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In a survey conducted on women regarding their preference of cosmetics

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aragonn
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In a survey conducted on women regarding their preference of cosmetics [#permalink] New post   09 Apr 2019, 07:24
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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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D
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Re: In a survey conducted on women regarding their preference of cosmetics [#permalink] New post   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] New post   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] New post   21 Apr 2019, 21:47
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Attachment:
2019-04-22_09-42-03.jpg
2019-04-22_09-42-03.jpg [ 36.84 KiB | Viewed 2385 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

Adding all the three equations,

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
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Re: In a survey conducted on women regarding their preference of cosmetics [#permalink] New post   21 Sep 2019, 07:22
Exactly 2 + Exactly 3 = Double overlap - 2*(Triple overlap)=At least 2

100=A+B+C-DO+TO+N
100=40+30+60-DO+20+20
DO=70

DO-2*TO=70-2*20=30

100=A+B+C-E2-2*E3+N
100=40+30+60-E2-2*20+20
E2=10

E2+E3=10+20=30
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Re: In a survey conducted on women regarding their preference of cosmetics [#permalink] New post   09 Apr 2020, 06:55
Archit3110 wrote:
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


Hi! There are two formulas for overlapping sets:

T= A+B+C - (Sum of 2) + All three + Neither
T A+B+C - Exactly 2 - 2*All three + Neither

Which one would we be able to use here? and how do we get to know which one is suitable here?
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gmatclubot
Re: In a survey conducted on women regarding their preference of cosmetics [#permalink]
09 Apr 2020, 06:55
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