Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 40403

Is the integer x divisible by 36 ? [#permalink]
Show Tags
14 Feb 2014, 01:58
Question Stats:
83% (01:39) correct
17% (00:39) wrong based on 431 sessions
HideShow timer Statistics
The Official Guide For GMAT® Quantitative Review, 2ND EditionIs the integer x divisible by 36 ? (1) x is divisible by 12. (2) x is divisible by 9. Data Sufficiency Question: 92 Category: Arithmetic Properties of numbers Page: 159 Difficulty: 650 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
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



Math Expert
Joined: 02 Sep 2009
Posts: 40403

Re: Is the integer x divisible by 36 ? [#permalink]
Show Tags
14 Feb 2014, 01:58



Manager
Joined: 04 Jan 2014
Posts: 121
GMAT 1: 660 Q48 V32 GMAT 2: 630 Q48 V28 GMAT 3: 680 Q48 V35

Re: Is the integer x divisible by 36 ? [#permalink]
Show Tags
14 Feb 2014, 03:17
1
This post received KUDOS
St1: x is divisible by 12.
If x = 12, x is not divisible by 36. If x = 36, x is divisible by 36.
Not sufficient.
St1: x is divisible by 9.
If x = 9, x is not divisible by 36. If x = 36, x is divisible by 36.
Not sufficient.
St1 + St2: LCM of 12 and 9 is 36. So, x is any multiple of 36 and hence divisible by 36. Sufficient.
Answer (C).



Director
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: Is the integer x divisible by 36 ? [#permalink]
Show Tags
14 Feb 2014, 09:59
1
This post received KUDOS
Is the integer x divisible by 36 ? (1) x is divisible by 12. (2) x is divisible by 9. Sol: 36= 2^2*3^2 So for any number to be divisible by 36, it should be divisible by 2 at least 2 times and by 3 at least 2 times. S1: x is divisible by 12 so x is divisible by 2 atleast 2 times why (12=2^2*3) So if x=36 then X is divisible by 36 but if x=24 then NO So A and D ruled out St2: X is divisible by 9 so x is divisible by 3 at least 2 times but we don't know if its divisble by 2 atleast 2 times Combining both statements we see that it is divisible by 36. Ans yes so option C
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Manager
Joined: 24 Apr 2013
Posts: 147
Location: India
Concentration: Operations, Other
GRE 1: 1330 Q530 V800
GPA: 3.9
WE: Engineering (Telecommunications)

Re: Is the integer x divisible by 36 ? [#permalink]
Show Tags
14 Feb 2014, 10:37
1
This post received KUDOS
Clearly, 1 and 2 are not sufficient by themselves! We need both 1 and 2 to be true to be definitive! It has to be C!



Senior Manager
Joined: 13 Jun 2013
Posts: 279

Re: Is the integer x divisible by 36 ? [#permalink]
Show Tags
14 Feb 2014, 14:20
1
This post received KUDOS
Statement 1: x is divisible by 12. therefore x can be written as x=12k (where k is an integer 1,2,3,4...) if k=1 x=12, which is not divisible by 36 if k=3, x=136 which is divisible by 36 hence 1 alone is not sufficient
Statement 2: x is divisible by 9 therefore x can be written as x=9k (where k is an integer 1,2,3,4...) if k=1 , x=9 which is not divisible by 36 if k=4, x=36 which is divisible by 36 hence 2 alone is not sufficient
combining 1 and 2 we have, x is something which is divisible by both 12 and 9. i.e. x must be divisible by the lcm of 12 and 9. hence x will be of the form x=36k ( where k is an integer 1,2,3,4..) which is divisible by 36.
hence C is the correct answer.



Senior Manager
Joined: 20 Dec 2013
Posts: 267
Location: India

Re: Is the integer x divisible by 36 ? [#permalink]
Show Tags
16 Feb 2014, 03:24
1
This post received KUDOS
Ans C
From S1:x could be 12=div by 12 but not by 36 or x=36 div by 12 & 36.Not sufficient
From S2:x=9 div by 9 not by 36 x=36 div by 9 & 36. Not sufficient
Combining the 2 statements we get x=div by 12 and 9 x= LCM of 12,9 or greater x=36 or multiples thereof Definitely div by 36 Sufficient



Math Expert
Joined: 02 Sep 2009
Posts: 40403

Re: Is the integer x divisible by 36 ? [#permalink]
Show Tags
17 Feb 2014, 03:22



Intern
Joined: 25 Sep 2014
Posts: 7

Is the integer x divisible by 36 ? [#permalink]
Show Tags
23 Nov 2014, 08:22
Is the integer x divisible by 36?
(1) x is divisible by 12. (2) x is divisible by 9.
I started approaching such questions is a very systematic way. Although most of the questions of this type are not very difficult to proof wrong or right by plugging in a few numbers (works for many DS questions), it is easy to miss something or to lose too much time testing cases. Instead, translate every number there is into its prime factors.
Is x divisible by 36? Is the same as asking is x divisible by 6^2, or is X/(3x2)^2 an integer?
Q:is X divisible by (3^2)x(2^2)
Statement 1: x is divisible by 12> X/(2^2x3) is an integer > INSUFFICIENT, there is 2 to the power of two, but we are missing a 3 to proof that X is divisible by 36.
Statement 2: x is divisible by 9 > X/(3^2) is an integer > INSUFFICIENT, there is 3 to the power of two, but we are missing 2^2 to proof that X is divisible by 36.
1)+2): If a number is divisible by number A and by number B, it must at least be divisible by the LCM (Lowest Common Multiple) of A and B. For instance, if you know that a number is divisible by 3 and by 4, that number is 12 or a multiple of 12. For easy numbers, you basically know the LCM anyway. As in the case of 3 and 4. In case you do not know that the LCM of 9 and 12 is 36, or for more complex numbers, simply multiply the prime factors but chose the highest power of any factor.
So LCM of 9 and 12: 3^2 (from 9) x 2^2 (from 12), which is the same as (3^2)x(2^2) or 36 > SUFFICIENT



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16573

Re: Is the integer x divisible by 36 ? [#permalink]
Show Tags
14 Sep 2016, 06:59
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



Senior Manager
Joined: 12 Nov 2016
Posts: 426

Re: Is the integer x divisible by 36 ? [#permalink]
Show Tags
17 Jul 2017, 17:21
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIs the integer x divisible by 36 ? (1) x is divisible by 12. (2) x is divisible by 9. Data Sufficiency Question: 92 Category: Arithmetic Properties of numbers Page: 159 Difficulty: 650 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you! Statement 1 This basically means X is a multiple of 12 (2 x 2 x 3)  24 , 36 , etc Insuff Statement 2 This basically means X is a multiple of 9 (3 x 3) 3 x 3 x 2 x 2 =LCM 36=LCM C




Re: Is the integer x divisible by 36 ?
[#permalink]
17 Jul 2017, 17:21







