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

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

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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.
[Reveal] Spoiler: OA

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

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New post 15 Mar 2018, 02:35
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Bunuel wrote:

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.


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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Re: A fair six-sided dice was rolled n times. What is the value of n? [#permalink]

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New post 15 Mar 2018, 05:01
Expert's post
Bunuel wrote:

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.


Question : Number of dice = ?

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

i.e. 6^n = 7776
but 6^5 = 7776 hence
n = 5
SUFFICIENT

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.[/quote]

Probability of getting a 6 on every role = 1/6
i.e. (1/6)*(1/6) = 1/36
i.e. when 3 fewer roles are thrown then 2 roles are thrown
i.e. Total Number of times the dice is rolled = 2+3 = 5
SUFFICIENT

Answer: option D
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Re: A fair six-sided dice was rolled n times. What is the value of n?   [#permalink] 15 Mar 2018, 05:01
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