Question

A student is taking a standardized test consisting of multiple choice questions for which there are five options for each question. Five points are awarded for each correct answer, but the student loses 2 points for an incorrect answer. Questions left blank neither receive nor lose points. What is the minimum number of options that the student should be able to rule out before making a guess on any particular question?

Answer 1

CHOOSE ONE

A Two

B None

C One

D Three

Answer 2

one [net gain per guessed q = 9*1/4 2*3/4 = 0.75 ]

Answer 3

Lets just say C as a simple answer

Answer 4

But where did you get the 9 from ?

Answer 5

Let's find the "average number of points earned" by guessing, by eliminating "x" answers.

x=1: Here we see that your odds of guessing it correctly is 1/4, and your odds of getting it wrong is 3/4. \[5 \times {1\over4} - 2 \times {3\over4} = {5\over4}-{6\over4} = -{1\over4}\]This means you'll average out to NEGATIVE 1/4, or in general, you'll be losing points whenever you make a guess after eliminating 1 answer.

x=2: Here your odds of guessing correctly are 1/3, and your odds of getting it wrong is 2/3.\[5 \times {1\over3} - 2 \times {2\over3} = {5\over3}-{4\over3} = {1\over3}\]Here your answer is POSITIVE 1/3, or in general, you'll be gaining points by making a guess after eliminating 2 answers.

Therefore your answer is TWO.

Answer 6

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