GMAT 700+ Quant Practice Question 22

The given question is a challenging GMAT 700+ level quant problem solving question testing concepts in permutation combination (counting methods). A very interesting practice question to understand how to list down possibilities and then count outcomes for each of those possibilities.

Question 22: A student is required to solve 6 out of the 10 questions in a test. The questions are divided into two sections of 5 questions each. In how many ways can the student select the questions to solve if not more than 4 questions can be chosen from either section?

1. 100
2. 210
3. 150
4. 200
5. 105

Video Explanation

Explanatory Answer | GMAT Permutation Combination Practice Question

Step 1: List Down Possibilities

The student is required to solve 6 out of 10 questions.
Questions are divided into 2 sections of 5 questions each.
Not more than 4 questions can be selected from any section.

Step 2: List Down Possibilities

Step 3: Count Number of Outcomes for each Possibility and Add

Possibility 1: Section 1: 4 Questions | Section 2: 2 Questions
This can be done in 5C₄ × 5C₂ = 5 × 10 = 50 ways

Possibility 2: Section 2: 3 Questions | Section 2: 3 Questions
This can be done in 5C₃ × 5C₃ = 10 × 10 = 100 ways

Possibility 3: Section 1: 2 Questions | Section 2: 4 Questions
This can be done in 5C₂ × 5C₄ = 10 × 5 = 50 ways

Total number of ways = 50 + 100 + 50 = 200 ways

Choice D is the correct answer.

The video solution also includes an alternative approach to solve this question.