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10 Oct 2019, 01:36
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
76% (02:59) correct
24%
(02:55)
wrong
based on 100
sessions
History
Date
Time
Result
Not Attempted Yet
A newspaper polled 1,000 likely voters about which of the following issues, if any, played an important role in their decision-making process for an upcoming election: education, crime, and/or taxes. Of the voters surveyed, a total of 495 named education, 490 named crime, and 440 named taxes. In the figure above, the overlapping areas between two circles represent the people who named only those two items; the overlapping area between the three circles represents those people who named all three issues. How many of the 1,000 people polled responded “none of the above” to the questions?
A. 140
B. 110
C. 80
D. 20
E. 0
Attachment:
2016-08-25_1216.png [ 5.43 KiB | Viewed 5421 times ]
siddharthkapoor
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11 Oct 2019, 23:55
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Bunuel
Number of people who named Education= 495= Number of people who only named Education+125+85+60
=> Number of people who only named Education= 225
Similarly, number of people who named Crime and Taxes are 165 and 90 respectively.
Thus, Total voters= Number of people who named only one of the three issues+ number of people who named only two of the three issues+ number of people who named all three issues+ number of people who didn't name any of the three issues
=> 1000=(225+165+90)+(85+60+140)+125+number of people who didn't name any of the three issues
=> Number of people who didn't name any of the three issues= 1000- 890=110
Therefore, the answer is option B.
18 Oct 2020, 06:32
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Bunuel
We can add the three values 495, 490, 440 up directly but in doing that we double-counted many of the overlapped areas. The areas with only 1 overlap have been counted twice and the middle 125 has been counted three times in that process, so we should subtract 60, 85, 140 once and 125 twice in order to count everybody only once.
Thus \(495 + 490 + 440 - 60 - 85 - 140 - 125*2 = (495 - 85) + (490 - 60) + (440 - 140) - 250 \)
\(= 410 + 430 + 300 - 250 = 840 + 50 = 890\)
is the grand total of voters surveyed. Then 110 did not participate.
Ans: B
