Hi,
This is a common type(Remainders and Divisibility) of Question in GMAT.
Let’s understand the question stem first,
Question: Is x divisible by 12?For the number to be divisible by 12, it should be multiple of 12.
Like 12, 24,36,…
Or else if you see when we prime factorize 12 i.e., 12 = 2^2 * 3
It has two 2’s and one 3.
So, a number which has two or more 2’s and one or more three is divisible by 12.
Let’s check the statements now,
Statement I is insufficient:x is divisible by 27.
So, x is a multiple of 27, like 27, 54, 81, 108 etc…
We can see that, 27,54,81 are not multiples of 12 but 108 is.
So, it is insufficient.
Also, Prime factorization of 27 = 3^3.
So, it has only 3’s but no 2’s.
So insufficient.
Statement II is insufficient:x is divisible by 6.
So, x is a multiple of 6, like, 6, 12, 18, 24, 30 etc…
We can see that, 6, 18, 30 are not multiples of 12 but 12,24, etc are multiples of 12.
So, it is insufficient.
Also prime factorization of 6 = 2 *3
It has only one 2 and only one three. But for a multiple of 12, we need minimum two 2’s and one three.
So insufficient.
Together also it is not sufficient.With both statements together, x should be a multiple of 6 and 27.
LCM of 6 and 27 is 54.
So, x is 54, 108, 162 etc…
54 is not a multiple of 12 but 108 is a multiple of 12.
So insufficient.
Even together, prime factorization of 54 = 3^3 * 2
But, we need minimum of two 2’s and a 3.
So answer is E.
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