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.
OA B
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Three dice, each with faces numbered 1 through 6, were
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BTGmoderatorDC
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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.
Information provided is One of Dice rolled 4.
In (1) , Sum of the 2 of the numbers that turned up was 10. We can get combination with 1st dice that rolled 4 and any of 2nd or 3 dice if they roll 6. For Instance suppose 2nd dice rolled 6. 1st+2nd is 10 which satisfies condition in (1) but 3rd dice can roll any number 1 to 6. So we cannot get definite value of sum of numbers turned up on all 3 dice.
In (2) Sum of 2 numbers turned up was 11. Because 1st dice rolled 4, we can cannot have combination of 11 with 1st dice (2nd or 3 dice cant roll 7) . So 11 is only possible with combination of 2nd and 3rd dice. 2 combination 5 and 6 and 6 and 5 are only possible . So 4+ 5+6 =15 or 4+6+5 =15 is sum of numbers that turned up on all three dice,
Answer is B, Option (2) by itself is sufficient to answer the question.
OA B
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Given: Three dice, each with faces numbered 1 through 6, were tossed onto a game board. One of the dice turned up 4BTGmoderatorDC 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.
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
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Brent
Brent Hanneson - Creator of GMATPrepNow.com
