# GMAT OFFICIAL GUIDE DS – In a survey of 200 college…

## Solution:

The easiest way to solve this problem is to set up a double set matrix.  In our matrix we have two main categories: student loans and scholarships. More specifically, our table will be labeled with:

2) Did not receive student loans (No Loans)

4) Did not receive a scholarship (No Scholarship)

(To save room on our table headings, we will use the abbreviations for these categories)

We are given that there are a total of 200 college graduates in the survey.  We also are given that 30 percent of those graduates received student loans and 40 percent received scholarships.

Thus,

200 x 0.3 = 60 received student loans

200 x 0.4 = 80 received scholarships

We are trying to determine what percent of those surveyed said that they had received neither student loans nor scholarships.

Let’s fill all this information into a table. Note that each row sums to create a row total, and each column sums to create a column total.  These totals also sum to give us the grand total, designated by 200 at the bottom right of the table.

Statement One Alone:

25 percent of those surveyed said that they had received scholarships but no loans.

Using statement one we can determine the number of students who received scholarships but no loans.

200 x 0.25 = 50 students who received scholarships but no loans.

We can fill the above information into our table.

Thus, the percent of those surveyed who said that they had received neither student loans nor scholarships is (90/200) x 100 = 45%.  Statement one is sufficient to answer the question.  We can eliminate answer choices B, C, and E.

Statement Two Alone: