Apr 20 07:00 AM PDT  09:00 AM PDT Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score. Apr 20 10:00 PM PDT  11:00 PM PDT The Easter Bunny brings … the first day of school?? Yes! Now is the time to start studying for the GMAT if you’re planning to apply to Round 1 of fall MBA programs. Get a special discount with the Easter sale! Apr 21 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Apr 21 10:00 PM PDT  11:00 PM PDT $84 + an extra $10 off for the first month of EMPOWERgmat access. Train to be ready for Round 3 Deadlines with EMPOWERgmat's Score Booster. Ends April 21st Code: GCENHANCED Apr 22 08:00 AM PDT  09:00 AM PDT What people who reach the high 700's do differently? We're going to share insights, tips, and strategies from data we collected on over 50,000 students who used examPAL. Save your spot today! Apr 23 08:00 PM EDT  09:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, April 23rd at 8 pm ET Apr 24 08:00 PM EDT  09:00 PM EDT Maximize Your Potential: 5 Steps to Getting Your Dream MBA Part 3 of 5: Key TestTaking Strategies for GMAT. Wednesday, April 24th at 8 pm ET
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 18 Jan 2012
Posts: 21

Is the integer x divisible by 24?
[#permalink]
Show Tags
Updated on: 17 Oct 2012, 03:44
Question Stats:
86% (00:46) correct 14% (00:44) wrong based on 184 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.
Originally posted by nimc2012 on 07 Feb 2012, 20:38.
Last edited by Bunuel on 17 Oct 2012, 03:44, edited 2 times in total.
Edited the question



Manager
Joined: 31 Jan 2012
Posts: 70

Re: Number Properties  Question
[#permalink]
Show Tags
07 Feb 2012, 22:20
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: 54369

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.
_________________



Manager
Joined: 11 Aug 2012
Posts: 114

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: 9119
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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13950
Location: United States (CA)

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*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/



Retired Moderator
Joined: 19 Mar 2014
Posts: 931
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5

Re: Is the integer x divisible by 24?
[#permalink]
Show Tags
18 Aug 2017, 14:39
Is the integer x divisible by 24 ?(1) x is divisible by 8x is divisible by 8 ==> Possible numbers: 0, 8, 16, 24, 32, 40 As the answer can be either "YES" or "NO", this information is not sufficient. Hence, (1) ===== is NOT SUFFICIENT(2) x is divisible 6x is divisible by 6 ==> Possible numbers: 0, 6, 12, 18, 24, 30 As the answer can be either "YES" or "NO", this information is not sufficient. Hence, (2) ===== is NOT SUFFICIENTCombining (1) & (2) x is divisible by 8 and 6 ==? Possible numbers: 0, 24, 48 All the above numbers are divisible by 24 and hence this information is sufficient. Hence, (1) & (2) ===== is SUFFICIENTHence, Answer is C
_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."
Best AWA Template: https://gmatclub.com/forum/howtoget60awamyguide64327.html#p470475




Re: Is the integer x divisible by 24?
[#permalink]
18 Aug 2017, 14:39






