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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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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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

Video Solution from Quant Reasoning:

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CONCEPT:HCF of Numbers (Highest common factor)

Let us say the number of bouquets to be made =x.
x has to be a whole number. This implies x has to be a factor of both 15 and 85.
x also has to the greatest such number.

Hence, we are looking for the HCF(5,85)that is 5.
Thus, number of bouquets or "x" =5. (B)

Hope this helps. Keep studying.
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I understand prime factoring but I don't understand why 15 bouquets can't be made with 1 white rose in each and 5 red.

15 bouquets with 5 red roses in each bouquet would require 75 red roses.
The question tells us that we have a 85 red roses and that we must use all of them
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Answer: Option B

Video solution by GMATinsight



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I have the same question as the one previously mentioned. The question only says the "ratio of white to red tulips" should be the same in each bouquet, but never says the number of tulips must be the same in each bouquet. Taking one example bouquet A has 2 white and 10 red tulips, so the ratio is 1:5; bouquet B has 4 white and 20 tulips, so the ratio is also 1:5. Why all solutions in the thread default to the same number of white/red tulips in each bouquet？

Need help, thanks in advance.

Bunuel

Bouquets are to be made using white tulips and red tulips, and the ratio of the number of white tulips to the number of red tulips is to be the same in each bouquet

the ration should be 1 :1 how can assume as 3:17?

"..the ratio of the number of white tulips to the number of red tulips is to be the same in each bouquet"

The above means that the RATIO of white to red tulips in EACH bouquet must be the same, say x:y in the first, second, ...

Hope it's clear.
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If you increase the number of tulips in one (or more) of the bouquets and keep the ratio (3:17), so if you put say 6 white and 34 red tulips in a bouquet, then by doing so (by increasing the number of flowers in a bouquet) you are decreasing the number of bouquets that can be made with 15 white tulips and 85 red tulips. But notice that we need "... the [i]greatest number of bouquets that can be made using all the tulips available"[/i] so we should put the lowest possible number of flowers in each bouquet to increase the number of bouquets.

Hope it's clear.
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