Is the integer x divisible by 36 ?

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

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!

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.

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

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

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

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.