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. If there are 15 white tulips and 85 red tulips available for the bouquets, what is the greatest number of bouquets that can be made using all the tulips available?
A. 3
B. 5
C. 8
D. 10
E. 13
B
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AbeNeedsAnswers
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Let's use some prime factorization...AbeNeedsAnswers wrote: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. If there are 15 white tulips and 85 red tulips available for the bouquets, what is the greatest number of bouquets that can be made using all the tulips available?
A. 3
B. 5
C. 8
D. 10
E. 13
B
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: B
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We could also say that we've got 100 flowers, forcing our bouquets to be some factor of 100.
That leaves 5 and 10 as options, but 10 won't work because we can't divide 15 bulbs into 10 bouquets without cutting them into fractions.
That leaves 5 and 10 as options, but 10 won't work because we can't divide 15 bulbs into 10 bouquets without cutting them into fractions.
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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.AbeNeedsAnswers wrote: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. If there are 15 white tulips and 85 red tulips available for the bouquets, what is the greatest number of bouquets that can be made using all the tulips available?
A. 3
B. 5
C. 8
D. 10
E. 13
B
Answer: B
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Hi All,
Here's a similar question that's based on the same logic/math:
https://www.beatthegmat.com/what-is-the- ... 58887.html
GMAT assassins aren't born, they're made,
Rich
Here's a similar question that's based on the same logic/math:
https://www.beatthegmat.com/what-is-the- ... 58887.html
GMAT assassins aren't born, they're made,
Rich
This is direct HCF question . Answer is HCF of 15 and 85 which is 5.AbeNeedsAnswers wrote: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. If there are 15 white tulips and 85 red tulips available for the bouquets, what is the greatest number of bouquets that can be made using all the tulips available?
A. 3
B. 5
C. 8
D. 10
E. 13
B
15 = 5*3
85 =5*17
so each bouquet will have 3 white tulips and 17 red tulips.
Answer is B
