Data Sufficiency

[GMAT math practice question]

If m and n are positive integers, is m/n a terminating decimal?

1) m is divisible by 9
2) n is divisible by 30

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

If m = 9 and n = 30, then m/n = 9 / 30 = 3/10 = 0.3 is a terminating decimal and the answer is 'yes'.
If m = 9 and n = 210, then m/n = 9 / 210 = 3/70 is not a terminating decimal since the denominator, 70, has a prime factor other than 2 and 5. The answer is 'no'.
Both conditions together are not sufficient, since they don't yield a unique solution.

Therefore, E is the answer.
Answer: E

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

A terminating decimal has a finite decimal.

Statement 1
m is divisible by 9
means that m is a multiple of 9 but values of n is not known, hence statement 1 is INSUFFICIENT.

Statement 2
n is divisible by 30 but the value of n is not known, hence statement 2 is INSUFFICIENT.

Combining statement 1 and 2 together.
m is a multiple of 9
n is a multiple of 30
If m = 9 and n = 30
$$\frac{m}{n}=\frac{9}{30}=0.3$$
if m = 18 and n = 60
$$\frac{m}{n}=\frac{18}{60}=0.3$$
If m = 9 and n = 6
$$\frac{m}{n}=\frac{9}{60}=0.15$$
If m = 18 and n = 30
$$\frac{m}{n}=\frac{18}{30}=0.6$$
Therefore
m/n is a terminating decimal,
statement 1 and 2 together are SUFFICIENT.

$$answer\ is\ Option\ C$$