Data Sufficiency

Source: GMAT EP2

A certain company has 255 employees. If an employee is to be selected at random from the company's employees, is the probabalility less than 1/2 that the employee selected will be a woman who has a college degree.

1. 130 of the company's employees do not have a college degree.
2. 125 of the company's employees are men.

Hi Machmeera,

This question is just a data analysis question presented in the guise of a probability. The easiest way to represent data is by either using a Venn diagram or a 2 x 2 matrix. Whenever you have sets of data which are mutually exclusive (for e.g. men and women or have a college degree and do not have a college degree) then you can always represent data using a 2 x 2 matrix.

Now if the probability that the employee selected will be a woman who has a college degree has to be less than 1/2 then the number of women who have a college degree needs to be less than 128 since the total employees is 255. The question now can be rephrased to 'Is the number of women who have a college degree less than 128'



Statement 1 : 130 of the company's employees do not have a college degree :

If 130 of the employees do not have a college degree then 125 employees have a college degree. This implies that the number of women who have a college degree will always be 125 or lesser. The probability here will always be less than 1/2. We get a definite YES. Sufficient.



Statement 2 : 125 of the company's employees are men :

If 125 of the employees are men then 130 employees are women. This implies that the number of women who have a college degree can be 130 or lesser. If the number here is 129 or 130, the probability will be greater than 1/2, which gives us a NO and if the number is less than 128 then the probability will be less than 1/2, which gives us a YES. Insufficient.



OA : A

CrackVerbal Academics Team