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 [#permalink]

Show Tags

27 Aug 2005, 04:55

6

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

62% (02:05) correct
38% (01:52) wrong based on 162 sessions

HideShow timer Statistics

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 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...

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 _________________

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.

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

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.

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

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

(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)).

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 * â€¦* 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.

Part 2 of the GMAT: How I tackled the GMAT and improved a disappointing score Apologies for the month gap. I went on vacation and had to finish up a...

Cal Newport is a computer science professor at GeorgeTown University, author, blogger and is obsessed with productivity. He writes on this topic in his popular Study Hacks blog. I was...

So the last couple of weeks have seen a flurry of discussion in our MBA class Whatsapp group around Brexit, the referendum and currency exchange. Most of us believed...