Data Sufficiency

[GMAT math practice question]

m/n is a fraction. What are the values of m and n?

1) the irreducible form of m/n is 3/4
2) if 11 is subtracted from numerator of m/n and 4 is added to denominator of m/n, then the result is 2/5

=>

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) and 2)
Using condition 1), m/n = 3/4, we must have 4m = 3n.
Condition 2) tells us that ( m - 11 ) / ( n + 4 ) = 2/5. Thus, 5(m-11) = 2(n+4) and 5m - 55 = 2n + 8. Rearranging yields 5m = 2n + 63 and 15m = 6n + 189.
Since 6n = 8m, 15m = 8m + 189, and 7m = 189. Thus, m = 27 and n = 36.
Both conditions together are sufficient.

Therefore, C is the answer.
Answer: C

If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

Statement 1=> The irreducible form of m/n is 3/4.
The lowest of m/n = 3/4
Therefore,
$$\frac{m}{n}=>\frac{3m}{4n}$$
Value of m and n still remain unknown. Hence, statement 1 is NOT SUFFICIENT.

Statement 2=> If 11 is subtracted from numerator of m/n and 4 is added to the denominator of m/n. Then, the result is 2/5.
$$\frac{m-11}{n+4}=\frac{2}{5}$$
The value of m and n is still unknown, hence, statement 2 is NOT SUFFICIENT.

Combining both statement together;
m=multiple of 3 and n is a multiple of 4.
The value of m is also greater than 11.
If m=18 and n=24.
$$\frac{18-11}{24+4}=\frac{7}{28}\ =\ \frac{1}{4}$$

If m=15 and n=20,
$$\frac{15-11}{20+4}=\frac{4}{24}\ =\ \frac{1}{6}$$

If m=21 and n=28,
$$\frac{21-11}{28+4}=\frac{10}{32}\ =\ \frac{5}{16}$$
Both statements combined together are NOT SUFFICIENT to answer the question. Hence, the answer is OPTION E.