Of 200 people surveyed, 80 percent own a cellular phone and

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Thu Jul 25, 2019 9:06 pm

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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

Source: Beat The GMAT — Problem Solving | Thu Jul 25, 2019 9:06 pm

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Sat Jul 27, 2019 11:20 am

80 % own cellular phone
$$=\frac{80}{100}\cdot20$$
$$45\%\ \ own\ pager\ =160$$
$$45\%of\ 200=90$$
Total no of people that own both = (160+90) - 200 = 50
People with just one device = 200 - 50 = 150
$$\%=\frac{150}{200}\cdot100\ =\ 75\%$$
$$answer\ isOption\ E$$

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Aug 06, 2019 4:49 pm

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

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