It is currently 24 Jun 2017, 17:31

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

X, Y, and Z are three different Prime numbers, the product

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

2 KUDOS received
Manager
Manager
User avatar
Joined: 13 Jul 2010
Posts: 167
X, Y, and Z are three different Prime numbers, the product [#permalink]

Show Tags

New post 09 Dec 2010, 22:03
2
This post received
KUDOS
9
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

67% (01:44) correct 33% (00:37) wrong based on 325 sessions

HideShow timer Statistics

X, Y, and Z are three different Prime numbers, the product XYZ is divisible by how many different positive numbers?

A. 4
B. 6
C. 8
D. 9
E. 12

Please describe method.
[Reveal] Spoiler: OA
2 KUDOS received
Manager
Manager
avatar
Joined: 30 Aug 2010
Posts: 91
Location: Bangalore, India
Re: xyz prime [#permalink]

Show Tags

New post 09 Dec 2010, 23:08
2
This post received
KUDOS
3
This post was
BOOKMARKED
gettinit wrote:
X, Y, and Z are three different Prime numbers, the product XYZ is divisible by how many different positive numbers?

4
6
8
9
12

Please describe method.


PRIME # is the # that has only 2 factors: One is 1 and another is the # itself.

infer that

FOR any given # 1 and the # iteself are the definite factors.

Knowing above conepts:

product of X,Y, and Z = XYZ

divisible by 1, xyz, x, y, z, xy,yz,xz ==> total 8

ANSWER "C"

ADDITIONAL INFO.

if question has 5 constants a,b,c,d,e, we do not have to count in the above way

Basically we are selecting, from the product, one constant, set of two constants, set of 3 constants ....and so on set of all the # of constants.

so if 5 varibales are given, total # ways to select is 5C1+5C2+5C3+5C4+5C5 = 5+10+10+5+1 = 31

And answer will be 31+1 =32 (as "1" is a factor for every #)

Regards,
Murali.

Kudos?
Expert Post
3 KUDOS received
Math Expert
User avatar
D
Joined: 02 Sep 2009
Posts: 39662
Re: xyz prime [#permalink]

Show Tags

New post 10 Dec 2010, 00:46
3
This post received
KUDOS
Expert's post
7
This post was
BOOKMARKED
gettinit wrote:
X, Y, and Z are three different Prime numbers, the product XYZ is divisible by how many different positive numbers?

4
6
8
9
12

Please describe method.


MUST KNOW FOR GMAT:

Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.


BACK TO THE ORIGINAL QUESTION:

\(n=xyz\) (n=x^1y^1z^1) where \(x\), \(y\), and \(z\) are different prime factors will have \((1+1)(1+1)(1+1)=8\) different positive factors including 1 and xyz itself.

Answer: C.

For more on number properties check: math-number-theory-88376.html

Hope it helps.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
User avatar
Status: Bring the Rain
Joined: 17 Aug 2010
Posts: 400
Location: United States (MD)
Concentration: Strategy, Marketing
Schools: Michigan (Ross) - Class of 2014
GMAT 1: 730 Q49 V39
GPA: 3.13
WE: Corporate Finance (Aerospace and Defense)
Re: xyz prime [#permalink]

Show Tags

New post 10 Dec 2010, 07:52
Thanks for the equation
_________________

Go Blue!

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
User avatar
Joined: 13 Jul 2010
Posts: 167
Re: xyz prime [#permalink]

Show Tags

New post 10 Dec 2010, 12:55
Thanks Bunuel very helpful, I thought I could do a quick calculation here to find out the number of factors but fell for the trap I guess:

2*3*5=30 so 30 is divisible by 1,30,15,6,5,3,2,10 but in my haste forgot to use 10,and 1 in here. One should just stick to the formula for a sure shot.
Manager
Manager
avatar
Joined: 30 Aug 2010
Posts: 91
Location: Bangalore, India
Re: xyz prime [#permalink]

Show Tags

New post 11 Dec 2010, 00:14
Friends,

The approach specified by Bunuel is an efficient, a quick and a standard one. Use the same. Ignore the one specified by me as it is a bit time consuming when compared to that given by Bunuel.

Regards,
Murali.
1 KUDOS received
Manager
Manager
avatar
Joined: 25 May 2011
Posts: 152
Re: xyz prime [#permalink]

Show Tags

New post 20 Oct 2011, 07:16
1
This post received
KUDOS
made a stupid mistake!

