Data Sufficiency

[GMAT math practice question]

At an entrance examination, the ratio of successful male applicants to successful female applicants is 5:2. What is the total number of applicants?

1) The ratio of male applicants to female applicants is 3:2.
2) The number of successful applicants is 140.

Solution:

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.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

Let x and y be the number of male and female applicants, respectively. Let 5k be the number of successful male applicants and 2k be the number of successful female applicants, giving us x = 5k. Then we have to find the total number of applicants, which is equal to x + y.

Follow the second and the third step: From the original condition, we have 3 variables (x, y, and k). To match the number of variables with the number of equations, we need 3 equations. Since conditions (1) and (2) will provide 1 equation each, E would most likely be the answer.

Recall 3 Principles and choose E as the most likely answer.

Let’s look at both conditions 1) & 2) together.

We know that the ratio of successful male applicants to successful female applicants is 5:2; there are 100 successful male applicants and 40 successful female applicants.

Then the number of male applicants is greater than or equal to 100, and the number of female applicants is greater than or equal to 40.

If the number of male applicants is 120 and that of female applicants is 80, then the total number of applicants is 200.
If the number of male applicants is 150 and that of female applicants is 100, then the total number of applicants is 250.

The answer is not unique, and both conditions 1) and 2) together are not sufficient, according to Common Mistake Type 2, which states that the number of answers must be only one.

Both conditions (1) and (2) together are not sufficient.

Therefore, E is the correct answer.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B, or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2) when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.