In a card game named Allemande, each of four players has a hand of 8 c

Question

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. Cards Ace through 10 have a point value of the number of their card: for example, the five of 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.

Kudos for a correct solution.

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

Kudos for a correct  solution .

DesiGmat · Answer

Here we go:

St1: Charles’ hand is worth 117 points.

This statement is clearly insufficient because no information is provided for other 3 players.

St2: No other player besides Charles has more than four face cards in his hand.

So here we have that charles has at least 5 cards with him.

So his score can range from 103 to 160. However no information is given for other 3 players.

This statement is also insufficient.

Combining two statements.

Charles’ hand is worth 117 points.
No other player besides Charles has more than four face cards in his hand.

So charles has 5 face cards with him -> 20 * 5 = 100 
Left over 17 can be made by many combinations. For example -> (5,5,7), (8,7,2) etc

but the catch here is ->

Say one of the other three players has 4 face cards-> 4 * 20 = 80
and other 4 cards with number 10 on them -> This makes the total score of 120.

Say we can not for sure say that Charles has the highest value final hand

According to me option E is correct.

chetan2u · Answer

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. Cards Ace through 10 have a point value of the number of their card: for example, the five of 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.

Kudos for a correct solution.

Total points  -- 4*4 face cards and remaining number cards -- 4*4*20+4(1+2+4+..10)=320+4*(10*11)/2=320+440=760
 Maximum possible points in hand of all 4 = 4*4 face cards and number cards of 10, 9, 8 and 7 -- 4*4*20+4(10+9+8+7)=320+132=452
MAXIMUM points with any one --- All face cards = 8*20=160

(1) Charles’ hand is worth 117 points.
Possible that Charles = 117 and remaining =(452-117)/3 ~111 or 112....Highest with charles
Possible that charles has 117, while someone else has 120 and remaining with 109 and 110
Insuff

(2) No other player besides Charles has more than four face cards in his hand.
We do not know about the remaining cards in hands of charles they may be just 1 each.. 
The other may have 4 face cards, four 10s ..
Insuff

combined insufficient... 
four face cards and four 10s=120 <117... 
also four face cards and four oness=84> 117 ..insufficient

E

ravihanda · Answer

We cannot solve the question from individual statements because we do not know either about Charles's hand or about other player's hands.

We should try by combining  both the statements together . 
No other player has more than 4 face cards.

With 4 face cards, maximum score possible is 4*20 + 4*10 = 120
In this case, we can assume Charles has 5 face cards, 1 nine, 1 seven and 1 ace = 5*20 + 9 + 7 + 1 = 117
So,  Charles does not have the maximum.

We can easily form a case where Charles with 117 points has the maximum.

So, even after  combining both the statements, we cannot find a unique answer.
Correct Answer: E

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

Statement #1 is obviously not sufficient, because it only tells us about Charles, and nothing about everyone else.

Statement #2 is obviously not sufficient, because it only tells us about everyone else, and nothing about Charles.

The whole question revolves around what happens with the combined statements.

Charles has 117 points, a strong hand. No one else has more than four face cards. Clearly, most players, say someone with no face cards, would have to be below Charles. We have no doubt that some players are below Charles. Could anyone possibly have more than Charles? Well, suppose one person had four face cards (4*20 = 80 points) and also had all four 10’s in the deck — then, that person would have a total point value of 80 + 10 + 10 + 10 + 10 = 120, higher than Charles. So, given the combined conditions, most people will have less than Charles, but someone could have a hand worth more than Charles’s hand, so even with the combined statements, we cannot say definitively that Charles has the highest value hand. Nothing is sufficient here.

Answer = (E)

kaaaaku · Answer

Total points in the deck: 4(1+2+3+4....+10) + (4)(3)(20)
-> 300

Basically, total points in the deck: 300
1st min hand: AAAA 2222 -> 12
2nd min hand: 3333 4444 -> 28
Total: 40

-> 3rd and Charles will share: 260 among them.

1)
Charles has 117
Then 3rd has: 143
So MAX: 143 MIN: 12
Since there are hands better than 117 and also some hands worse than 117, it can't be definitely said that Charles has the best hand -> INSUFF

2) MIN is the same: 12
MAX is now: 20x4 + 10x4 (FFFF 10,10,10,10)
-> 120
Again: Charles does not have a better hand, for certain. Could be, could be not. -> INSUFF

Combine)
MIN: 12
MAX: 120
117 is in between. Y or N, -> INSUFF

RK84 · Answer

Straight E.
1. Insufficient as the max value can go up to 160 and that too two players can have 160 each insufficient 
2. This statement gives us no definite answer as different combinations yield both a higher value and a lower value than Charles points-insufficient 
3. 20x+10y can yield both a lesser value and higher than 117 insufficient 
Hence E

Sent from my iPhone using  GMAT Club Forum mobile app

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In a card game named Allemande, each of four players has a hand of 8 c

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In a card game named Allemande, each of four players has a hand of 8 c

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