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All of the arrangements made in a flower shop yesterday contained rose

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All of the arrangements made in a flower shop yesterday contained rose  [#permalink]

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New post 06 Jun 2017, 11:39
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A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

56% (02:26) correct 44% (02:26) wrong based on 103 sessions

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All of the arrangements made in a flower shop yesterday contained roses, tulips, or lilies, or some combination of the three types. 32 of the arrangements made yesterday contained roses, 42 contained tulips, and 41 contained lilies. 16 of the arrangements made yesterday contained roses and tulips, 18 contained lilies and tulips, and 8 contained roses and lilies. If 5 of the arrangements made yesterday contained all three types, how many total arrangements were made?

A. 63
B. 68
C. 78
D. 83
E. 115

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All of the arrangements made in a flower shop yesterday contained rose  [#permalink]

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New post 06 Jun 2017, 11:54
1
Given data
P(R) = 32 | P(T) = 42 | P(L) = 41
P(R and T) = 16
P(L and T) = 18
P(R and L) = 8
P(R and T and L) = 5

Since P(R and T), P(L and T) and P(R and L) include P(R and T and L) their actual values are as follows:
P(R and T) = 11
P(L and T) = 13
P(R and L) = 3
P(Any 2) = 11 + 13 + 3 = 27

Also, since P(only R) contains P(R and T), P(R and L) and P(R and T and L), the actual value is 13
P(Only R) = 32-11-3-5
Similarly, we can deduce P(Only T) = 13 and P(Only L) = 20

P(Total) = P(Only R) + P(Only T) + P(Only L) + P(Any 2) + P(All 3) = 13 + 13 + 20 + 27 + 5 = 78

Therefore, 78(Option C) is total arrangements that could be made in the flower shop.
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All of the arrangements made in a flower shop yesterday contained rose  [#permalink]

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New post 29 May 2018, 00:40
Bunuel wrote:
All of the arrangements made in a flower shop yesterday contained roses, tulips, or lilies, or some combination of the three types. 32 of the arrangements made yesterday contained roses, 42 contained tulips, and 41 contained lilies. 16 of the arrangements made yesterday contained roses and tulips, 18 contained lilies and tulips, and 8 contained roses and lilies. If 5 of the arrangements made yesterday contained all three types, how many total arrangements were made?

A. 63
B. 68
C. 78
D. 83
E. 115



We have a formula for 3 sets.
Image

The answer is C.
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Re: All of the arrangements made in a flower shop yesterday contained rose  [#permalink]

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New post 15 Oct 2019, 19:52
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Bunuel wrote:
All of the arrangements made in a flower shop yesterday contained roses, tulips, or lilies, or some combination of the three types. 32 of the arrangements made yesterday contained roses, 42 contained tulips, and 41 contained lilies. 16 of the arrangements made yesterday contained roses and tulips, 18 contained lilies and tulips, and 8 contained roses and lilies. If 5 of the arrangements made yesterday contained all three types, how many total arrangements were made?

A. 63
B. 68
C. 78
D. 83
E. 115



We can create the equation:

Total = total single overlaps - total double overlaps + triple overlap

Total = 32 + 42 + 41 - 16 - 18 - 8 + 5

Total = 115 - 42 + 5

Total = 78

Answer: C
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Re: All of the arrangements made in a flower shop yesterday contained rose  [#permalink]

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New post 16 Oct 2019, 00:48
Here is the Venn Diagram process to solve the question without having to use the formula.

Attachment:
File comment: Venn Diagram
Capture.PNG
Capture.PNG [ 151.22 KiB | Viewed 320 times ]


Hope this helps!
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Re: All of the arrangements made in a flower shop yesterday contained rose   [#permalink] 16 Oct 2019, 00:48
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