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09 Apr 2019, 07:24
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D
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Difficulty:
45%
(medium)
Question Stats:
71% (02:28) correct
29%
(02:43)
wrong
based on 233
sessions
History
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Not Attempted Yet
In a survey conducted on women regarding their preference of cosmetics, it was found that 80% of the women surveyed were using at least one of the three brands-H & S, Dove and Pantene. 40% of those surveyed were using H & S, 30% of those surveyed were using Dove and 60% of those surveyed were using Pantene. 20% of the surveyed women use all the three brands. What percentage of the women surveyed use two or all of the given three brands?
A. 10
B. 20
C. 25
D. 30
E. 40
A. 10
B. 20
C. 25
D. 30
E. 40
21 Apr 2019, 17:02
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Let's denote H & S, Dove, and Pantene with H, D, and P respectively. Also, let's assume that the total number of people be 100.
Given that 80% of the women surveyed were using at least one of the three brands: H, D, and P.
So, n(H u D u P) = 80
Also, 40% of those surveyed were using H & S, 30% of those surveyed were using Dove and 60% of those surveyed were using Pantene.
n(H) = 40
n(D) = 30
n(P) = 60
Also, 20% of the surveyed women use all three brands.
So, n(H n D n P) = 20
We know, n(H u D u P) = n(H) + n(D) + n(P) - n(H n D) - n(D n P) - n(P n H) + n(H n D n P)
So, 80 = 40 + 30 + 60 - n(H n D) - n(D n P) - n(P n H) + 20
n(H n D) + n(D n P) + n(P n H) = 70
The number of women who use two or all of the given three brands = n(H n D) + n(D n P) + n(P n H) - 2 n(H n D n P) = 70 - 2X20 = 70 - 40 = 30
Therefore, the percentage of the women surveyed who two or all of the given three brands =30. Hence, the correct answer is D. 30
Given that 80% of the women surveyed were using at least one of the three brands: H, D, and P.
So, n(H u D u P) = 80
Also, 40% of those surveyed were using H & S, 30% of those surveyed were using Dove and 60% of those surveyed were using Pantene.
n(H) = 40
n(D) = 30
n(P) = 60
Also, 20% of the surveyed women use all three brands.
So, n(H n D n P) = 20
We know, n(H u D u P) = n(H) + n(D) + n(P) - n(H n D) - n(D n P) - n(P n H) + n(H n D n P)
So, 80 = 40 + 30 + 60 - n(H n D) - n(D n P) - n(P n H) + 20
n(H n D) + n(D n P) + n(P n H) = 70
The number of women who use two or all of the given three brands = n(H n D) + n(D n P) + n(P n H) - 2 n(H n D n P) = 70 - 2X20 = 70 - 40 = 30
Therefore, the percentage of the women surveyed who two or all of the given three brands =30. Hence, the correct answer is D. 30
21 Apr 2019, 21:27
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aragonn
total sample size = 80
h&s= 40
D= 30
P= 60
both = 20
both h&s+p, p +d & h&s+d = x
so
80=40+30+60-(x)-20
solve we get (x) = 30
IMO D
