Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10161
GPA: 3.82
Re: When a die that has one of six consecutive integers on each
[#permalink]
15 Dec 2015, 04:50
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
When a die that has one of six consecutive integers on each of its sides is rolled twice, what is the probability of getting the number 1 on both rolls?
(1) the probability of NOT getting an eight is 1.
(2) the probability of NOT getting a seven is 25/36
In the original condition, there are 6 consecutive integers and 1 variable(you only need to know the first number of the consecutive integers), which should match with the number of equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
In 1), there are 2 cases; {1,2,3,4,5,6} and {2,3,4,5,6,7}. the probability of getting the number 1 from the both front sides is 1/36, but from the both back sides is 0, which is not unique and not sufficient.
In 2), there are a number of cases like {2,3,4,5,6,7}, {3,4,5,6,7,8}........ In all cases, the probability of getting the number 1 from the both sides is 0, which is unique and sufficient. Therefore, the answer is B.
-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.