Dice Problem

[viveksavita]

Three Dices, each with faces numbered from 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 dices ?

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

[ibmagladry]

Three Dices, each with faces numbered from 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 dices ?

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

The Answer is B

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.

[ibmagladry]

Three Dices, each with faces numbered from 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 dices ?

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

The Answer is B

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.

[[email protected]]

Hi viveksavita,

ibmagladry has presented a great explanation for this question (and it's the same approach that I would take). It's worth noting that many questions on the GMAT can be solved if you just TEST Values (or come up with examples that fit the description in the prompt).

Here, we're rolling 3 dice (and each die will result in 1, 2, 3, 4, 5 or 6). That means there are limited possibilities. We're told that one of the dice is a 4, so we really have just 2 unknowns.

Each of the two Facts limits the possibilities even further. Writing down those possibilities is what is required to get to the correct answer. Be prepared to use this approach often during your studies and on Test Day - it's fairly easy to do and it's a great way to pick up points.

GMAT assassins aren't born, they're made,
Rich