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A bouquet contains 16 flowers, each of them either a rose, tulip, dais

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A bouquet contains 16 flowers, each of them either a rose, tulip, dais [#permalink]

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New post 13 Apr 2018, 03:27
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A bouquet contains 16 flowers, each of them either a rose, tulip, daisy, or daffodil. If no two types of flower appear the same number of times in the bouquet, and there are more tulips than any other type of flower, what is the minimum number of tulips?

A. 4
B. 5
C. 6
D. 7
E. 8
[Reveal] Spoiler: OA

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A bouquet contains 16 flowers, each of them either a rose, tulip, dais [#permalink]

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New post Updated on: 13 Apr 2018, 06:27
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Bunuel wrote:
A bouquet contains 16 flowers, each of them either a rose, tulip, daisy, or daffodil. If no two types of flower appear the same number of times in the bouquet, and there are more tulips than any other type of flower, what is the minimum number of tulips?

A. 4
B. 5
C. 6
D. 7
E. 8



Test option A. 4 cannot be the answer for tulips. as there will be at least 1 greater than or equal to tulips.
Test option B. 5 cannot be the answer for tulips. 16-5 = 11. There will be at least 1 other type equal or greater than tulip.
Test option C. 6 can be the answer. since 16-6 = 10. For example tulips = 6, rose = 5, daisy = 3 and daffodil = 2. 6+5+3+2 =16

Hence option C = 6 is the answer.


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Originally posted by houston1980 on 13 Apr 2018, 04:44.
Last edited by houston1980 on 13 Apr 2018, 06:27, edited 1 time in total.
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Re: A bouquet contains 16 flowers, each of them either a rose, tulip, dais [#permalink]

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New post 13 Apr 2018, 04:52
The only possibility that I can see here is tulip should be 6 and either of the three (rose,daisy,daffodil) should be among (5,4,1). This adds upto 6+5+4+1 = 16. Answer should be option C. 6
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Re: A bouquet contains 16 flowers, each of them either a rose, tulip, dais [#permalink]

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New post 14 Apr 2018, 11:09
IMO E.

If other number of flowers = 1, 2, 5.
Then, maximum number of tulips in this case = 8.
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Re: A bouquet contains 16 flowers, each of them either a rose, tulip, dais [#permalink]

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New post 15 Apr 2018, 17:04
We need to find the min number of tulips. I interpret this as the least number of tulips with which we can make a 16-flower bouquet. If we have 5 tulips, we can have a maximum of 14 flowers in the bouquet (e.g. 2 roses, 3 daisies, 4 daffodils), so a 16-flower bouquet is not possible. If we have 6 tulips, a 16-flower bouquet is possible (e.g. 1 rose, 4 daisies, 5 daffodils).

Answer: C
Re: A bouquet contains 16 flowers, each of them either a rose, tulip, dais   [#permalink] 15 Apr 2018, 17:04
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