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# In a survey conducted on women regarding their preference of cosmetics

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SC Moderator
Joined: 23 Sep 2015
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In a survey conducted on women regarding their preference of cosmetics  [#permalink]

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09 Apr 2019, 07:24
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Difficulty:

45% (medium)

Question Stats:

58% (02:18) correct 42% (02:56) wrong based on 31 sessions

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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

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Re: In a survey conducted on women regarding their preference of cosmetics  [#permalink]

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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

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Re: In a survey conducted on women regarding their preference of cosmetics  [#permalink]

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21 Apr 2019, 21:27
aragonn wrote:
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

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
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Re: In a survey conducted on women regarding their preference of cosmetics  [#permalink]

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21 Apr 2019, 21:47
Attachment:

2019-04-22_09-42-03.jpg [ 36.84 KiB | Viewed 175 times ]

Let the total number of women surveyed be 100.

80% use at least one of the three brands. So 20% use no brand. From the above fig, we need to find the value of d+e+f+20 (use two products or all).

a + d + e = 20
b + d + f = 40
c + e + f = 10

a + b + c + 2(d + e + f) = 70 ________________ (1)

a + b + c + d + e + f + 20 = 80

a + b + c + d + e + f = 60 _________________ (2)

Substituting eq (1) in eq (2),

70 - 2(d + e + f) + (d + e + f) = 60

70 - (d + e + f) = 60

d + e + f = 10

We have to find the value of d+e+f+20 --> 10 + 20 => 30.

So 30 out of 100 women surveyed use 2 or 3 products.

OPTION: D
Attachments

2019-04-22_09-42-03.jpg [ 33.27 KiB | Viewed 175 times ]

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Re: In a survey conducted on women regarding their preference of cosmetics   [#permalink] 21 Apr 2019, 21:47
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