lheiannie07 wrote:A bowl is filled with consecutively numbered tiles from 1 to x. Joe pulls out a tile and uses it to construct Sequence Q, which consists of 10 consecutive integers starting with the number drawn. If Joe then selects one number from Sequence Q, what is the probability that the selected number is a multiple of 3?

(1) The last number in Sequence Q is a prime number that is less than 20.
(2) x <= 10

Case 1: The tile drawn = 1
In this case, Q = the consecutive integers between 1 and 10, inclusive.
Multiples of 3 between 1 and 10, inclusive:
3, 6, 9.
Since 3 of the 10 integers in Q are divisible by 3, the probability that a number selected from Q is a multiple of 3 = 3/10.

Case 2: The tile drawn = 2
In this case, Q = the consecutive integers between 2 and 11, inclusive.
Multiples of 3 between 2 and 11, inclusive:
3, 6, 9.
Since 3 of the 10 integers in Q are divisible by 3, the probability that a number selected from Q is a multiple of 3 = 3/10.

Case 3: The tile drawn = 3
In this case, Q = the consecutive integers between 3 and 12, inclusive.
Multiples of 3 between 3 and 12, inclusive:
3, 6, 9, 12.
Since 4 of the 10 integers in Q are divisible by 3, the probability that a number selected from Q is a multiple of 3 = 4/10.

Implication of the cases above:
If the tile drawn is NOT a multiple of 3, then the probability that a number selected from Q is a multiple of 3 = 3/10.
If the tile drawn IS a multiple of 3, then the probability that a number selected from Q is a multiple of 3 = 4/10.
Thus:
To determine whether the probability is 3/10 or 4/10, we need to know whether the tile drawn is a MULTIPLE OF 3.

Statement 1:
Test whether it's possible for the tile drawn to be a multiple of 3.
If the tile drawn = 3, then Q = the consecutive integers between 3 and 12, inclusive.
If the tile drawn = 6, then Q = the consecutive integers between 6 and 15, inclusive.
If the tile drawn = 9, then Q = the consecutive integers between 9 and 18, inclusive.
The red values indicate that -- if the tile drawn is a multiple of 3 -- the last number in Q will NOT be a prime number less than 20.
Implication:
For Statement 1 to be satisfied, the tile drawn must NOT be a multiple of 3.
SUFFICIENT.

Statement 2:
Let x=10, implying that the bowl consists of tiles numbered from 1 to 10, inclusive.
If the tile drawn from the bowl = 3, then the tile drawn IS a multiple of 3.
If the tile drawn from the bowl = 1, then the tile drawn is NOT a multiple of 3.
INSUFFICIENT.

The correct answer is A.