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An LCM DS Problem

Is x divisible by 12?

(1) x is divisible by 3 and 4.

(2) is divisible by 2 and 6.

GOOD ENOUGH: We’ll start with statement (1).

Let’s look at the multiples of 3 and 4. Multiples of 3: 0 (don’t forget about this guy), 3, 6, 9, 12, 15, 18, 21, 24, 27, and so on. Multiples of 4: 0, 4, 8, 12, 16, 20, 24, 28, and so on. These lists overlap at 0, 12, and 24. All

cing. So, (1) is almost certainly sufficient – AD.

Now, let’s look at statement (2)

We can try the same approach. The pattern we saw when we tested statement (1) does quite work here. Where do the multiples of 2 and 6 overlap? Easy – 0, 6, 12, etc. Zero and 12 are divisible by 12, but not 6. So we have a yes and a no example. Statement (2) is insufficient. The answer is A.

BETTER: A better approach would be to consider the least common multiples of 3 and 4, and 2 and 6. LCM(3, 4) = 12, and LCM(2, 6) = 6. Multiples of 3 and 4 must be multiples of LCM(3, 4), and therefore multiples of 12, which are all divisible by 12. Multiples of 2 and 6 must be multiples of LCM(2, 6), and therefore multiples of 6. Only half of the multiples of 6 are divisible by 12 – (1) Sufficient; (2) Insufficient; A.

of these are divisible by 12. This number testing has a certain logic, and the pattern is very convin