Question: 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?

1. 3
2. 5
3. 8
4. 10
5. 13

Correct Answer: B
Solution and Explanation:
Approach Solution 1:

The problem statement states that:

Given:

• Bouquets are to be made using white tulips and red tulips.
• The ratio of the number of white tulips to the number of red tulips is to be the same in each bouquet.
• There are 15 white tulips and 85 red tulips available for the bouquets.

Find out:

• The greatest number of bouquets can be made using all the tulips available.

As per the problem statement, it is required to use all the tulips available.
Therefore, the number of bouquets needs to be a factor of both 15 and 85.
Because we need to make use of all the tulips at our disposal, the number of bouquets must be a figure that is equal to either 15 or 85
To solve this problem we have to find the greatest common factor of 15 and 85.
For instance, we cannot hold 2 bouquets since we cannot divide 15 white tulips into 2 bouquets without one tulip left over.
Therefore, the greatest common factor of 15 and 85 is 5.
Hence, the greatest number of bouquets can be made using all the tulips available = 5.

Approach Solution 2:

The problem statement informs that:

Given:

• Bouquets are to be made using white tulips and red tulips.
• The ratio of the number of white tulips to the number of red tulips is to be the same in each bouquet.
• There are 15 white tulips and 85 red tulips available for the bouquets.

Find out:

• The greatest number of bouquets can be made using all the tulips available.

In the first step, there are 15 white tulips and 85 red tulips available for use in bouquets. To make the bouquets out of these tulips, we need to use the same proportion of white tulips and red tulips. We need to utilise the 15 white tulips and 85 red tulips that are given.

In the second step, the question states that there can be no leftover tulips and all of those that are available must be utilized. The number of bouquets that may be made must be a factor in the total number of tulips. As a result, the highest potential common factor of 15 white tulips and 85 red tulips may be found by using the following calculation:

Let’s do the prime factorisation of 15 and 85.
15 = 3 x 5
85 = 5 x 17

The number 5 is shared by both 15 and 85. Because of this, the highest number of bouquets that may be created using all the tulips available is 5.

Approach Solution 3:

The problem statement informs that:

Given:

• Bouquets are to be made using white tulips and red tulips.
• The ratio of the number of white tulips to the number of red tulips is to be the same in each bouquet.
• There are 15 white tulips and 85 red tulips available for the bouquets.

Find out:

• The greatest number of bouquets can be made using all the tulips available.

As per the given conditions of the problem statement: all tulips should be used, and the ratio of white to red flowers in each bouquet must be the same.
Therefore, the ratio of white to red flowers in each of the bouquets must be equal to 15:85 or 3:17.

Hence, the number of white tulips in each bouquet = 3x and the number of red tulips in each bouquet = 17x (where x is an integer).
Therefore, each bouquet contains 3x + 17x = 20x tulips.

It is recommended that we should take x as little as possible so that we can produce the greatest number of flowers.
In this case, since the quantities of tulips cannot be 0 or a negative number, the least integer value of x might possibly be 1.
Then, there are a total of 20(1) = 20 tulips in each bouquet, and there is no more than 100/20 = 5 bouquets total.

Hence, the greatest number of bouquets can be made using all the tulips available = 5.

“Bouquets are to be made using white tulips and red tulips”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “GMAT Official Guide 2022”. GMAT Problem Solving questions encourage the candidates to evaluate every condition of the question in order to crack numerical problems. GMAT Quant practice papers assist the candidates to go through several sorts of questions that will enable them to enhance their mathematical understanding.

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