Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 13 Jul 2010
Posts: 159

X, Y, and Z are three different Prime numbers, the product [#permalink]
Show Tags
09 Dec 2010, 21:03
2
This post received KUDOS
9
This post was BOOKMARKED
Question Stats:
68% (00:43) correct 32% (00:36) wrong based on 339 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.
Official Answer and Stats are available only to registered users. Register/ Login.



Manager
Joined: 30 Aug 2010
Posts: 91
Location: Bangalore, India

Re: xyz prime [#permalink]
Show Tags
09 Dec 2010, 22:08
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?



Math Expert
Joined: 02 Sep 2009
Posts: 43901

Re: xyz prime [#permalink]
Show Tags
09 Dec 2010, 23:46
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 IntegerFirst 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: mathnumbertheory88376.htmlHope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Status: Bring the Rain
Joined: 17 Aug 2010
Posts: 387
Location: United States (MD)
Concentration: Strategy, Marketing
Schools: Michigan (Ross)  Class of 2014
GPA: 3.13
WE: Corporate Finance (Aerospace and Defense)

Re: xyz prime [#permalink]
Show Tags
10 Dec 2010, 06:52



Manager
Joined: 13 Jul 2010
Posts: 159

Re: xyz prime [#permalink]
Show Tags
10 Dec 2010, 11:55
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
Joined: 30 Aug 2010
Posts: 91
Location: Bangalore, India

Re: xyz prime [#permalink]
Show Tags
10 Dec 2010, 23:14
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.



Manager
Joined: 25 May 2011
Posts: 141

Re: xyz prime [#permalink]
Show Tags
20 Oct 2011, 06:16
1
This post received KUDOS
made a stupid mistake!
Yes the answer is C
1 x y z xy xz yz xyz



Intern
Joined: 19 Oct 2011
Posts: 2
Location: United States
Concentration: Finance, General Management
GMAT Date: 01062012
GPA: 2.6
WE: Business Development (Consulting)

Re: xyz prime [#permalink]
Show Tags
20 Oct 2011, 10:07
1
This post received KUDOS
Ans 8
1 x y z xy yz zx xyz



NonHuman User
Joined: 09 Sep 2013
Posts: 13762

Re: X, Y, and Z are three different Prime numbers, the product [#permalink]
Show Tags
21 Jan 2014, 22:03
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
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 518
Location: India

Re: X, Y, and Z are three different Prime numbers, the product [#permalink]
Show Tags
21 Jan 2014, 22:33
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
_________________
Join Free 4 part MBA Through GMAT Video Training Series here  https://gmat.crackverbal.com/mbathroughgmatvideo2018
Enroll for our GMAT Trial Course here  http://gmatonline.crackverbal.com/
For more info on GMAT and MBA, follow us on @AskCrackVerbal



NonHuman User
Joined: 09 Sep 2013
Posts: 13762

Re: X, Y, and Z are three different Prime numbers, the product [#permalink]
Show Tags
24 Apr 2015, 03:50
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



NonHuman User
Joined: 09 Sep 2013
Posts: 13762

Re: X, Y, and Z are three different Prime numbers, the product [#permalink]
Show Tags
15 May 2016, 08:45
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



Retired Moderator
Joined: 12 Aug 2015
Posts: 2430
GRE 1: 323 Q169 V154

Re: X, Y, and Z are three different Prime numbers, the product [#permalink]
Show Tags
15 Jan 2017, 23:03
Since X,Y,Z are different primes=> Number of factors of X*Y*Z => 2*2*2=> 8 Hence C.
_________________
Getting into HOLLYWOOD with an MBA Stone Cold's Mock Tests for GMATQuant(700+)



Intern
Joined: 06 Oct 2016
Posts: 4
Location: Germany

X, Y, and Z are three different Prime numbers, the product [#permalink]
Show Tags
20 Jan 2017, 00:51
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
Joined: 02 Sep 2016
Posts: 786

Re: X, Y, and Z are three different Prime numbers, the product [#permalink]
Show Tags
03 Apr 2017, 10:01
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.



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2192
Location: United States (CA)

Re: X, Y, and Z are three different Prime numbers, the product [#permalink]
Show Tags
06 Apr 2017, 09:03
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 WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Director
Joined: 07 Dec 2014
Posts: 907

Re: X, Y, and Z are three different Prime numbers, the product [#permalink]
Show Tags
07 Apr 2017, 12:53
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, 12:53






