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In a card game named Allemande, each of four players has a

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In a card game named Allemande, each of four players has a

by BTGmoderatorLU » Tue Oct 22, 2019 1:32 am
Source: Magoosh

In a card game named Allemande, each of four players has a hand of 8 cards from a standard deck of 52. Through a series of discards, players try to maximize the point value of their final hand. Suits are irrelevant. Card Ace through 10 have a point value of the number of their card: for example, the five and any suit would be worth 5 points. Face cards (Jack, Queen, and King) are worth 20 points each. Does Charles have the highest value final hand?

1) Charles' hand is worth 117 points.
2) No other player besides Charles has more than four face cards in his hand.

The OA is E
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by Jay@ManhattanReview » Tue Oct 22, 2019 9:48 pm
BTGmoderatorLU wrote:Source: Magoosh

In a card game named Allemande, each of four players has a hand of 8 cards from a standard deck of 52. Through a series of discards, players try to maximize the point value of their final hand. Suits are irrelevant. Card Ace through 10 have a point value of the number of their card: for example, the five and any suit would be worth 5 points. Face cards (Jack, Queen, and King) are worth 20 points each. Does Charles have the highest value final hand?

1) Charles' hand is worth 117 points.
2) No other player besides Charles has more than four face cards in his hand.

The OA is E
Let's take each statement one by one.

1) Charles' hand is worth 117 points.

Certainly, there are cases in which the other three players' hands are worth less than 117. Let's find out at least one case in which one of the other three players have a hand worth more than 117.

Say Charle's cards are 2 Jacks, 2 Queens, 1 King, 1 Nine, 1 Seven, and 1 One. This makes 117 points.

Say other player's cards are 2 Jacks, 2 Queens, 3 Kings, and 1 Ten. This makes 150 points > 117 points. The answer is no.

No unique answer. Insufficient.

2) No other player besides Charles has more than four face cards in his hand.

Case 1: Say Charle's cards are 2 Jacks, 2 Queens, 2 Kings, and 2 Tens. This makes 140 points. Other players will certainly have less than 140 score. The answer is yes.
Case 2: Say Charle's cards are 2 Jacks, 3 Queens, and 3 Ones. This makes 103 points.
One of the other players has 2 Jacks, 1 Queen, 1 King and 4 Tens. This makes 120 points > 103 points.

The answer is no. No unique answer. Insufficient.

(1) and (2) together

Again, certainly, there are cases in which the other three players' hands are worth less than 117. Let's find out at least one case in which one of the other three players have a hand worth more than 117.

Case 3: Say Charle's cards are 2 Jacks, 3 Queens, 1 Nine, 1 Seven and 1 Ones. This makes 117 points.
One of the other players has 2 Jacks, 1 Queen, 1 King and 4 Tens. This makes 120 points > 117 points.

The answer is no. No unique answer. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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