Question: A candidate is required to answer 6 out of 10 questions divided into 2 groups each containing 5 questions. He can attempt maximum 4 questions from each group. In how many ways can he make up his choice ?
(A) 660
(B) 566
(C) 260
(D) 200
(E) 100
Correct Answer: D
Solution and Explanation:
Approach Solution 1:
So two sets of 5 questions each. We are looking at ways to select these 6 questions.
Thus, a combination question.
Two ways
1) 5C4*5C2=5*10=50.
Vice versa too is possible, so another 50.
2) 5C3*5C3=10*10=100
Total: 50+50+100= 200
Approach Solution 2:
We can split the two groups into group A and group B, thus the groups are independent.
We need to answer 6 questions while picking more than 4 from any group, so we can do 4 + 2, 3 + 3, or 2 + 4. This corresponds to :
5C4∗5C2+5C3∗5C3+5C2∗5C4=5∗10+10∗10+10∗5= 200
Approach Solution 3:
Solution:
The question can be answered in one of the following cases:
1) 4 questions from group one and 2 questions from group two
2) 3 questions from group one and 3 questions from group two
3) 2 questions from group one and 4 questions from group two
The two groups have the same number of questions. Therefore, the number of ways to answer the questions in case 3 is the same as in case 1. Now, let’s determine the number of ways to answer the questions in the first two cases:
Case 1: 4 questions from group one and 2 questions from group two
5C4 x 5C2 = 5 x 10 = 50
Case 2: 3 questions from group one and 3 questions from group two
5C3 x 5C3 = 10 x 10 = 100
Case 3:
(gives the same result as Case 1), or 50
Therefore, the answer to the questions in 50 + 100 + 50 = 200 ways.
“A candidate is required to answer 6 out of 10 questions divided into 2”- 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
- Which of the Following is Equal to x^18 For All Positive Values of x? GMAT Problem Solving
- 16 Ounces of Fresh Orange Juice Contains 216 Calories GMAT Problem Solving
- An Urn Contains 6 Red, 4 Blue, 2 Green and 3 Yellow marbles GMAT Problem Solving
- The price of raw materials has gone up by 15%, labour cost has also increased GMAT Problem Solving
- In a Class of 100 Students 70 Passed in Physics, 62 Passed in Mathematics, GMAT Problem Solving
- If x and y Are Positive Odd Integers, And Both Numbers Have An Odd Number Of Positive Divisors GMAT Problem Solving
- Copper Pipe Costs x Cents Per Foot in 8-Foot Lengths GMAT Problem Solving
- Find The Smallest Positive 4-Digit Number Which, When Increased by 8, is Divisible by 12, 18, 30, and 45 GMAT Problem Solving
- How Much Pure Alcohol Should Be Added To 400 ml of a 15% Solution To Make The Strength Of The Solution 32%? GMAT Problem Solving
- 16 Ounces of Birdseed Mix Contains 10% Sesame Seed by WeightGMAT Problem Solving
- The Diameter of Circle S is Equal in Length to a Side of a Certain Square GMAT Problem Solving
- In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. GMAT Problem Solving
- If The Sum of 9 Consecutive Integers is 90 GMAT Problem Solving
- If a Carton Containing a Dozen Mirrors is Dropped GMAT Problem Solving
- The Number 2 - 0.5 is How Many Times the Number 1 - 0.5? GMAT Problem Solving
- If n = 3, What is The Value of 2^2n+1? GMAT Problem Solving
- A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain GMAT Problem Solving
- In a Group of 6 Boys and 4 Girls, Four Children Are to be Selected GMAT Problem Solving
- Which of the Following Fractions has a Decimal Equivalent that is a Terminating Decimal? GMAT Problem Solving
- The Price of Onions Increases by 25%, by what Percent should a Housewife Reduces the Consumption GMAT Problem Solving
- A and B are Two Alloys of Gold and Copper Prepared By Mixing Metals in GMAT problem Solving
- For integers x and y, 2^x+2^y=2^30. What is the value of x+y? GMAT Problem Solving
- United Telephone charges a base rate of $10.00 for service, plus an additional charge of $0.25 per minute. GMAT Problem Solving
- Lamp A Flashes Every 6 seconds, Lamp B Flashes Every 8 seconds, Lamp C Flashes Every 10 seconds GMAT Problem Solving
- At a Sandwich Shop, There are 2 Breads, 3 Kinds of Meat, 4 Types of Cheeses GMAT Problem Solving
- A Survey was Conducted Among 1000 People to Know About their Eating Habits GMAT Problem Solving
- Jake Rides His Bike for the First 2/3 of the Distance From Home to School GMAT Problem Solving
- Two Trains Running in Opposite Directions Cross a Man Standing on the Platform GMAT Problem Solving
- Initial Population of a Town was 8000 People GMAT Problem Solving
- The Volume of a Sphere with Radius r is (4/3)*pi*r^3. A Solid Sphere GMAT Problem Solving
- Which of the Following is Equal to 5^17×4^9? GMAT Problem Solving
- In a Shooting Competition, Probability of A Hitting Target is 2/5, by B is 2/3 and C is ⅗ GMAT Problem Solving
- The Sides of a Quadrilateral Taken in Order are 16,16,14 and 10 GMAT Problem Solving
- If 80 Lamps Can Be Lighted, 5 Hours Per Day For 10 Days GMAT Problem Solving GMAT Problem Solving
- If
denotes the area of a circle with diameter d, then which of the following is equal to <4>*<6> GMAT Problem Solving - At exactly what time past 7:00 will the minute and hour hands of an accurate working clock be precisely GMAT Problem Solving
- There is a 120 Liter Mixture of Alcohol and Water GMAT Problem Solving
- When X Is Divided By 13, The Answer Is Y With a Remainder of 3. GMAT Problem Solving
- If a/b = 2/3 Which of the Following is Not True? GMAT Problem Solving
- 1/3 of the Cookies in a Jar are Chocolate Chip, 2/3 of the Remaining Cookies are Peanut Butter GMAT Problem Solving
- The Kinetic Energy K, in Joules, Provided by the Mass of a Particle m GMAT Problem Solving
- A Recent Survey Showed That 50 Percent of People Polled Believe that Elected Officials Should Resign GMAT Problem Solving
- The Perimeter of a Square is Equal to the Perimeter of a Rectangle Whose Length And Width are 6m and 4m Respectively GMAT Problem Solving
- The Closing Price of Stock X Changed on Each Trading Day Last Month GMAT Problem Solving
- An Exam Consists of 8 True/False Questions GMAT Problem Solving
- From her Collection of 9 Different Hats Ellen Wants to Wear one Different Hat GMAT Problem Solving
- Company C Sells a Line of 25 Products with an Average Retail Price of $1,200 GMAT Problem Solving
- A Man has 1044 Candles. After Burning, He can Make a New Candle GMAT Problem Solving
- An Equilateral Triangle ABC is Inscribed in Square ADEF GMAT Problem Solving
- A Popular Website Requires Users to Create a Password Consisting of Digits Only GMAT Problem Solving
Comments