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# Bonnie and Clyde play a card game. In the beginning they have an equal

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Posts: 55266
Bonnie and Clyde play a card game. In the beginning they have an equal  [#permalink]

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07 Sep 2016, 04:33
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Difficulty:

25% (medium)

Question Stats:

84% (02:27) correct 16% (03:05) wrong based on 72 sessions

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Bonnie and Clyde play a card game. In the beginning they have an equal number of cards. Each player, in turn, gives the other a half of his cards. Clyde plays first, giving Bonnie half of his cards. Bonnie plays next, and Clyde follows. At this stage, Bonnie has 44 cards. How many cards did each player have in the beginning of the game?

A. 14
B. 16
C. 20
D. 24
E. 32

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Bonnie and Clyde play a card game. In the beginning they have an equal  [#permalink]

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Updated on: 10 Sep 2016, 07:54
Bunuel wrote:
Bonnie and Clyde play a card game. In the beginning they have an equal number of cards. Each player, in turn, gives the other a half of his cards. Clyde plays first, giving Bonnie half of his cards. Bonnie plays next, and Clyde follows. At this stage, Bonnie has 44 cards. How many cards did each player have in the beginning of the game?

A. 14
B. 16
C. 20
D. 24
E. 32

Initially , each has x cards.

After Round 1, B has 3x/2 cards and C has x/2 cards.

After Round 2 , B has 3x/4 Cards and C ha 5x/4 Cards

After Round 3, B has 11x/8 Cards and C has 5x/8

ow, 11x/8 = 44

or x=32.
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Originally posted by abhimahna on 07 Sep 2016, 05:23.
Last edited by abhimahna on 10 Sep 2016, 07:54, edited 1 time in total.
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Re: Bonnie and Clyde play a card game. In the beginning they have an equal  [#permalink]

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07 Sep 2016, 17:58
Back solving:

Option A can be ruled out because after the 1st exchange, C and B will have 7 and 21 cards respectively. Both are odd and hence cannot be evenly divided.

Option B:

C B
16 16
8 24
20 12
10 22

Reject. But, wait!
Note that if both start with 16 cards, after 3 exchanges, B has 22. As per question, B has 44 which is twice of 22. This should tell you that both had 32 cards.

Validation:

C B
32 32
16 48
40 24
20 44

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Re: Bonnie and Clyde play a card game. In the beginning they have an equal  [#permalink]

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07 Sep 2016, 19:28
abhimahna wrote:
Bunuel wrote:
Bonnie and Clyde play a card game. In the beginning they have an equal number of cards. Each player, in turn, gives the other a half of his cards. Clyde plays first, giving Bonnie half of his cards. Bonnie plays next, and Clyde follows. At this stage, Bonnie has 44 cards. How many cards did each player have in the beginning of the game?

A. 14
B. 16
C. 20
D. 24
E. 32

Initially , each has x cards.

After Round 1, B has 3x/2 cards and C has x/2 cards.

After Round 2 , B has 3x/4 Cards and C ha 5x/4 Cards

After Round 3, B has 11x/4 Cards and C has 5x/8

ow, 11x/4 = 44

or x=32.

This gives x=16. Can you please explain how you got 32? Is there an intermediate step which I am missing??
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Re: Bonnie and Clyde play a card game. In the beginning they have an equal  [#permalink]

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10 Sep 2016, 07:54
acegmat123 wrote:
abhimahna wrote:
Bunuel wrote:
Bonnie and Clyde play a card game. In the beginning they have an equal number of cards. Each player, in turn, gives the other a half of his cards. Clyde plays first, giving Bonnie half of his cards. Bonnie plays next, and Clyde follows. At this stage, Bonnie has 44 cards. How many cards did each player have in the beginning of the game?

A. 14
B. 16
C. 20
D. 24
E. 32

Initially , each has x cards.

After Round 1, B has 3x/2 cards and C has x/2 cards.

After Round 2 , B has 3x/4 Cards and C ha 5x/4 Cards

After Round 3, B has 11x/4 Cards and C has 5x/8

ow, 11x/4 = 44

or x=32.

This gives x=16. Can you please explain how you got 32? Is there an intermediate step which I am missing??

There is a typo at the highlighted fraction above. It will be 11x/8.

or 11x/8 = 44

or x=32.

Corrected the original solution.
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Re: Bonnie and Clyde play a card game. In the beginning they have an equal  [#permalink]

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15 Sep 2018, 08:32
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Re: Bonnie and Clyde play a card game. In the beginning they have an equal   [#permalink] 15 Sep 2018, 08:32
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