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Math Expert V
Joined: 02 Sep 2009
Posts: 58446
Is the integer x divisible by 36 ?  [#permalink]

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Question Stats: 84% (00:55) correct 16% (00:59) wrong based on 481 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Is 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

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Math Expert V
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Posts: 58446
Re: Is the integer x divisible by 36 ?  [#permalink]

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SOLUTION

Is the integer x divisible by 36 ?

(1) x is divisible by 12. If x=12, then the answer is NO but if x=36, then the answer is YES. Not sufficient.

(2) x is divisible by 9. If x=9, then the answer is NO but if x=36, then the answer is YES. Not sufficient.

(1)+(2) From above it follows that x must be divisible by the least common multiple of 12 and 9, which is 36. Sufficient.

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GMAT 1: 660 Q48 V32 GMAT 2: 630 Q48 V28 GMAT 3: 680 Q48 V35 Re: Is the integer x divisible by 36 ?  [#permalink]

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2
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.

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Re: Is the integer x divisible by 36 ?  [#permalink]

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1
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
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Re: Is the integer x divisible by 36 ?  [#permalink]

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1
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!
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Re: Is the integer x divisible by 36 ?  [#permalink]

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1
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.
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Re: Is the integer x divisible by 36 ?  [#permalink]

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1
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 V
Joined: 02 Sep 2009
Posts: 58446
Re: Is the integer x divisible by 36 ?  [#permalink]

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SOLUTION

Is the integer x divisible by 36 ?

(1) x is divisible by 12. If x=12, then the answer is NO but if x=36, then the answer is YES. Not sufficient.

(2) x is divisible by 9. If x=9, then the answer is NO but if x=36, then the answer is YES. Not sufficient.

(1)+(2) From above it follows that x must be divisible by the least common multiple of 12 and 9, which is 36. Sufficient.

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Is the integer x divisible by 36 ?  [#permalink]

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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
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Re: Is the integer x divisible by 36 ?  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Is 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 Project

Each 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
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Re: Is the integer x divisible by 36 ?  [#permalink]

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_________________ Re: Is the integer x divisible by 36 ?   [#permalink] 20 Feb 2019, 14:23
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