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 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

eg:

5! = 5*4*3*2*1 = 120 largest prime factor is 5

120+1 = 121 the smallest prime factor is 11 bigger than the largest prime of 120

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

between 2 and 10
between 10 and 20
between 20 and 30
between 30 and 40
greater than 40 _________________

If an integer > 1 divides x then it doesn't divide x + 1.

Any prime factor p less than 50 divides h(100) because 2*p is in the product h(100). Thus, the smallest prime factor that divides h(100) + 1 must be greater than 50.

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

I believe this question had been covered recently. If you'd like some explaination on this question, I think doing a search for keywords such as prime would get you the answer.

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

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

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) betwen 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 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

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

question!

h(2) = 2 = (2x1)
h(4) = 2 x 4 = (2x1) x (2x2) = (2^2) * 2!
h(6) = 2 x 4 x 6 = (2x1) x (2x2) x (2x3) = (2^3) * 3!
Therefore,
h(n) = (2^(n/2) * (n/2)!
h(100) = (2^50) * 50!

If p is the smallest prime factor of h(100) + 1, then p is?
Keep dividing the term above with each prime number. 2, 3, 5, 7, 11, 13, 17, 19, 23, ... and see what number can divide it evenly.

Assuming p = 2; (h(100) + 1)/2 = (2^50) * (3x4x5...x50) + 1/2
This means that by using 2, the remainder = 1/2

Assuming p = 3; (h(100) + 1)/3 = (2^50) * (2 x 4 x 5 x 6... x50) + 1/3
This means that by using 3, the remainder = 1/3

We can conclude that All prime number from 2 to 47 will give the remainder of 1/2, 1/3, 1/5, 1/11, ..., 1/47

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.

between 2 and 10
between 10 and 20
between 20 and 30
between 30 and 40
above 40

The answer is above 40, but why? From the problem I figure that
h(100)+1 is a really large odd number, but where do you go from there?

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.

between 2 and 10 between 10 and 20 between 20 and 30 between 30 and 40 above 40

The answer is above 40, but why? From the problem I figure that h(100)+1 is a really large odd number, but where do you go from there?

Thanks

I have answered this question before .

Here is the solution.

h(2) = 2 = (2x1) = (2^1)*(1!)
h(4) = 2 x 4 = (2x1) x (2x2) = (2^2) * (2!)
h(6) = 2 x 4 x 6 = (2x1) x (2x2) x (2x3) = (2^3) * (3!)

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

gmatclubot

gmat prep question
[#permalink]
02 Mar 2007, 10:31

Final decisions are in: Berkeley: Denied with interview Tepper: Waitlisted with interview Rotman: Admitted with scholarship (withdrawn) Random French School: Admitted to MSc in Management with scholarship (...

Last year when I attended a session of Chicago’s Booth Live , I felt pretty out of place. I was surrounded by professionals from all over the world from major...

The London Business School Admits Weekend officially kicked off on Saturday morning with registrations and breakfast. We received a carry bag, name tags, schedules and an MBA2018 tee at...

I may have spoken to over 50+ Said applicants over the course of my year, through various channels. I’ve been assigned as mentor to two incoming students. A...