Three dice, each with faces numbered 1 through 6, were tossed onto a

Let there be three numbers D1,D2 and D3
D1=4
There are two possibilties for statement one...
(5,5,4) and (4,6,anything)
If D1=4 and D2=6 then D3 can be anything and we cannot find the sum.
Hence statement 1 is insufficient.

For statement 2...there is only one combination for making 11 i.e. (4,5,6)
Here we have two combinations
1. D1=4 D2=5 D3=6
2 D1=4 D2=6 D3=5
but since in both cases the sum is 15...hence statement 2 is sufficient.

The question conditions you to think of one case and ignores the case as provided by bunuel I fell for the trap answer choice.

From question: One Dice was 4.

(1) Two of the dice add up to 10. Hence it could be the original 4 + 6 of the second dice and any number on the third dice. IS.
(2) Original: 4. Thus it is impossible for this Dice to be one of the dice which give us the sum 11. hence we have first dice 4 and the other 2 dice 5 and 6. Suff. B.

Pretty straightforward.
From S1:We could have diff combinations like 4,6,2 or 4,6,3 that'd give us a different answer for sum of all three.Not suff.

From S2:If 2 numbers add up to be 11 the dice with 4 on top wont be there in these 2.So it's only possible that sum of nos. on other 2 dice is 11 in which case total of all three is 15.Suff.

Option B.

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When testing (1), you have two possible answers: you rolled the identified 4 and a 6 and an unknown 3rd die or you rolled the identified 4 and a 5 and a 5. (1) is insufficient to answer to sum of all 3 dice.

When testing (2), you only have one possible answer: the maximum value of each die is 6 so the sum of the two numbers that equal 11 cannot include the identified 4 die because there are no 7 value dice. So the only combination of two dice that sums 4 is 5 and 6. Because we don't care which die is 5 or 6, only in the summed value, we can answer the original question with only statement (2) thus the answer would be B.

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

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.

The sum of two can be (5, 5), (4,6), etc. There are many options. INSUFFICIENT.

(2) The sum of two of the numbers that turned up was 11.

The only way to get a sum of 11 is with 5 and 6. Since neither of those values are 4, we can conclude the sum of the three die.

SUFFICIENT.

Answer is B.

Trick is to realize the upper bound of 10 for the sum pair, IF the pair has to include the given number dice (with value of 4).

So, with 10, we have all the options open to make combinations of the pair that generates a sum of 10.

BUT with 11, since now you cannot pair it with the given number dice, you HAVE to use the 2 unknown pairs to form a sum of 11.

Thus, you know 4 (given) and you know 11 by logically narrowing it down to the other 2 dice. so 11+4 = 15.

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