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
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Of 200 people surveyed, 80 percent own a cellular phone and
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BTGmoderatorDC
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Jay@ManhattanReview
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Total number of people who own either phone or pager = Total number of people who own phone + Total number of people who own pager - Total number of people who own both phone and pagerBTGmoderatorDC 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
Taking percent values...
100% = 80% + 45% - Both
Both = 25%
Percent of those surveyed either do not own a cellular phone = 80% - 25% = 55%
Percent of those surveyed either do not own a pager = 45% - 25% = 20%
Percent of those surveyed either do not own cellular phone or do not own a pager = 55% + 20% = 75%
The correct answer: E
Hope this helps!
-Jay
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we can try as follows:
\(80%\) who own cellular phone \(= 160\).
\(45%\) own pager \(= 90\)
Total who own cellular phone \(= 160+90=250\). However, the total number of people is \(200\) so \(250-200=50\) people own both.
Now we need people who either own a cp or a pager (but not both), so we subtract the \(50\) from \(200=150\) is our required population.
\(\left(\frac{150}{200}\right)*100 = 75\).
Option __E__
\(80%\) who own cellular phone \(= 160\).
\(45%\) own pager \(= 90\)
Total who own cellular phone \(= 160+90=250\). However, the total number of people is \(200\) so \(250-200=50\) people own both.
Now we need people who either own a cp or a pager (but not both), so we subtract the \(50\) from \(200=150\) is our required population.
\(\left(\frac{150}{200}\right)*100 = 75\).
Option __E__
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Scott@TargetTestPrep
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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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