Question: A mixed doubles tennis game is to be played between two teams. There are four married couples. No team is to consist of a husband and his wife. What is the maximum number of games that can be played.
- 12
- 21
- 36
- 42
- 46
Correct Answer: D
Solution and Explanation:
Approach Solution 1:
One married couple only:
Select one married couple out of 4 in 4C1 ways.
Select one male for the other team in 3 ways and one non-wife female in 2 ways.
Number of games with only one married couple = 4*3*2 = 24
Both married couples
Select 2 married couples in 4C2 = 6 ways
Number of games in which at least there will be one couple = 24+6 = 30
Total number of games = (4*4 * 3*3)/2 = 72
Select team 1 in 4*4 ways and team 2 in 3*3 ways. Divide by 2 because you don't want to arrange the teams in team 1 and team 2. They are just 2 teams.
So in 72 - 30 = 42 games, there will be no married couple.
Approach Solution 2:
Married couples: MF MF MF MF
ab cd ef gh
Possible teams: ad cd eb gb
af cf ed gd
ah ch eh gf
Now, team ad can play only with: cb, cg, ch, eb, eh, gb, gf, i.e. 7
The same will apply with all teams.
So no. of total match = 12 × 7 = 84
Since every match includes 2 teams,
so the no. of matches = 84/2 = 42
Approach Solution 3:
After we have chosen the pair of husbands, A and B:
We can choose a and b and we have to pair them as (A,b) and (B,a) - 1 possibility.
We can choose one of the wives, a or b, but we have to pair her with the other husband and in addition, we have to choose another partner for the second husband.
This we can do in 2*2 = 4 ways, as there are two possibilities to choose from a and b, then we have 2 possibilities to choose the other wife, c or d - 4 possibilities
Finally, we can choose the other two wives, c and d, and we have two possibilities to team them up with the men, (A,c), (B,d) or (A,d), (B,c) - 2 possibilities.
In conclusion, for every pair of husbands, we have 1 + 4 + 2 = 7 possibilities to choose their partners for the game.
Total number of possibilities 6 * 7 = 42.
“A mixed doubles tennis game is to be played between two teams.”- 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 Questions
- If p#q Denotes the Least Common Multiple of p and q, Then ((12#16) GMAT Problem Solving
- The Smallest of Six Consecutive Odd Integers Whose Average (arithmetic mean) is x + 2 GMAT Problem Solving
- The Greatest 6-Digit Number When Divided by 6, 7 ,8 , 9, and 10 Leaves a Remainder of 4, 5, 6, 7, and 8 Respectively GMAT Problem Solving
- Is Zero Even Integer or Odd Integer? GMAT Problem Solving
- If 20 Men or 24 Women or 40 Boys can do a Job in 12 Days GMAT Problem Solving
- If 10 millimeters equal 1 centimeter, how many square centimeters does 1 square millimeter equal?
- How many Terminating Zeroes does 200 Have GMAT Problem Solving
- Properties of Circle GMAT Problem Solving
- If 10, 12 and ‘x’ are Sides of an Acute Angled Triangle, How Many Integer Values of ‘x’ are Possible? GMAT Problem Solving
- For How Many Values of k is 12^12 the Least Common Multiple GMAT Problem Solving
- Two Vessels A and B Contain Milk and Water Mixed in the Ratio 8:5 GMAT Problem Solving
- A Dealer Offers a Cash Discount of 20%. Further, a Customer Bargains GMAT Problem Solving
- There are Two Vessels A and B. Vessel A is Containing 40 Litres of GMAT Problem Solving
- At A Certain Fruit Stand, The Price Of Each Apple Is 40 Cents GMAT Problem Solving
- The Coordinates Of Vertices P And Q Of An Equilateral Triangle PQR Are GMAT Problem Solving
- A Certain Roller Coaster has 3 Cars, and A Passenger is Equally Likely GMAT Problem Solving
- A Manufacturer Produces a Certain Men's Athletic Shoe in GMAT Problem Solving
- In The Figure Shown Below, The Area of Square Region ACEG is 729 GMAT Problem Solving
- How Many Dimes are There in 4x - 1 Cents? (1 dime = 10 cents) 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
- 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
- There Were R Red Balls And Y Yellow Balls In A Bag. Three Red Balls GMAT Problem Solving
- With An Average Speed Of 40 Km/H, A Train Reaches Its Destination On GMAT Problem Solving
- A Photographer Will Arrange 6 People Of 6 Different Heights GMAT Problem Solving
- What Is The Radius Of The Incircle Of The Triangle Whose Sides Measure GMAT Problem Solving
- The Value Of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 Is GMAT Problem Solving
- Points A And B Are 120 Km Apart. A Motorcyclist Starts From GMAT Problem Solving
- A student took five papers in an examination, where the full marks GMAT Problem Solving
- In how many ways can letters the word ATTITUDE be rearranged such that GMAT Problem Solving
- A merchant mixes three varieties of rice costing $20/kg, $24/kg GMAT Problem Solving
- ABC is an equilateral triangle, and point D is the midpoint of side BC GMAT Problem Solving
- A Batsman Makes a Score of 87 Runs in the 17th Match and Thus Increases GMAT Problem Solving
- If M= √4+3√4+4√4, Then the Value of M is GMAT Problem Solving
- An Octagon Is Inscribed In A Circle As Shown Above. What Of The Area GMAT Problem Solving
- In a Company of Only 20 Employees, 10 Employees make $80,000/yr GMAT Problem Solving
- A bag contains blue and red balls only GMAT Problem Solving
- (4.8*10^9)^(1/2) is closest in value to GMAT Problem Solving
- What Is The Units Digit Of 2222^333 ∗ 3333^222? GMAT Problem Solving
- What Is The Tens Digit Of 6^17? GMAT Problem Solving
- If m=−2, What Is −m^(−m)? GMAT Problem Solving
- An Automated Manufacturing Plant Uses Robots To Manufacture Products GMAT Problem Solving
- The Surface Distance Between 2 Points on the Surface of a Cube is the GMAT Problem Solving
- The Average Monthly Expenditure of a Family for the First Four Months GMAT Problem Solving
- When a Certain Perfect Square is Increased by 148, the Result is GMAT Problem Solving
Comments