Data Sufficiency

ardz24 wrote:In a multiple-choice test, each question is followed by n options. What is the value of n?

(1) The test is designed in such a way that if a candidate appearing for the test, decides to mark the options for every question in a random manner, the candidate would expect to receive '0' marks in the test.
(2) For every correct answer, a candidate is awarded 1 mark and for every wrong answer, there are −1/3 marks assigned.

What's the best way to determine whether statement 1 is sufficient?

(1) The test is designed in such a way that if a candidate appearing for the test, decides to mark the options for every question in a random manner, the candidate would expect to receive '0' marks in the test.

We do not know how many marks are given for the correct answer and how many marks are deducted for the incorrect answer. Insufficient.

(2) For every correct answer, a candidate is awarded 1 mark and for every wrong answer, there are −1/3 marks assigned.

The mark for the correct answer = 1*1/n = 1/n
The negative mark for each incorrect answer = (-1/3)*(n - 1)/n = (1 - n )/3n; for n options, there would be (n - 1) incorrect answers.

Final score = 1/n + (1 - n )/3n; can't get n.

(1) and (2) together

We have 1/n + (1 - n )/3n = 0 => n = 4. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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