Arithmetic Sets

[danjuma]

In a survey of 200 college graduates, 30% said they had received student loans during their college careers, and 40% said they had received scholarships. What percent of those surveyed said that they had received neither student loans nor scholarships during their college careers?

1. 25% of those surveyed said that they had received scholarships but no loans.

2.50% of those surveyed who said that they had received loans also said that they had received scholarships

[Rahul@gurome]

In a survey of 200 college graduates, 30% said they had received student loans during their college careers, and 40% said they had received scholarships. What percent of those surveyed said that they had received neither student loans nor scholarships during their college careers?

• 1. 25% of those surveyed said that they had received scholarships but no loans.
  2. 50% of those surveyed who said that they had received loans also said that they had received scholarships

Given: 30% of 200 = 60 received loan and 40% of 200 = 80 received scholarship.

Statement 1: 25% of 200 = 50 received scholarship but no loan.
(80 - 50) = 30 received both loan and scholarship.
(60 - 30) = 30 received loan but no scholarship.

200 - (30 + 30 + 50) = 90 received neither loan nor scholarship.
90 = 45% of 200.

Sufficient.

Statement 2: 50% of 60 = 30 received both loan and scholarship.

Same as statement 1.

Sufficient.

The correct answer is D.