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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.

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

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14 Feb 2014, 08:59

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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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14 Feb 2014, 13:20

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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.

(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

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

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14 Sep 2016, 05:59

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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.

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Statement 1

This basically means X is a multiple of 12 (2 x 2 x 3) - 24 , 36 , etc