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.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer?

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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.

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed

Correct answer is option 'D'. Can you explain this answer?

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A fair six-sided dice was rolled n times. What is the value of n?(1) T...

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

If we roll a fair six-sided dice n times, the total number of possible outcomes would be 6ⁿ since each roll has 6 possible outcomes. Therefore, statement (1) tells us that 6ⁿ = 7776.

By taking the logarithm of both sides, we can determine the value of n. log(6^n) = log(7776), which simplifies to n log(6) = log(7776).

We can calculate log(7776) ≈ 3.89 and log(6) ≈ 0.78. Dividing both sides of the equation by log(6), we have n ≈ 3.89 / 0.78 ≈ 5.

So, statement (1) alone is sufficient to determine that n is approximately 5.

Statement (2): If the dice has been rolled 3 times fewer, the probability of getting a 6 on every roll would have been 1/36.

Let's denote the original number of rolls as n. According to statement (2), if we roll the dice n - 3 times, the probability of getting a 6 on every roll would be 1/36.

The probability of getting a 6 on a single roll of a fair six-sided dice is 1/6. Therefore, the probability of getting a 6 on every roll in n - 3 rolls would be (1/6)^{(n - 3)}.

According to statement (2), (1/6)^{(n - 3)} = 1/36.

To solve this equation, we can raise both sides to the power of -1/2, resulting in (1/6)^{(n - 3)} = (1/36)^(-1/2).

Simplifying further, (1/6)^{(n - 3)} = 6.

Taking the logarithm of both sides, we get (n - 3) log(1/6) = log(6).

Here, log(1/6) ≈ -0.78. Dividing both sides by log(1/6), we have n - 3 ≈ log(6) / (-0.78).

Approximately, n - 3 ≈ -7.69. Adding 3 to both sides, we get n ≈ -4.69.

The value of n cannot be negative, so this solution is not valid. Hence, statement (2) alone does not provide a valid solution for the value of n.

Considering both statements together, we know from statement (1) that n ≈ 5. Since statement (2) does not contradict this value, it is consistent with the value of n obtained from statement (1).

Therefore, each statement alone is sufficient to answer the question asked. The answer is (D) EACH statement ALONE is sufficient to answer the question asked.

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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.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer?

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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.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about 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.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer?.

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