GMAT 700+ Quant Practice Question 22

Counting Methods | Permutation Combination Practice | GMAT Sample Questions

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

Get to Q51 in GMAT Quant


Online GMAT Course
@ INR 3000


Video Explanation


GMAT Live Online Classes


Next Batch | December 3, 2020


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

Section Possibility 1 Possibility 2 Possibility 3
Section 1 4 3 2
Section 2 2 3 4

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.

GMAT Online Course - Quant
Try it free!

Register in 2 easy steps and
Start learning in 5 minutes!

★ Sign up for Free

Already have an Account?

★ Login to Continue

GMAT Live Online Classes

Next Batch Dec 3, 2020

★ GMAT Live Info

GMAT Coaching in Chennai

Next Integrated (Online + Offline) GMAT Batch
Dec 3, 2020

★ GMAT Class Info

GMAT Hard Math Videos On YouTube


GMAT Sample Questions | Topicwise GMAT Questions


Where is Wizako located?

Wizako - GMAT, GRE, SAT Prep
An Ascent Education Initiative
48/1 Ramagiri Nagar
Velachery Taramani Link Road.,
Velachery, Chennai 600 042. India

How to reach Wizako?

Phone: (91) 44 4500 8484
Mobile: (91) 95000 48484
WhatsApp: WhatsApp Now
Email: learn@wizako.com
Leave A Message