There are 12 Yes or No Questions. How Many Ways can these be Answered? GMAT Problem Solving

Question: There are 12 yes or no questions. How many ways can these be answered? (Assume that each question must be answered either YES or NO)

1. 144
2. 1024
3. 2048
4. 4096
5. 12!

“There are 12 yes or no questions. How many ways can these be answered?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Premier 2017 with 6 Practice Tests”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:
Approach Solution 1:

Given

In this question, we are given that

• There are 12 yes or no questions
• Each question must be answered either YES or NO

To find

We need to determine

• The number of ways the questions can be answered

Approach and Working out

As each question can be answered either YES or NO, for each question there are 2 choices.
(question 1 can be answered in 2 ways AND question 2 can be answered in 2 ways AND so on…)

Hence, for 12 questions, the total number of choices = 2^12 = 4096

Correct Answer: D

Approach Solution 2:

Since there are 12 questions, and each question can be answered in 2 ways then:

The 1st question can be answered in 2 ways.
The 2nd question can be answered in 2 ways.

The 2 questions can be answered in 2×2 ways.

The 3 questions can be answered in 2×2×2 ways and so on.

So we have:

2×2×2×2×2×2×2×2×2×2×2×2⇒2^12= 4096

Correct Answer: D

Approach Solution 3:

Each of the questions can be answered in 2 ways (yes or no)
Therefore, no. of ways of answering 12 questions = 212 = 4096 ways.

Correct Answer: D

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