Author
Message
TAGS:
Manager

Joined: 13 Jul 2010

Posts: 169

Followers: 1

Kudos [? ]:
15
[1 ] , given: 7

X, Y, and Z are three different Prime numbers, the product [#permalink ]
09 Dec 2010, 21:03
1

This post received KUDOS

1

This post was BOOKMARKED

Question Stats:

62% (01:47) correct

38% (00:32) wrong

based on 107 sessions
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.

Manager

Joined: 30 Aug 2010

Posts: 93

Location: Bangalore, India

Followers: 3

Kudos [? ]:
94
[0 ] , given: 27

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: 18737

Followers: 3243

Kudos [? ]:
22384
[3 ] , given: 2616

3

This post received KUDOS

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 MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!! PLEASE READ AND FOLLOW: 11 Rules for Posting!!! RESOURCES: [GMAT MATH BOOK ]; 1. Triangles ; 2. Polygons ; 3. Coordinate Geometry ; 4. Factorials ; 5. Circles ; 6. Number Theory ; 7. Remainders ; 8. Overlapping Sets ; 9. PDF of Math Book ; 10. Remainders ; 11. GMAT Prep Software Analysis NEW!!! ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!! ; 12. Tricky questions from previous years. NEW!!! ;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 ? 25 extra-hard Quant Tests Get the best GMAT Prep Resources with GMAT Club Premium Membership

Current Student

Status: Bring the Rain

Joined: 17 Aug 2010

Posts: 408

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)

Followers: 7

Kudos [? ]:
43
[0 ] , given: 46

Manager

Joined: 13 Jul 2010

Posts: 169

Followers: 1

Kudos [? ]:
15
[0 ] , given: 7

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: 93

Location: Bangalore, India

Followers: 3

Kudos [? ]:
94
[0 ] , given: 27

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: 164

Followers: 2

Kudos [? ]:
34
[1 ] , given: 71

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 : 01-06-2012

GPA: 2.6

WE: Business Development (Consulting)

Followers: 0

Kudos [? ]:
6
[1 ] , given: 8

1

This post received KUDOS

Ans 8 1 x y z xy yz zx xyz

SVP

Joined: 09 Sep 2013

Posts: 1731

Followers: 165

Kudos [? ]:
33
[0 ] , given: 0

Re: X, Y, and Z are three different Prime numbers, the product [#permalink ]
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

Manager

Affiliations: CrackVerbal

Joined: 03 Oct 2013

Posts: 150

Location: India

GMAT 1 : 780 Q51 V46

Followers: 15

Kudos [? ]:
69
[0 ] , given: 2

Re: X, Y, and Z are three different Prime numbers, the product [#permalink ]
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

_________________

If you find our response valuable, please encourage us with Kudos! Aiming for 40+ in Verbal? Attend our 2-Day Verbal Score Booster Workshop! http://gmat.crackverbal.com/advanced-verbal-workshop-bangalore Get a FREE profile evaluation from CrackVerbal experts! http://applications.crackverbal.com/free-resources/profile-evaluation/

Re: X, Y, and Z are three different Prime numbers, the product
[#permalink ]
21 Jan 2014, 22:33

Similar topics
Author
Replies
Last post
Similar Topics:

6
If x, y, and z are 3 different prime numbers, which of the
karishmatandon
16
25 May 2013, 02:45

Is a product of three integers XYZ a prime? (1) X=-Y (2) Z=1
yezz
2
10 Aug 2009, 09:59

Is a product of three integers XYZ a prime? (1) X= Y (2) Z=1
yezz
9
05 Sep 2006, 08:33

K=(X^3)(Y^2)(Z), X, Y and Z represent three different prime
getzgetzu
5
06 May 2006, 04:30

If x, y, and z are different prime numbers, and A=x*y*z, how
getzgetzu
2
23 Nov 2005, 22:21