FRESH GMAT CLUB QUESTION:

A fair six-sided dice was rolled n times. What is the value of n?

(1) The number of different possible sequences of n-digit numbers when a dice is rolled n times is 7776.

(2) If the dice has been rolled 3 times fewer, the probability of getting a 6 on every roll would have been 1/36.
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We need to see if we can create an equation with only variable, n.
We'll look for an answer that gives us this information, a Logical approach.

(1) Even if we don't know that 'the number of possible sequences...' is 6^n, then we should know that this has only one solution.
That is, there is only equation that can be created from this statement and it has only one variable - n.
Sufficient.

(2) There is only one way to get a 6 on every roll so a probability of 1/36 means the total number of options is 36.
That is, at 3 less rolls the total number of possible sequences is 36.
This is almost exactly the same as (1).
Sufficient.

(D) is our answer.
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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 sufficient

Statement 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 too

Hence, answer is D
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Statement 1: 6 ^n=7776

n = 5. Since we get a unique value of n, this statement is sufficient

Statement 2:
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.

Hence, answer is D