In a recent survey 200 students had undergraduate degrees in

In a recent survey, 200 students had undergraduate degrees in arts, 95 had undergraduate degrees in science and 120 had graduate degrees. Art undergrads with graduate degree totaled 55 while 40 science undergrads also had graduate degrees. Some students had multiple degrees, 25 had both art and science undergraduate degrees while 5 had both art and science undergraduate degrees with a graduate degree. The number of students with at least one type of degree mentioned above was            
A. 244

B. 250

c. 300

d. 321

How many integers from 1 to 600 are divisible by 5 or 7?            

A.178

B. 170

C. 178

D. 188

Solution

Part one is C - 300 students

Add together students with undergraduate degrees (200 +95) then add students with graduate degrees (120). Then subtract students with multiple degrees (-55 -40) and then subtract students with two undergraduate degrees (-25) and finally add back in the 5 students that have all three degrees since we will have subtracted them twice.

So 200+95+120-55-40-25+5= 300 students

Part two - D

Find the number of integers divisible by 5, add to that the number of integers divisible by 7, but then some of those integers will be divisible by both 5 and 7 so you must subtract the number of integers divisible by 35 (5*7). So the answer is 188