Source: GMAT Prep
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%
The OA is E
Of 200 people surveyed, 80 percent own a cellular phone and 45 percent own a pager. If all 200 people surveyed...
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Solution:BTGmoderatorLU wrote: ↑Tue Feb 16, 2021 11:19 amSource: GMAT Prep
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%
The OA is E
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
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