Data Sufficiency

[GMAT math practice question]

m, n and 2/m+3/n are positive integers. What is the value of mn?

1) m and n are prime numbers
2) The greatest common divisor of m and n is 1

Statement 1:
Option 1
- M =2, N = 3
- 2/M + 3/N = 1 + 1 = 2
- MN = 2 * 3 = 6

Option 2
- M = 5, N = 5
- 2/M + 3/N = .4 + .6 = 1
- MN = 5 * 5 = 25

Since we can get two values for MN that satisfy the statement it's INSUFFICIENT





Statement 2:
- Possible values for M ====> 1 & 2
- possible values for N =====> 1 & 3

Option 1:
- M =1, N = 1
- M * N = 1

Option 2:
- M = 2, N = 3
- M * N = 6

-------> INSUFFICIENT

Statement 1 & 2 Together
- Together we know M * N are prime numbers that CANNOT be equal to each other(otherwise GCF wouldn't be 1)
- Using the examples we already came up with only M =2 and N =3 satisfy the criteria
- MN = 2 * 3 = 6 ======> SUFFICIENT

Answer: C

-

=>

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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
The possible pairs (m,n) are (1,1),(1,3),(2,1),(2,3) and (5,5).

Since we have 2 variables (m and n) 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)
There is a unique pair of integers which satisfies both conditions.
This is m = 2 and n = 3.
So, mn = 6.
Conditions 1) & 2) are sufficient, when applied together.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
If m = 2 and n = 3, then mn = 6.
If m = 5 and n = 5, then mn = 25.
Condition 1) is not sufficient since it does not yield a unique solution.

Condition 2)
If m = 2 and n = 3, then mn = 6.
If m = 1 and n = 1, then mn = 1.
Condition 2) is not sufficient since it does not yield a unique solution.

Therefore, C is the answer.
Answer: C

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.