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Nina and Teri are playing a dice game. Each girl rolls a

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Nina and Teri are playing a dice game. Each girl rolls a [#permalink] New post 15 Nov 2009, 21:17
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Nina and Teri are playing a dice game. Each girl rolls a pair of 12-sided dice, numbered with the integers from -6 through 5, and receives a score that is equal to the negative of the sum of the two die. (E.g., If Nina rolls a 3 and a 1, her sum is 4, and her score is -4.) If the player who gets the highest score wins, who won the game?

(1) The value of the first die Nina rolls is greater than the sum of both Teri's rolls.
(2) The value of the second die Nina rolls is greater than the sum of both Teri's rolls.

I hope i have tagged the question correctly.
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Re: Dice Game [#permalink] New post 15 Nov 2009, 21:49
But how? :?
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Re: Dice Game [#permalink] New post 15 Nov 2009, 21:54
Nina and Teri are playing a dice game. Each girl rolls a pair of 12-sided dice, numbered with the integers from -6 through 5, and receives a score that is equal to the negative of the sum of the two die. (E.g., If Nina rolls a 3 and a 1, her sum is 4, and her score is -4.) If the player who gets the highest score wins, who won the game?

(1) The value of the first die Nina rolls is greater than the sum of both Teri's rolls.
(2) The value of the second die Nina rolls is greater than the sum of both Teri's rolls.


Statement 1 - Insufficient (As we do not know what would be the result of Nina's second die)
Statement 2 - Insufficient (As we do not Know what was the result of Nina's first die)

Both combined, Teri wins (as the greater the value, the more negative the score value, hence Nina will have a high negative score)

IMO C

What is the OA?
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Re: Dice Game [#permalink] New post 15 Nov 2009, 22:01
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ctrlaltdel wrote:
But how? :?


stmt 1 and stmt 2 are not sufficient on their own.
Combining,
nina: 4,6 Teri: 1,2 => Nina wins
nina: -1,-2, Teri: -3,-6=> Teri wins.
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Re: Dice Game [#permalink] New post 15 Nov 2009, 22:12
OA:E, Kudos to Economist
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Re: Dice Game [#permalink] New post 19 Feb 2013, 11:19
Economist wrote:
ctrlaltdel wrote:
But how? :?


stmt 1 and stmt 2 are not sufficient on their own.
Combining,
nina: 4,6 Teri: 1,2 => Nina wins
nina: -1,-2, Teri: -3,-6=> Teri wins.



hey,
I think both the statements are sufficient as
statement 1 says nina's first die value is already greater than teri's both values.

and simililarly 2nd statement aswell..

I need help in getting to insufficient conclusion.

thanks in advance
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Re: Dice Game [#permalink] New post 22 Feb 2013, 01:17
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sujitrj wrote:
Economist wrote:

stmt 1 and stmt 2 are not sufficient on their own.
Combining,
nina: 4,6 Teri: 1,2 => Nina wins
nina: -1,-2, Teri: -3,-6=> Teri wins.



hey,
I think both the statements are sufficient as
statement 1 says nina's first die value is already greater than teri's both values.

and simililarly 2nd statement aswell..

I need help in getting to insufficient conclusion.

thanks in advance


The given example is a little messed up. In case
nina: 4,6 Teri: 1,2 => then Nina's score is -10 and Teri's score is -3 so Teri wins, not Nina.

There are two different things here: Sum of the die and overall score

Overall score is negative of sum of the die.

If Nina's first die value is greater than Teri's sum of the die, Nina's sum of the die could be greater than or less than Teri's sum of the die depending on Nina's second die value (since the die value can be negative too). Thereafter, the overall score of Nina could be less than or greater than Teri's.

Using both statements together, we can find cases in which Nina wins and other cases in which Teri wins.

Say, Teri's die values are -3 and -3. Sum of both dice is -6 (and overall score is 6).
Say, Nina's first die value is -1 and second die value is -1 (Nina's each die value is more than the sum of Teri's both dice) . Sum of both dice is -2 and overall score is 2.
Teri wins

Say, Teri's die values are -4 and -1. Sum of both dice is -5 (and overall score is 5).
Say, Nina's first die value is -4 and second die value is -4 (Nina's each die value is more than the sum of Teri's both dice) . Sum of both dice is -8 and overall score is 8.
Nina wins
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Re: Nina and Teri are playing a dice game. Each girl rolls a [#permalink] New post 22 Feb 2013, 01:32
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ctrlaltdel wrote:
Nina and Teri are playing a dice game. Each girl rolls a pair of 12-sided dice, numbered with the integers from -6 through 5, and receives a score that is equal to the negative of the sum of the two die. (E.g., If Nina rolls a 3 and a 1, her sum is 4, and her score is -4.) If the player who gets the highest score wins, who won the game?

