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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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New post 14 Mar 2018, 22:47
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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.

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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, 01:35
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, 04:01
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1
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]

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New post 24 Dec 2018, 01:38
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.


Par of GMAT CLUB'S New Year's Quantitative Challenge Set


_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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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 29 Dec 2018, 03:04
1
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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Re: A fair six-sided dice was rolled n times. What is the value of n? &nbs [#permalink] 29 Dec 2018, 03:04
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