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Bouquets are to be made using white tulips and red tulips, and the rat

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Bouquets are to be made using white tulips and red tulips, and the rat  [#permalink]

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New post 16 Jun 2017, 04:46
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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

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Re: Bouquets are to be made using white tulips and red tulips, and the rat  [#permalink]

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New post 16 Jun 2017, 04:53
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AbdurRakib 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


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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Re: Bouquets are to be made using white tulips and red tulips, and the rat  [#permalink]

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New post 16 Jun 2017, 04:54
Bunuel wrote:
AbdurRakib 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


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.


Similar question to practice: https://gmatclub.com/forum/what-is-the- ... 67914.html
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Re: Bouquets are to be made using white tulips and red tulips, and the rat  [#permalink]

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New post 02 Jul 2017, 06:40
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AbdurRakib 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


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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Re: Bouquets are to be made using white tulips and red tulips, and the rat  [#permalink]

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New post 03 Jul 2017, 23:09
AbdurRakib 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


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
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Re: Bouquets are to be made using white tulips and red tulips, and the rat  [#permalink]

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New post 07 Aug 2017, 10:05
AbdurRakib 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


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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Re: Bouquets are to be made using white tulips and red tulips, and the rat  [#permalink]

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New post 15 Nov 2017, 16:41
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AbdurRakib 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


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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Re: Bouquets are to be made using white tulips and red tulips, and the rat  [#permalink]

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New post 16 Sep 2018, 15:12
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
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Re: Bouquets are to be made using white tulips and red tulips, and the rat  [#permalink]

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New post 16 Sep 2018, 23:45
HCF of 85 and 15 = 5

Hence B
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Re: Bouquets are to be made using white tulips and red tulips, and the rat   [#permalink] 16 Sep 2018, 23:45
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