Yes the answer is C

1- x- y- z- xy- xz- yz- xyz
1 KUDOS received
Intern
Intern
avatar
Joined: 19 Oct 2011
Posts: 2
Location: United States
Concentration: Finance, General Management
GMAT Date: 01-06-2012
GPA: 2.6
WE: Business Development (Consulting)
Re: xyz prime [#permalink]

Show Tags

New post 20 Oct 2011, 11:07
1
This post received
KUDOS
Ans 8

1
x
y
z
xy
yz
zx
xyz
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 15956
Premium Member
Re: X, Y, and Z are three different Prime numbers, the product [#permalink]

Show Tags

New post 21 Jan 2014, 23:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Director
Director
User avatar
S
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 509
Location: India
GMAT 1: 780 Q51 V46
Re: X, Y, and Z are three different Prime numbers, the product [#permalink]

Show Tags

New post 21 Jan 2014, 23:33
gettinit wrote:
X, Y, and Z are three different Prime numbers, the product XYZ is divisible by how many different positive numbers?

A. 4
B. 6
C. 8
D. 9
E. 12

Please describe method.


Let us say X = 2, Y = 3 and Z = 5. Then XYZ = 30 - it is divisible by

1, 2, 3, 5, 6, 10, 15, 30 - 8 different numbers
_________________

Enroll for our GMAT Trial Course here -
http://gmatonline.crackverbal.com/

Learn all PS and DS strategies here-
http://gmatonline.crackverbal.com/p/mastering-quant-on-gmat

For more info on GMAT and MBA, follow us on @AskCrackVerbal

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 15956
Premium Member
Re: X, Y, and Z are three different Prime numbers, the product [#permalink]

Show Tags

New post 24 Apr 2015, 04:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 15956
Premium Member
Re: X, Y, and Z are three different Prime numbers, the product [#permalink]

Show Tags

New post 15 May 2016, 09:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

BSchool Forum Moderator
User avatar
P
Joined: 12 Aug 2015
Posts: 2185
GMAT ToolKit User Premium Member CAT Tests
Re: X, Y, and Z are three different Prime numbers, the product [#permalink]

Show Tags

New post 16 Jan 2017, 00:03
Since X,Y,Z are different primes=>
Number of factors of X*Y*Z => 2*2*2=> 8
Hence C.

_________________

Give me a hell yeah ...!!!!!

Intern
Intern
User avatar
Joined: 06 Oct 2016
Posts: 4
Location: Germany
X, Y, and Z are three different Prime numbers, the product [#permalink]

Show Tags

New post 20 Jan 2017, 01:51
X, Y, and Z are three different Prime numbers, the product XYZ is divisible by how many different positive numbers?

A. 4
B. 6
C. 8
D. 9
E. 12


Suppose
X = 2,
Y = 3 and
Z = 5.

Then XYZ = 30 - it is divisible by

1, 2, 3, 5, 6, 10, 15, 30 -
so ther are 8 different numbers

answer :-C
Director
Director
avatar
S
Joined: 02 Sep 2016
Posts: 524
Premium Member CAT Tests
Re: X, Y, and Z are three different Prime numbers, the product [#permalink]

Show Tags

New post 03 Apr 2017, 11:01
Given:x,y,z are prime factors that means they have no factors other than 1 and the no. itself.

Therefore the power of these prime nos. is 1.

The total no. of factors (thus) = 2*2*2=8
_________________

Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it. :)

Expert Post
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1158
Location: United States (CA)
Re: X, Y, and Z are three different Prime numbers, the product [#permalink]

Show Tags

New post 06 Apr 2017, 10:03
gettinit wrote:
X, Y, and Z are three different Prime numbers, the product XYZ is divisible by how many different positive numbers?

A. 4
B. 6
C. 8
D. 9
E. 12


To determine the number of factors of XYZ, or (X^1)(Y^1)(Z^1), we add 1 to each exponent of each unique prime factor and multiply those values together. The result will equal the number of factors of the given number.

Thus, XYZ has (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8 factors.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Director
Director
avatar
S
Joined: 07 Dec 2014
Posts: 710
Re: X, Y, and Z are three different Prime numbers, the product [#permalink]

Show Tags

New post 07 Apr 2017, 13:53
gettinit wrote:
X, Y, and Z are three different Prime numbers, the product XYZ is divisible by how many different positive numbers?

A. 4
B. 6
C. 8
D. 9
E. 12

Please describe method.


let p=number of prime numbers=3
total positive factors=2(p+1)=8
C
Re: X, Y, and Z are three different Prime numbers, the product   [#permalink] 07 Apr 2017, 13:53
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic If the sum of two prime numbers x and y is odd, then the product of x Bunuel 3 21 Jun 2017, 01:12
Experts publish their posts in the topic Three positive numbers x, y, and z have the following relationships y Bunuel 2 21 May 2017, 18:55
8 Experts publish their posts in the topic If three positive real numbers x, y, z satisfy y – x = z – y and x y z excelingmat 6 08 Jan 2016, 09:11
23 Experts publish their posts in the topic If x, y, and z are 3 different prime numbers, which of the karishmatandon 22 15 Jan 2017, 23:27
1 Experts publish their posts in the topic If x and y are two different prime numbers, which of the sarb 8 26 Mar 2017, 00:46
Display posts from previous: Sort by

X, Y, and Z are three different Prime numbers, the product

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.