Architj wrote:Is the integer x divisible by 36?
(1) x is divisible by 12.
(2) x is divisible by 9.
i think the answer here should be D, but the correct is C, how?
Solution:
We are asked whether x is divisible by 36. This could also be re-written as:
Is x/36 = integer?
Statement One Alone:
x is divisible by 12.
Thus, x could be values such as 12 or 36.
We can see that when x is 12, x/36 is not an integer. That is when x is 12,
x is not divisible by 36.
However, when x is 36, x/36 is an integer. That is when x is 36,
x is divisible by 36.
Since we have a yes and a no answer, statement one alone is not sufficient.
Statement Two Alone:
x is divisible by 9.
Thus, x could be values such as 9 or 36.
We can see that when x is 9, x/36 is not an integer. That is when x is 9,
x is not divisible by 36.
However, when x is 36, x/36 is an integer. That is when x is 36,
x is divisible by 36.
Since we have a yes and a no answer, statement two alone is not sufficient.
Statements One and Two Together:
Using both statements, we know x can take values that are multiples of 9 and 12. Thus, we need to determine the least common multiple of 9 and 12.
Although there are technical ways for determining the least common multiple, the easiest method here is to analyze the multiples of 9 and 12 until we find one in common.
Starting with 9, we have: 9, 18, 27, 36, and 45
For 12, we have: 12, 24, 36
For the multiples of 12, we stopped at 36, because we see that 36 is also a multiple of 9. Thus, 36 is the least common multiple of 9 and 12, and therefore we know that 36 is the lowest possible value for x. Since x is either 36 or a multiple of 36, we know that x must be divisible by 36.
The answer is
C
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