Find all School-related info fast with the new School-Specific MBA Forum

It is currently 25 Oct 2014, 14:29

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the positive integer x is a multiple of 4?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 13 Dec 2005
Posts: 64
Followers: 1

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

If the positive integer x is a multiple of 4? [#permalink] New post 02 Dec 2006, 06:01
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

66% (01:41) correct 34% (00:34) wrong based on 124 sessions
If the positive integer x is a multiple of 4 and the positive integer y is a multiple of 6, then xy must be a multiple of which of the following?

I. 8
II. 12
III 18

A) II only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III

Official Guide 12 Question

GMAT Official Guide 12

Question: 23
Page: 23
Difficulty: 600

Find All Official Guide Questions

Video Explanations:
[Reveal] Spoiler: OA
Kaplan Promo CodeKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
Director
Director
avatar
Joined: 28 Dec 2005
Posts: 922
Followers: 2

Kudos [?]: 37 [0], given: 0

 [#permalink] New post 02 Dec 2006, 06:06
nah, not necessarily:


Ans B.

From question x/4 is an integer.

x/4 = 2*2*q/4 ---> where q is the integer


Also y/6 = p => y/6 = 2*3*p/6

So, xy = 2*2*2*3 *pq

Thus 2*2*2 = 8 and 2*3*2 = 12 satisfy
Senior Manager
Senior Manager
avatar
Joined: 20 Feb 2006
Posts: 375
Followers: 1

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 02 Dec 2006, 06:38
B for me

x/4 = integer or 4p/4 = integer and y/6 = integer or yq/6 = integer

x and y are positive integers so limiting factor is when x and y are at theier minumum. Min values of x and y are when p=q=1
4*1 = 4 6*1 = 6
4*6 = 24

Hence multipe of 8 and 12
Director
Director
User avatar
Status:
Joined: 24 Jul 2011
Posts: 557
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 64

Kudos [?]: 288 [0], given: 11

Re: xy multiple. [#permalink] New post 11 Sep 2011, 10:24
xy = 4 * 6 = 2 * 2 * 2 * 3 = 8 * 3 = 2 * 12

We can see that xy is a multiple of both 8 and 12, but not 18.

Option (B)
_________________

GyanOne | http://www.GyanOne.com | +91 9899831738

Get a free detailed MBA profile evaluation

Top MBA Rankings and MBA Admissions blog


Image

Senior Manager
Senior Manager
User avatar
Joined: 11 May 2011
Posts: 375
Location: US
Followers: 2

Kudos [?]: 61 [0], given: 46

Re: xy multiple. [#permalink] New post 11 Sep 2011, 10:52
GyanOne wrote:
xy = 4 * 6 = 2 * 2 * 2 * 3 = 8 * 3 = 2 * 12

We can see that xy is a multiple of both 8 and 12, but not 18.

Option (B)


@GyanOne - LCM of 4 and 6 = 12 or if I compare as mentioned in the below series... I can see only multiple of 12.
Multiple of 4 - 4, 8, [highlight]12[/highlight], 16, 20, [highlight]24[/highlight]...
Multiple of 6 - 6, [highlight]12[/highlight], 18, [highlight]24[/highlight]...

Can you pls elaborate more?
_________________

-----------------------------------------------------------------------------------------
What you do TODAY is important because you're exchanging a day of your life for it!
-----------------------------------------------------------------------------------------

Director
Director
avatar
Joined: 01 Feb 2011
Posts: 768
Followers: 14

Kudos [?]: 58 [0], given: 42

CAT Tests
Re: xy multiple. [#permalink] New post 11 Sep 2011, 14:08
x is a multiple of 4 = 4p

y is a multiple of 6 = 6q

=> xy = 24pq

by quick observation we can see 8 and 12 are factors of 24. so i and iii must be true.

also 24 = 2*2*2*3

so xy may or may not have 18 as a factor depending on the values of p and q.

if p or q = 3 , then 18 is also a factor xy.
if p and q do not have 3, then 18 is not a factor or xy.


