Let's use some prime factorization...

We have 15 white tulips and 85 red tulips
15 = (3)(5)
85 = (5)(17)

So, for the white tulips, we can create 5 groups of 3 flowers
So, for the red tulips, we can create 5 groups of 17 flowers

This means we can create 5 BOUQUETS in which each bouquet has 3 red tulips and 17 white tulips
In other words, the ratio of red tulips to white tulips is the same for each bouquet (3 : 17).

Answer:

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Video Solution from Quant Reasoning:

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Since we should use all the tulips available, then the number of bouquets must be a factor of both 15 and 85. For example, we cannot have 2 bouquets since we cannot divide 15 white tulips into 2 bouquets without one tulip left over.

The greatest common factor of 15 and 85 is 5.

Answer: B.
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Similar question to practice: https://gmatclub.com/forum/what-is-the- ... 67914.html
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w=3*5
R=17*5

As 3 and 17 are prime numbers .In addition,we have to maintain same ratio and use all the tulips available at the same time .
greatest number of bouquets that can be made using all the tulips=5

W Tulips = 15 = 5*3
R Tulips = 85 = 5*17
Both are multiples of 5
=> W Tulips : Red Tulips = 3 : 17 per bouquet.

So we can have 5 bouquets from the available tulips.
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Since all the tulips should be used and since the white to red ratio must be the same in all the bouquets, the white to red ratio in each bouquet must be 15:85 or 3:17. Thus, for some integer x, the number of white tulips in each bouquet is 3x and the number of red tulips in each bouquet is 17x. So, each bouquet contains 3x + 17x = 20x tulips. To maximize the number of bouquets, we should take x to be as small as possible. In this scenario, since the number of tulips cannot be zero or a negative number, the smallest possible integer value of x is 1. Then, each bouquet contains 20(1) = 20 tulips and there are at most 100 / 20 = 5 bouquets.

Answer: B
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Solution:

Step 1: 15 white tulips and 85 red tulips are available for bouquets. The bouquets must be made from these tulips using the same ratio of white tulips and red tulips from the 15 white tulips and 85 red tulips provided.

Step 2: Since all the tulips available must be used without any left over, then the number of bouquets possible must be a factor of the available tulips. Hence, the highest possible common factor of 15 white tulips and 85 red tulips is obtained as follows:

15 = 3 x 5
85 = 5 x 17

5 is common to both 15 and 85. Therefore, the greatest number of bouquets that can be made is 5 and the answer is

HCF of 85 and 15 = 5

Hence B

I don't really understand why to choose such a scholar way to solve questions: My approach is quite limited, but i had a correct answer in 14 seconds thanks to it:

As simply as it sounds, imagine to multiply 15 until you reach 85: 15x1=15; 15x2=30...;15x5=75. In this case, it is the maximum number of flowers you can put. Answer B

Pretty similar to the approaches mentioned above but for a layman this might help:

The ratio of the white tulip to Red = 15/85 = 3/17, which means that in 1 bouquet there will be 3 white tulips and 17 red. The total is 20. The total tulips we have is 100(15+85) so 100/20 = 5. "B"

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For this particular problem, I arrived to the correct answer of 5 bouquets, but used a slightly different method and want to confirm whether this would be a correct approach to solve problems like this moving forward:

Since there is a total of 15 white tulips and 85 red tulips to be made into separate bouquets, I reduced that fraction to 3:17 - 3 white tulips to every 17 red tulips. I added 3+17 to total the number of tulips in one bouquet, which would be 20 tulips.

I then totaled the number of actual available flowers 15 + 85, which is 100. I then divided 100 by 20, which resulted in 5 bouquets.

Definitely appreciate any insight to this methodology!

GMATStudying2020
Your approach is totally fine. A similar type of solution is given by other fellow GC members. The point is this question tests prime factorization so if this question had been 700+ level then your solution would take slightly longer time. However, if you master your solution then it altogether different scenario. Most importantly cheers.

You may like to visit another official question for a better perspective.
https://gmatclub.com/forum/what-is-the- ... 14-20.html
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Due to my conditioning of solving GMAT PS problems, I read the question and it struck me as an HCF question and I arrived at B as the correct answer.

Though I couldn't help but notice one weird possibility, say each bouquet contains only 1 white and 1 red tulip.

The maximum number of bouquets using this ratio (1:1) would be 15 and hence I double checked the options for 15.

I want to know if 1:1 is the wrong approach for this question. Kindly help.

Its good to approach with flexibility in mind but how would you ensure the highlighted text with your approach.
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Didn't see anyone mention this method, so I thought I'd share it.

Since all bouquets have the same number of flowers, and all flowers need to be used, (15, 85) needs to be divible by one of the answer choices.

You will immediately see that 5 is the answer.

Posted from my mobile device

I am prepping using the GMAT Official Guide 2020, and this question came up. In the solutions, the authors write "Because all tulips are to be used and the same number of white tulips will be in each bouquet, the number of white tulips in each bouquet times the number of bouquets must equal the total number of white tulips, or 15." I don't follow this line of reasoning. The question clearly states that each bouquet must have the same ratio of white to red tulips, but it doesn't say that each bouquet must have the same number of white tulips in it. Therefore, why does the author say that each bouquet must have the same number of white tulips in it? I'm guessing the key lies in the fact that all of the tulips have to be used.
My question: How does the fact that all tulips have to be used lead to the corollary that each bouquet has to have the same number of white tulips?
The only stipulation in the question is that each bouquet has to have the same RATIO OF WHITE TO RED TULIPS.
Thanks in advance.

given that ratio white / red = constant for each bouquets.
Available
White = 15
Red = 85

Ratio of 15/85 will be same only in 5 bouquets. Since, common is 5 between numerator & denominator (to keep ratio constant)

Answer 5 (B)