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

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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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

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

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

IMO E.

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

Tulips minimum number needs to be calculated

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

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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.

We have been asked to find to MINUMUM number for Tulips possible.
Your explanation stands true for MAXIMUM number of Tulips possible

Total flowers are 16.

Variety: Rose(R), Tulip(T), Daisy(Da), or Daffodil(Df).

Conditions: no two types of the flower appear the same number of times in the bouquet (All appears distinctively).
and More tulips than any other type of flower.

If we suppose each flower appears equal then:\(\frac{16}{4}\) = 4

T = 4 ; R = 4 ; Da = 4 ; Df = 4

=> Tulips are more and no two appear same number times.

=> T = 7 ; R = Da = Df = 3 but no two appears same and we need minimum number possible for Tulip

=> T = 6 ; Others will be 5,4, 1 or 5, 3 , 2 .

Answer C

Since EITHER is said, none of the varieties can have '0' flowers.
Hence the least any variety can have is '1'. But as the number of tulips are more than any other and minimum(integers) is asked, we need to put as low a number for tulips and as high a number for other varieties i.e. the numbers of flowers of the four varieties would be near to each other.
So, either we can test number from the options or go for hit and trials(brute force) or go for 4(16/4) and test various numbers.

Therefore, the number of tulips has to be more than 4 since 1 + 2 + 3 + 4 ≠ 16
Also, 5 is not possible since we can't repeat numbers to sum 16.
6, with combination of 1, 2, 3, 4 and 5, is possible to sum 16 - 1, 4, 5, 6.

ANSWER C.
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