Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 18 Jan 2012
Posts: 22

Is the integer x divisible by 24? [#permalink]
Show Tags
07 Feb 2012, 20:38
1
This post received KUDOS
1
This post was BOOKMARKED
Question Stats:
80% (01:27) correct
20% (00:24) wrong based on 125 sessions
HideShow timer Statistics
Is the integer x divisible by 24 ? (1) x is divisible by 8 (2) x is divisible 6
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 17 Oct 2012, 03:44, edited 2 times in total.
Edited the question



Manager
Joined: 31 Jan 2012
Posts: 74

Re: Number Properties  Question [#permalink]
Show Tags
07 Feb 2012, 22:20
1
This post was BOOKMARKED
Is X divisible by 24? Question can become does x have prime factors of 2*2*2*3 (prime factors of 24) 1. x is divisible by 8 = 2*2*2 (The number of prime factors in 8) Not enough info 2. x is divisible by 6 = 2*3 (The number of prime factors in 6) Not enough info
1+2) = First set (2*2*2) second set (2*3). There is a repeat of common factor of 2 in the second set, so ignore 2. First set + second set = (2*2*2*3) = Prime factors of 24.
Another way you can think about it is just find the LCF of 8 and 6. The answer of 24 is the same.
Logically speaking you need to know if the number is a multiple of 24 (I know sounds redundant). 1. Something that is divisible by 8 CAN be a multiple of 24 (24,48,72) or it CAN'T (8,16,32) 2. Exact same thing
We need to find a number that can be divided by both 8&6, so naturally we find the LCF, since it is the smallest number that can divide into the both of them and any other number that can by divided by the both of them are multiples of the LCF. So if LCF = 24 we know that regardless of what X is it is a multiple of 24.



Math Expert
Joined: 02 Sep 2009
Posts: 39725

Is the integer x divisible by 24? [#permalink]
Show Tags
08 Feb 2012, 02:06
nimc2012 wrote: Please explain clearly.
a few questions form number properties that are bothering me alot
1) Is the integer x divisible by 24 ? a) x is divisible by 8 b) x is divisible 6 Is the integer x divisible by 24 ?(1) x is divisible by 8 > x can be: ..., 0, 8, 16, 24, 32, ... So it may or may not be divisible by 24. Not sufficient. (2) x is divisible 6 > x can be: ..., 6, 12, 16, 24, 30, ... So it may or may not be divisible by 24. Not sufficient. (1)+(2) x is a divisible by both 8 and 6 which means that it's divisible by the least common multiple of 8 and 6, which is 24. Sufficient. Answer: C. Generally, if a positive integer n is a multiple of positive integer a and positive integer b, then n is a multiple of LCM(a,b).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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 11 Aug 2012
Posts: 127

Is the integer x divisible by 24? [#permalink]
Show Tags
16 Oct 2012, 21:42
Is the integer x divisible by 24? (1) x is divisible by 8. (2) x is divisible by 6.
The solution is easy. However, I have some conceptual doubts related to this problem. To solve the problem we have to find the LCM, which is 24 in this question. Therefore, x is divisible by 24.
But what about the number 0. According to the MGMAT guide, 0 is a multiple of every integer. Let's see: "any integer * 0 = 0 " In this sense, and based on that definition, the LCM wouldn't be 24 but it would be 0. Because 0 is a multiple of 8 and 6 and also is less than 24. Why is 0 not considered the LCM of any set of integers?, Should we calculate the LCM or only analyze whether 0 is divisible by 24?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7447
Location: Pune, India

Re: Is the integer x divisible by 24? [#permalink]
Show Tags
16 Oct 2012, 22:07
danzig wrote: Is the integer x divisible by 24? (1) x is divisible by 8. (2) x is divisible by 6.
The solution is easy. However, I have some conceptual doubts related to this problem. To solve the problem we have to find the LCM, which is 24 in this question. Therefore, x is divisible by 24.
But what about the number 0. According to the MGMAT guide, 0 is a multiple of every integer. Let's see: "any integer * 0 = 0 " In this sense, and based on that definition, the LCM wouldn't be 24 but it would be 0. Because 0 is a multiple of 8 and 6 and also is less than 24. Why is 0 not considered the LCM of any set of integers?, Should we calculate the LCM or only analyze whether 0 is divisible by 24? When you say LCM is Lowest Common Multiple, you are including only positive multiples. LCM is at least as great as the greater of the numbers. Also, 0 is divisible by every number.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16014

Re: Is the integer x divisible by 24? [#permalink]
Show Tags
08 Jun 2015, 07:01
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



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 9284
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: Is the integer x divisible by 24? [#permalink]
Show Tags
09 Jun 2015, 18:49
Hi All, Variations of this DS question have been appearing on the GMAT for years. It's a great test of your 'thoroughness' and it often catches Test Takers who are moving too quickly and not thinking about all of the possible values of X.... We're told that X is an INTEGER. We're asked if X is divisible by 24. This is a YES/NO question. Fact 1: X is divisible by 8 X COULD be 0, 8, 16, 24, 32, 40, 48, etc. IF...X = 8, then the answer to the question is NO. IF...X = 24, then the answer to the question is YES. Fact 1 is INSUFFICIENT Fact 2: X is divisible 6 X COULD be 0, 6, 12, 18, 24, 30, 36, 42, 48, etc. IF...X = 6, then the answer to the question is NO. IF...X = 24, then the answer to the question is YES. Fact 2 is INSUFFICIENT Combined, we know... X is a multiple of 8 X is a multiple of 6 X COULD be 0, 24, 48, 72, etc. In ALL cases, X is divisible by 24, so the answer to the question is ALWAYS YES. Combined, SUFFICIENT. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************




Re: Is the integer x divisible by 24?
[#permalink]
09 Jun 2015, 18:49







