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03 Jul 2017, 03:34
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42% (02:19) correct
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In a survey, 2000 executives were each asked whether they read newsletter A or newsletter B. According to the survey, 55 percent of the executives read newsletter A, 62 percent read newsletter B, and 37 percent read both newsletter A and newsletter B. How many of the executives surveyed read at most one among newsletter A and newsletter B?
(A) 1600
(B) 1260
(C) 900
(D) 860
(E) 760
(A) 1600
(B) 1260
(C) 900
(D) 860
(E) 760
03 Jul 2017, 05:11
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Given data :
55 percent of the executives read newsletter A
62 percent read newsletter B
37 percent read both newsletter A and newsletter B
Total = 2000
From the data we can infer
P(A) = \(\frac{55}{100} * 2000 = 1100\)
P(B) = \(\frac{62}{100} * 2000 = 1240\)
P(Both) = \(\frac{37}{100} * 2000 = 740\)
P(Only A) = P(A) - P(Both) = 1100 - 740 = 360
P(Only B) = P(B) - P(Both) = 1240 - 740 = 500
P(Total) = P(Only A) + P(Only B) + P(Both) + P(Neither)
Hence, P(Neither) = P(Total) - {P(Only A) + P(Only B) + P(Both)}
Substituting values,
P(Neither) = 2000 - 360 - 500 - 740 = 400
P(At most 1) = P(Neither) + P(Only A) + P(Only B) = 400 + 500 + 360 = 1260(Option B)
55 percent of the executives read newsletter A
62 percent read newsletter B
37 percent read both newsletter A and newsletter B
Total = 2000
From the data we can infer
P(A) = \(\frac{55}{100} * 2000 = 1100\)
P(B) = \(\frac{62}{100} * 2000 = 1240\)
P(Both) = \(\frac{37}{100} * 2000 = 740\)
P(Only A) = P(A) - P(Both) = 1100 - 740 = 360
P(Only B) = P(B) - P(Both) = 1240 - 740 = 500
P(Total) = P(Only A) + P(Only B) + P(Both) + P(Neither)
Hence, P(Neither) = P(Total) - {P(Only A) + P(Only B) + P(Both)}
Substituting values,
P(Neither) = 2000 - 360 - 500 - 740 = 400
P(At most 1) = P(Neither) + P(Only A) + P(Only B) = 400 + 500 + 360 = 1260(Option B)
General Discussion
Benacher07
Joined: 12 Jul 2016
Last visit: 15 Jul 2017
Posts: 16
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Given Kudos: 212
Schools: HEC Sept 2018 Intake (II)
04 Jul 2017, 03:58
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55% of 2000 =1100
62% of 2000=1240
37% of 2000=740
We need people who read only A and those who read only B, so using the double matrix method we can deduce the following,
1-people reading A but not B =1100-740 =360
2-people reading B but not A = 1240-740 =500
From 1 and 2 = 500+360 = 860
hence, the answer is : D
Kudos ?
62% of 2000=1240
37% of 2000=740
We need people who read only A and those who read only B, so using the double matrix method we can deduce the following,
1-people reading A but not B =1100-740 =360
2-people reading B but not A = 1240-740 =500
From 1 and 2 = 500+360 = 860
hence, the answer is : D
Kudos ?
