BTGmoderatorDC wrote:Of 200 people surveyed, 80 percent own a cellular phone and 45 percent own a pager. If all 200 people surveyed own a cellular phone, or a pager, or both, what percent of those surveyed either do not own a cellular phone or do not own a pager?

(A) 35%
(B) 45%
(C) 55%
(D) 65%
(E) 75%

OA E

Source: GMAT Prep

We can use the formula for overlapping sets for this problem:

Total = #Cell + #Pager - Both + Neither

200 = 160 + 90 - x + 0

200 = 250 - x

50 = x

We see that 50 individuals own both a cell phone and a pager. Thus, the number of people who own a cell phone and not a pager is 160 - 50 = 110.

Similarly, of the 90 individuals who own a pager, there are 90 - 50 = 40 who own a pager and not a cell phone.

Thus, there are 110 + 40 = 150 who either do not own a cell phone or do not own a pager.
This number represents 150/200 = 3/4 x 100% = 75% of the people surveyed.

Answer: E