Bouquets are to be Made Using White Tulips and Red Tulips GMAT Problem Solving

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.

Suggested GMAT Problem Solving Samples

• If ^5\sqrt{-37} then Which of the Following Must be True? GMAT Problem Solving
• Given (x^3 + 12x)/(6x^2 + 8) = (y^3 + 27y)/(9y^2 + 27) GMAT Problem Solving
• If today is Monday, what day of the week will it be in 347 days? GMAT Problem Solving
• What is the unit’s digit of {(7^3)^4 - (1973^3)^2} ? GMAT Problem Solving
• Jacob is Now 12 Years Younger than Michael. If 9 Years from Now Michael GMAT Problem Solving
• A Metal Company's Old Machine Makes Bolts at a Constant Rate of 100 GMAT Problem Solving
• A Husband and Wife, Started Painting their House, but Husband Left GMAT Problem Solving
• A Circular Clock has a Minute Hand Measuring 12 Inches Long GMAT Problem Solving
• When a Rectangular Vat that is 3 Feet Deep is Filled to 2/3 of its Capacity GMAT Problem Solving
• If the Tens Digit x and the Units Digit y of a Positive GMAT Problem Solving
• ABCD is a Trapezium, in which AD and BC are Parallel. If the Four Sides GMAT Problem Solving
• If 9^(x−1/2) –2^(2x–2) = 4^x – 3^(2x–3), then What is the Value GMAT Problem Solving
• Solve for x: 0<|x|-4x<5 = ? GMAT Problem Solving
• After the division of a number successively by 3, 4, and 7 GMAT Problem Solving
• If x^2−5x+6=2−|x−1|, what is the product of all possible values of x? GMAT Problem Solving
• What is the value of square root{25 + 10square root(6)} + square root{25 - 10square root(6)} GMAT Problem Solving
• In the figure shown above, what is the perimeter of parallelogram ABCD GMAT Problem Solving
• Which of the Following Represents the Range for all x Which Satisfy Inequality GMAT Problem Solving
• If the length of the longest chord of a certain circle is 10, what is GMAT problem solving
• A restaurant buys fruit in cans containing 3 1/2 cups of fruit each GMAT problem solving
• If 65 Percent of a Certain Firm’s Employees are Full-Time GMAT Problem Solving
• What is the Remainder When 3^24 is Divided by 5? GMAT Problem Solving
• A={1,2,3,4,5} is Given. If There are 1,2,…,n Subsets of A, Let A1 GMAT Problem Solving
• If 100 Centimetres = 1 Meter, then What is the Value of 100 Centimetre GMAT Problem Solving
• A Positive Integer x is Divisible by 2,3, and 5. What is The Smallest GMAT Problem Solving
• A Solid Metallic Cube is Melted to Form Five Solid Cubes Whose Volumes GMAT Problem Solving
• At a Supermarket, John Spent 1/2 of his Money on Fresh Fruits GMAT Problem Solving
• Positive Integer y is 50 Percent of 50 Percent of Positive GMAT Problem Solving
• A Pizza Can be Assembled from Given Choices, with Customer’s GMAT Problem Solving
• If y= 4 + (x - 3)^2, Then y is Lowest When x = GMAT Problem Solving
• What is the Value of w in Terms of x and y GMAT Problem Solving
• A New Flag is to be Designed with Six Vertical Stripes Using Some GMAT Problem Solving
• If x^2 + 1/x^2 = 4, What is the Value of x^4 + 1/x^4 GMAT Problem Solving
• A Dog Breeder Currently has 9 Breeding Dogs. 6 of the Dogs have GMAT Problem Solving
• The interior angles of a convex polygon are in arithmetic progression GMAT Problem Solving
• (x^2 + 2x - 8)/(x^2 - 6x + 8) = ? GMAT Problem Solving
• Which of the following is equal to the average (arithmetic mean) GMAT Problem Solving
• A trader has 400kg of rice, a part of which he sells at 36% GMAT Problem Solving
• A Number, x is Chosen at Random from the Set of Positive Integers Less GMAT Problem Solving
• Which of the following could be the area of an isosceles triangle with GMAT problem solving
• After M Students Took a Test, There was a Total of 64% GMAT Problem Solving
• Perimeter of a Triangle with Integer Sides is Equal to 15 GMAT Problem Solving
• PQRS is a Quadrilateral Whose Diagonals are Perpendicular to Each Other GMAT Problem Solving
• Which of the following is closest to (10.001)^2 ? GMAT Problem Solving
• A Train of Length L is Traveling at a Constant Velocity and Passes a Pole GMAT Problem Solving
• A circle is inscribed in an equilateral triangle of side 24 cm GMAT Problem Solving
• After 200 grams of water were added to the 24%- solution of alcohol GMAT Problem Solving
• Which of the following numbers is a perfect square? GMAT Problem Solving
• What is 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + 1/(5*6) + 1/(6*7) GMAT Problem Solving
• What is the Remainder When2^99 is Divided by 99? GMAT Problem Solving