In a Question paper there are 4 multiple choice questions.

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Mon Apr 13, 2020 3:36 pm

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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

Answer: D
Source: Princeton Review

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8156; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: In a Question paper there are 4 multiple choice questions.

by Scott@TargetTestPrep » Fri Apr 17, 2020 3:38 am

BTGModeratorVI wrote: ↑
Mon Apr 13, 2020 3:36 pm
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

Answer: D
Source: Princeton Review

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
Founder and CEO
[email protected]

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

Re: In a Question paper there are 4 multiple choice questions.

by Brent@GMATPrepNow » Fri Apr 17, 2020 6:30 am

BTGModeratorVI wrote: ↑
Mon Apr 13, 2020 3:36 pm
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

Answer: D
Source: Princeton Review

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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