BTGmoderatorDC wrote:Three dice, each with faces numbered 1 through 6, were tossed onto a game board. If one of the dice turned up 4, what was the sum of the numbers that turned up on all three dice?
(1) The sum of two of the numbers that turned up was 10.
(2) The sum of two of the numbers that turned up was 11.
Given: Three dice, each with faces numbered 1 through 6, were tossed onto a game board. One of the dice turned up 4
Target question: What was the sum of the numbers that turned up on all three dice?
Statement 1: The sum of two of the numbers that turned up was 10.
The statement is not sufficient because we cannot determine whether the
4 we already know about is among those two dice.
To better understand what I mean consider these two possible cases:
Case a: The two dice that add to 10 are 5 and 5, and the other die is the
4. In this case, the answer to the target question is
the sum = 5 + 5 + 4 = 14
Case b: The two dice that add to 10 are 6 and
4, and the other die is a 1. In this case, the answer to the target question is
the sum = 6 + 4 + 1 = 11
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The sum of two of the numbers that turned up was 11.
This statement doesn't have the same issue that statement 1 had.
Since the sum of the two mentioned dice is 11, we can be certain that those two dice are 5 and 6, since those are the only two possible values that will add to 11.
This means the three dice are 5, 6 and
4
So, the answer to the target question is
the sum = 5 + 6 + 4 = 15
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
