What made me really think about this question is the wording of statement 2. It took me a seconds to understand what it meant.
Let's break this down
Statement 1: This statement is essentially asking for the number of different possibilities that can come when a dice is rolled n times.
The number of possibilities is 7776
Now, if a die is rolled once, the number of possibilities is 6. And if rolled twice, possibilities are 6*6 (i.e. \(6^2\))
Thus, in our case \(6^n\)=7776
Now, its a matter of using basic arithmetic to get value of n which turns out to be 5. Since we get a unique value of n,
this statement is sufficientStatement 2: Now, if we were to roll a dice once, the probability of getting number 6 on it would be 1/6 (number of favourable possible outcomes/total possible outcomes).
Thus, for probability to be 1/36, the die has to be rolled twice with each time giving us number 6 on the face of the die (1/6*1/6)
Now, this number (i.e. 2) is 3 less than n. Thus n=5. Since we get a unique value of n,
this statement is sufficient tooHence, answer is D
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