OG If n is the product

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 394
Joined: Sun Jul 02, 2017 10:59 am
Thanked: 1 times
Followed by:5 members

OG If n is the product

by AbeNeedsAnswers » Tue Jul 25, 2017 8:16 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1 does n have?

A) Four
B) Five
C) Six
D) Seven
E) Eight

A

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Tue Jul 25, 2017 8:52 pm
AbeNeedsAnswers wrote:If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1 does n have?

A) Four
B) Five
C) Six
D) Seven
E) Eight

A
We have n = 1*2*3*4*5*6*7*8 = 8!

Thus, the different prime factors greater than 1 are; 2, 3, 5, and 7: Four

The correct answer: A

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Singapore | Doha | Lausanne | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

GMAT/MBA Expert

User avatar
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 Jul 26, 2017 6:15 am
AbeNeedsAnswers wrote:If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1 does n have?

A) Four
B) Five
C) Six
D) Seven
E) Eight

A
n = (1)(2)(3)(4)(5)(6)(7)(8)
= (1)(2)(3)(2)(2)(5)(2)(3)(7)(2)(2)(2)
The prime factors are 2, 3, 5 and 7

Answer: A
Brent Hanneson - Creator of GMATPrepNow.com
Image

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Wed Jul 26, 2017 6:52 pm
Hi AbeNeedsAnswers,

With these types of Prime Factorization questions, it often helps to 'break down' the math into 'pieces' (since the individual pieces are rarely all that difficult to deal with.

Here, we're asked for the number of different prime factors in the product of 1 to 8, inclusive (essentially 8!). That product would include the following factors:
1
2
3
4 = (2)(2)
5
6 = (2)(3)
7
8 = (2)(2)(2)

Thus, the different primes are: 2, 3, 5 and 7... and there are 4 of them.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7222
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Mon Aug 14, 2017 11:52 am
AbeNeedsAnswers wrote:If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1 does n have?

A) Four
B) Five
C) Six
D) Seven
E) Eight

A
n = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

We can prime factorize and we have:

n = 2^7 x 3^2 x 5^1 x 7^1

Thus, n has 4 different prime factors.

Alternate solution:

In general, the number of distinct prime factors that k! (where k > 1) has is the number of prime numbers less than or equal to k. We have n = 8!, so k = 8; the number of prime numbers less than or equal to 8 is 4, namely, 2, 3, 5, and 7.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Fri Aug 18, 2017 2:15 pm
Count the unique primes in 2 * 3 * 4 * 5 * 6 * 7 * 8