(1) The value of the first die Nina rolls is greater than the sum of both Teri's rolls.
(2) The value of the second die Nina rolls is greater than the sum of both Teri's rolls.

I hope i have tagged the question correctly.


You can use algebra to give you a starting point to think.

N1 > T1 + T2
N2 > T1 + T2

Adding

N1 + N2 > 2(T1 + T2)
-(N1 + N2) < 2(-T1 - T2)
Nina's score < 2*Teri's score

Nina's score must be less than twice of Teri's score but it may be less or more than Teri's score. This can help you think of values: One in which Nina's score is more than Teri's score and another in which Nina's score is less than Teri's score provided Nina's score is less than twice of Teri's score.

Nina's score could be 8 and Teri's could be 5.
Nina's score could be 2 and Teri's could be 6.
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Re: Nina and Teri are playing a dice game. Each girl rolls a [#permalink] New post 22 Feb 2013, 02:49
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Nina and Teri are playing a dice game. Each girl rolls a pair of 12-sided dice, numbered with the integers from -6 through 5, and receives a score that is equal to the negative of the sum of the two die. (E.g., If Nina rolls a 3 and a 1, her sum is 4, and her score is -4.) If the player who gets the highest score wins, who won the game?

(1) The value of the first die Nina rolls is greater than the sum of both Teri's rolls.
(2) The value of the second die Nina rolls is greater than the sum of both Teri's rolls.

Let us try to substitute values to find the answer.

Statement (1):

Nina I = 4 Teri I = 1 Teri II = 2

We don't anything more than that from the first statement. If Nina scored a negative 6 on the turn II then she will win and if she scores a negative 4 then she would lose. So statement I is insufficient.

Statement (2):

The second statement is same as the first statement.

Nina II = 4 Teri I = 1 Teri II = 2

If Nina scored a negative 6 on the turn I then she will win and if she scores a negative 4 then she would lose. So statement II is insufficient.

If we combine both the statements, then:

Nina I = 5
Nina II = 5
Teri I = 1 Teri II = 2
Then Teri wins


Nina I = 5
Nina II = 5
Teri I = 1 Teri II = 2
Then Teri wins

Nina I = -5
Nina II = -6
Teri I = -5 Teri II = -2
Then Nina wins

Hence both the statements are insufficient.
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Re: Nina and Teri are playing a dice game. Each girl rolls a [#permalink] New post 22 Feb 2013, 03:58
Expert's post
ctrlaltdel wrote:
Nina and Teri are playing a dice game. Each girl rolls a pair of 12-sided dice, numbered with the integers from -6 through 5, and receives a score that is equal to the negative of the sum of the two die. (E.g., If Nina rolls a 3 and a 1, her sum is 4, and her score is -4.) If the player who gets the highest score wins, who won the game?

(1) The value of the first die Nina rolls is greater than the sum of both Teri's rolls.
(2) The value of the second die Nina rolls is greater than the sum of both Teri's rolls.

I hope i have tagged the question correctly.


From F.S.1
Let the value of the first die rolled by Nina be 5. Let Teri's rolls be 0 & -1.
If the second roll of Nina is -6, NO ONE wins. But if it is -5, Teri wins. NOT SUFFICIENT.

F.S. 2:

Let the value of the second die rolled by Nina be 5. Let Teri's rolls be -1 & 4.
If the first roll of Nina was -6, Nina wins. If it is 3, Teri wins. NOT SUFFICIENT.

Combining both :

first and second roll of Nina : 0 and -1.

first and second roll of Teri : -1 and -2.

Teri wins.

first and second roll of Nina : -3 and -1.

first and second roll of Teri : -3 and -1.

No one wins. NOT SUFFICIENT.

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Re: Nina and Teri are playing a dice game. Each girl rolls a   [#permalink] 22 Feb 2013, 03:58
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