For every even positive integer m, f(m) represents the

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

For every even positive integer m, f(m) represents the

by AAPL » Wed Mar 06, 2019 6:31 am

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For every even positive integer \(m\), \(f(m)\) represents the product of all even integers from 2 to m, inclusive. For example, \(f(12)=2*4*6*8*10*12\). What is the greatest prime factor of \(f(24)\)?

A. 23
B. 19
C. 17
D. 13
E. 11

OA E

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Source: Beat The GMAT — Problem Solving | Wed Mar 06, 2019 6:31 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Wed Mar 06, 2019 8:23 am

AAPL wrote:Official Guide

For every even positive integer \(m\), \(f(m)\) represents the product of all even integers from 2 to m, inclusive. For example, \(f(12)=2*4*6*8*10*12\). What is the greatest prime factor of \(f(24)\)?

A. 23
B. 19
C. 17
D. 13
E. 11

OA E

f(24) = 2 x 4 x 6 x 8 x 10 x 12 x 14 x 16 x 18 x 20 x 22 x 24

Rewrite as prime factorization: f(24) = 2 x (2)(2) x (2)(3) x (2)(2)(2) x (2)(5) x (2)(2)(3) x (2)(7) x (2)(2)(2)(2) x (2)(3)(3) x (2)(2)(5) x (2)(11) x (2)(2)(2)(3)

Answer: E

ASIDE: As you can see from the answer choice, I really didn't need to find the prime factorization of EVERY value.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Mar 08, 2019 6:46 am

AAPL wrote:Official Guide

For every even positive integer \(m\), \(f(m)\) represents the product of all even integers from 2 to m, inclusive. For example, \(f(12)=2*4*6*8*10*12\). What is the greatest prime factor of \(f(24)\)?

A. 23
B. 19
C. 17
D. 13
E. 11

OA E

We are given that for every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive.
Thus, f(24) = 2 x 4 x 6 x 8 x 10 x 12 x 14 x 16 x 18 x 20 x 22 x 24.

If we were to break each value into primes, we would see that the greatest prime factor is contained in 22 (which equals 2 x 11).
Thus, the largest prime factor in f(24) is 11.

Answer: E

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