Re: Is the integer x divisible by 36 ?
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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