In a Question paper there are 4 multiple choice questions.

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

In a Question paper there are 4 multiple choice questions.

by BTGmoderatorLU » Sat Nov 23, 2019 3:17 am

Source: Princeton Review

In a question paper, there are 4 multiple-choice questions. Each question has 5 choices with only one choice as the correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?

A. 19
B. 85
C. 120
D. 624
E. 1024

The OA is D

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Source: Beat The GMAT — Problem Solving | Sat Nov 23, 2019 3:17 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sat Nov 23, 2019 7:11 am

BTGmoderatorLU wrote:Source: Princeton Review

In a question paper, there are 4 multiple-choice questions. Each question has 5 choices with only one choice as the correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?

A. 19
B. 85
C. 120
D. 624
E. 1024

The OA is D

Let's first determine the TOTAL number of ways the test can be completed.
The 1st question can be answered in 5 different ways (A, B, C, D, or E).
The 2nd question can be answered in 5 different ways (A, B, C, D, or E).
The 3rd question can be answered in 5 different ways (A, B, C, D, or E).
The 4th question can be answered in 5 different ways (A, B, C, D, or E).

By the Fundamental Counting Principle (FCP), the total number of ways we can complete test = (5)(5)(5)(5) = 625 ways

So, there 625 possible outcomes
Among those 625 possible outcomes, ONLY 1 outcome is such that all four questions ARE answered correctly.
This means, in the remaining 624 outcomes, the four questions are NOT all answered correctly.

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

by deloitte247 » Fri Nov 29, 2019 7:03 am

Total questions = 4
For each question, there are 5 choices
Total possible selection for each question = 5
This means 4 different questions can be answered in 5 different ways
Therefore, the total ways in which all questions can be answered = $$5^4=5\cdot5\cdot5\cdot5=625$$
Given that only ONE choice is the correct answer
The possible outcome for a wrong answer = 625 - 1 = 624
Answer = option D

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Dec 08, 2019 7:37 pm

BTGmoderatorLU wrote:Source: Princeton Review

In a question paper, there are 4 multiple-choice questions. Each question has 5 choices with only one choice as the correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?

A. 19
B. 85
C. 120
D. 624
E. 1024

The OA is D

We can use the following equation:

Total number of ways to answer all questions - number of ways to get all questions correct = the total number of ways in which a candidate will not get all four answers correct

5 x 5 x 5 x 5 - 1 x 1 x 1 x 1 = 625 - 1 = 624

Answer: D

Scott Woodbury-Stewart
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