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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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13 Apr 2018, 03:27
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45% (medium)

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62% (01:56) correct 38% (01:53) wrong based on 131 sessions

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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

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

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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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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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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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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).

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

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28 Apr 2018, 19:08
Tulips minimum number needs to be calculated

So 3,4,5,6 as sum would have to make 16 also

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

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28 Apr 2018, 19:31
Option C

- 16 flowers;
- no two types of flower appear the same number of times in the bouquet;
- more tulips than any other type of flower;

- minimum number of tulips?

x + (x-1) + (x-2) + (x-3) = 16

4x = 22

x = 5,5

5 cannot be the answer (there will be at least 1 other type equal or greater than tulip), so 6 is the answer.
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Re: A bouquet contains 16 flowers, each of them either a rose, tulip, dais  [#permalink]

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29 Apr 2018, 02:31
urvashis09 wrote:
IMO E.

If other number of flowers = 1, 2, 5.
Then, maximum number of tulips in this case = 8.

We have been asked to find to MINUMUM number for Tulips possible.
Your explanation stands true for MAXIMUM number of Tulips possible
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Re: A bouquet contains 16 flowers, each of them either a rose, tulip, dais  [#permalink]

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21 Jul 2018, 02:46
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

A way to go about it is as follows,
As the number of tulips has to be minimum possible, with the given condition, we can agree that all the flower must be as close to each other as possible (can not be equal) and would have the average value of 4.
(how? 16/4=4)
Now let's divide the 4 numbers into two sets, if a>b>c>d, then a and d are one set and b and c are another
Hence the two numbers (in a set) will have to be at equal distances from 4 in opposite directions to have the same sum as 4+4, ie 4+1, coupled with 4-1 and 4+2 coupled with 4-2.
(Why not 4+0? because 4+0 = 4-0, hence the numbers become equal, which is not allowed)
Therefore clearly the closest (from each other) set of numbers fulfilling this questions conditions are 6,5,3,2
Therefore no. of tulips = 6.
Side note: This method only works because min value is asked, in the case of max, it is better to simply subtract the smallest possible values (1,2,3)
Please do leave a kudos if I could introduce a new method to you
Re: A bouquet contains 16 flowers, each of them either a rose, tulip, dais   [#permalink] 21 Jul 2018, 02:46
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