the first term completely but it cant divide 1. So I think that required prime factor should be > 50

Can someone help me with this question? I felt a tickle in my brain when I saw this

For every positive even integer n, 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

I know the answer is E, but I haven't a clue as to why or how. HELP!

Can someone help me with this question? I felt a tickle in my brain when I saw this :oops:

For every positive even integer n, 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

I know the answer is E, but I haven't a clue as to why or how. HELP! :cry:

I am using . as multiplication.
h(100) = 2 . 4 . 6 . ... . 98 . 100
or h(100) = 2(1 . 2. 3. 4. ... . 49.50)

Now h(100) + 1 = 2(1 . 2. 3. 4. ... . 49.50) + 1
now every number from 2 t0 50 will divide the first term but not the second term so the divisor has to be > 50
Answer E

I am not sure if this is the most elegant answer but it makes sense to me. Any comments?

Can someone help me with this question? I felt a tickle in my brain when I saw this

For every positive even integer n, 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

I know the answer is E, but I haven't a clue as to why or how. HELP!

I am using . as multiplication. h(100) = 2 . 4 . 6 . ... . 98 . 100 or h(100) = 2(1 . 2. 3. 4. ... . 49.50)

Now h(100) + 1 = 2(1 . 2. 3. 4. ... . 49.50) + 1 now every number from 2 t0 50 will divide the first term but not the second term so the divisor has to be > 50 Answer E

I am not sure if this is the most elegant answer but it makes sense to me. Any comments?

Hey Tech -

Thanks for the explanation ... what puzzles me about this question is the part where it mentions p as being "the smallest prime factor"; intuitively, doesn't that sound like p would be one of the first 10 primes? Maybe my thinking is screwed up, but that's what I initially gravitate towards.

This was the third question of my practice GMAT that I downloaded from the site. It must be pretty easy if you know a certain rule, but I am stumped...

For every positive 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

This was the third question of my practice GMAT that I downloaded from the site. It must be pretty easy if you know a certain rule, but I am stumped...

For every positive 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 Goalsnr. Wilfred's explanation was a little confusing for me, but it got me on the right track and I get it now. I posted the solution in my own words to help out anyone else confused by Wilfred's...

h(100) is a multiple of all even numbers from 2 to 100, so it's also a multiple of all numbers from 1 to 50 (Dividing the even numbers by 2).

h(100) + 1 is a number next to h(100), so it can't have a factor from 2 to 50. So, the smallest prime factor should be greater than 50. Hence the answer is E.

Edit: I seem to have repeated the solution already provided.

GmatPrep 1: Real tough problem [functions] [#permalink]

Show Tags

01 Jun 2007, 07:24

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 100
b. between 10 and 20
c. between 20 and 30
d. between 30 and 40
e. greater than 40

How do you solve this? It's from the gmat prep practice exam.

For every positve 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

gmatclubot

Prime number problem
[#permalink]
05 Jun 2007, 08:01

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...