Answer is B.
Manager
Manager
avatar
Status: Prepping for the last time....
Joined: 28 May 2010
Posts: 200
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 630 Q47 V29
GPA: 3.2
Followers: 0

Kudos [?]: 16 [0], given: 21

Re: xy multiple. [#permalink] New post 12 Sep 2011, 01:36
simple way to answer these questions is to pick multiples of 4 and 6 and compare with answers.
_________________

Two great challenges: 1. Guts to Fail and 2. Fear to Succeed

Manager
Manager
avatar
Joined: 08 Sep 2011
Posts: 77
Concentration: Finance, Strategy
Followers: 3

Kudos [?]: 1 [0], given: 5

Re: xy multiple. [#permalink] New post 15 Sep 2011, 12:49
I did the prime factor box method:

4= 2*2
6= 2*3

so all factors of x has to have 2*2 in it and y has to have 2*3 in it.

lets look at our options

i) 8= 2*2*2. If we look at our prime factor boxes above we see that we have to have at least three 2's. (two in 4 and one in 6) so yes 8 is a multiple.

ii) 12= 2*2*3. Again if we look at our prime factor boxes above we see that it contains 2*2*3.

iii) 18= 2*3*3. For 18 we need two 3's and if you look at your prime factor boxes you see that we only have one 3, therefore 18 is not an option.

B both i and ii
Intern
Intern
avatar
Joined: 14 Feb 2012
Posts: 40
Location: Germany
Concentration: Technology, Strategy
GMAT Date: 06-13-2012
Followers: 0

Kudos [?]: 17 [0], given: 13

Re: If the positive integer x is a multiple of 4? [#permalink] New post 05 May 2012, 01:11
Hello,

quick question, I got the answer right, though I am having some problems with the "plug in numbers" approach here. Can anybody help real quick with an example?

Thanks in advance!
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23422
Followers: 3617

Kudos [?]: 28972 [0], given: 2874

Re: If the positive integer x is a multiple of 4? [#permalink] New post 05 May 2012, 02:40
Expert's post
andih wrote:
Hello,

quick question, I got the answer right, though I am having some problems with the "plug in numbers" approach here. Can anybody help real quick with an example?

Thanks in advance!


If the positive integer x is a multiple of 4 and the positive integer y is a multiple of 6, then xy must be a multiple of which of the following?
I. 8
II. 12
III 18

A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III

First of all notice that we are asked xy MUST be a multiple of which of the following, not COULD be a multiple.

x is a multiple of 4 --> x=4m, for some positive multiple m, so x can be: 4, 8, 12, ...
y is a multiple of 6 --> y=6n, for some positive multiple n, so y can be: 6, 12, 18, ...

So, xy=(4m)*(6n)=24mn, so xy is in any case a multiple of 24, which means it must be a multiple of 8 and 12, but not necessarily of 18. For example the least value of x is 4 and the least value of y is 6, so the least value of xy is 24, which is a multiple of both 8 and 12, but not 18.

Answer: B.

Hope it's clear.
_________________

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

Intern
Intern
avatar
Joined: 05 Apr 2012
Posts: 42
Followers: 0

Kudos [?]: 8 [0], given: 12

Re: If the positive integer x is a multiple of 4? [#permalink] New post 07 May 2012, 15:52
ellisje22 wrote:
If the positive integer x is a multiple of 4 and the positive integer y is a multiple of 6, then xy must be a multiple of which of the following?

I. 8
II. 12
III 18

A) II only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III

Official Guide 12 Question

GMAT Official Guide 12

Question: 23
Page: 23
Difficulty: 600

Find All Official Guide Questions

Video Explanations:

Hello
I try !
X can be written as X=2x2K where K is a whole number which belongs to R
Y can be written as Y= 3X2 L where L is a whole number which belongs to R
HENCE XY can BE WRITTEN as 2x2x3x2xKxL

Hence XY must be a multiple of 8 and 12
For 18 we misse a 3

Hope I am right

best regards
CEO
CEO
User avatar
Joined: 09 Sep 2013
Posts: 2870
Followers: 208

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

Premium Member
Re: If the positive integer x is a multiple of 4? [#permalink] New post 05 Aug 2014, 22:50
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

Re: If the positive integer x is a multiple of 4?   [#permalink] 05 Aug 2014, 22:50
    Similar topics Author Replies Last post
Similar
Topics:
5 Experts publish their posts in the topic If the positive integer x is a multiple of 4 and the Bunuel 5 16 Jul 2012, 03:42
1 Experts publish their posts in the topic If positive integer x is a multiple of 6 and positive rahulraao 23 09 Oct 2005, 00:53
If X is a positive integer and (405)^4 is a multiple of 3^X, HIMALAYA 2 14 Aug 2005, 19:44
If positive integer x is a multiple of 6 and positive perezhan 1 16 Mar 2005, 18:23
If positive integer x is a multiple of 6 and positive pb_india 4 23 Jan 2005, 20:40
Display posts from previous: Sort by

If the positive integer x is a multiple of 4?

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| 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®.