Question: A bouquet contains 16 flowers, each of them either a rose, tulip, daisy, or daffodil. If no two types of flower appear the same number of times in the bouquet, and there are more tulips than any other type of flower, what is the minimum number of tulips?

1. 4
2. 5
3. 6
4. 7
5. 8

Correct Answer: C
Solution and Explanation:
Approach Solution 1:
Total flowers are 16.

Variety: Rose(R), Tulip(T), Daisy(Da), or Daffodil(Df).

Conditions: no two types of the flower appear the same number of times in the bouquet (All appears distinctively).
and More tulips than any other type of flower.

If we suppose each flower appears equal then: 16/4= 4

T= 4 ; R= 4 ; Da= 4 ; Df= 4
=> Tulips are more and no two appear the same number of times.
=> T = 7 ; R = Da = Df = 3 but no two appears same and we need minimum number possible for Tulip
=> T = 6 ; Others will be 5,4, 1 or 5, 3 , 2 .

Approach Solution 2:
Test option A. 4 cannot be the answer for tulips as there will be at least 1 greater than or equal to tulips.
Test option B. 5 cannot be the answer for tulips. 16-5= 11. There will be at least 1 other type equal or greater than tulip.
Test option C. 6 can be the answer. Since 16-6 = 10. For example tulips = 6, rose = 5, daisy = 3 and daffodil = 2. 6+5+3+2 =16

Approach Solution 3:
Since either is said, none of the varieties can have '0' flowers.
Hence the least any variety can have is '1'. But as the number of tulips are more than any other and minimum(integers) is asked, we need to put as low a number for tulips and as high a number for other varieties i.e. the numbers of flowers of the four varieties would be near to each other.
So, either we can test numbers from the options or go for hits and trials(brute force) or go for 4(16/4) and test various numbers.

Therefore, the number of tulips has to be more than 4 since 1 + 2 + 3 + 4 ≠ 16
Also, 5 is not possible since we can't repeat numbers to sum 16.
6, with a combination of 1, 2, 3, 4 and 5, is possible to sum 16 - 1, 4, 5, 6.

“A bouquet contains 16 flowers, each of them either a rose, tulip”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

Suggested GMAT Problem Solving Samples

• There are 12 Pipes that are Connected to a Tank. Some of them are fill GMAT Problem Solving
• A wire is cut into three equal parts. The resulting segments are then cut GMAT Problem Solving
• If x = -3, What Is The Value Of -3x^2? GMAT Problem Solving
• A Trader Has 400 kg 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 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
• In United States Currency, a Nickel is Worth 5 Cents 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 When\( 2^{99}\) is Divided by 99? GMAT Problem Solving
• The First Five Numbers in a Regular Sequence are 4, 10, 22, 46, and 94 GMAT Problem Solving
• A Bar is Creating a New Signature Drink. There are Five possible Alcohol GMAT Problem Solving
• A Can Complete a Certain Job in 12 Days. B is 60% More Efficient than GMAT Problem Solving
• An Alloy of Gold,Silver and Bronze Contain 90% Bronze, 7% Gold and GMAT Problem Solving
• When Positive Integer n is Divided by 5, the Remainder is 1 GMAT Problem Solving
• A is Thrice as Efficient as B and Hence Takes 12 Days Less to Complete GMAT Problem Solving
• A Tank is Filled by Three Pipes with Uniform Flow. The First Two Pipes GMAT Problem Solving
• Each Person in a Group of 110 Investors Has Investments in Either GMAT Problem Solving
• Jim Travels the First 3 Hours of His Journey at 60 mph Speed GMAT Problem Solving
• A Committee Of 7 Members Is To Be Formed To Put Up The Christmas GMAT Problem Solving
• In A Class Of 60 Students, 23 Play Hockey, 15 Play Basketball GMAT Problem Solving
• The Area Of An Equilateral Triangle With Side Length X Is The Same GMAT Problem Solving
• Which Of The Following Has A Decimal Equivalent That Is A GMAT Problem Solving
• A Number when Divided by a Divisor Leaves a Remainder of 24 GMAT Problem Solving
• How many Integers Less than 1000 have no Factors (other than 1) GMAT Problem Solving
• How Many Prime Numbers are there Between 50 and 70? GMAT Problem Solving
• If a Circle Passes through Points (1, 2) (2, 5), and (5, 4) GMAT Problem Solving
• If the Perimeter of Square Region S and the Perimeter of Rectangular GMAT Problem Solving
• If x^9= 9^9^9, What is the Value of x? GMAT Problem Solving
• In a Competition, a School Awarded Medals in Different Categories GMAT Problem Solving
• In How Many Ways can 5 Apples (Identical) be Distributed Among 4 Children? GMAT Problem Solving
• What is Greatest Positive Integer n such that 2^n is a Factor of 12^10? GMAT Problem Solving
• All The Five Digit Numbers In Which Each Successive Digit Exceeds Its GMAT Problem Solving
• A Box Contains Two White Balls, Three Black Balls And Four Red Balls GMAT Problem Solving
• Consider An Obtuse-Angled Triangles With Sides 8 Cm, 15 Cm GMAT Problem Solving
• I Travel The First Part Of My Journey At 40 Miles Per Hour GMAT Problem Solving
• Profit Earned By Selling An Article At 1060 Is 20 % More Than The Loss GMAT Problem Solving
• A Perfect Square is a Number that Becomes an Integer when Square GMAT Problem Solving
• If x + y = 2 and x^2 + y^2 = 2, What is the Value of xy? GMAT Problem Solving
• In How Many Ways The Letter Of The Word "Family" Can Be When GMAT Problem Solving
• A Fair Coin Is Tossed 4 Times. What Is The Probability Of Getting At GMAT Problem Solving
• In A Sequence 1, 2, 4, 8, 16, 32, ... Each Term After The First Is Twice GMAT Problem Solving
• What Is The Sum Of Odd Integers From 35 To 85, Inclusive? GMAT Problem Solving
• If 2p + 1/p = 4, Then what is the Value of p^3 + 1/8p^3 ? GMAT Problem Solving