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# When a player in a certain game tossed a coin a number of ti

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Senior Manager
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When a player in a certain game tossed a coin a number of ti [#permalink]

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15 Jan 2008, 11:01
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When a player in a certain game tossed a coin a number of times, 4 more heads than tails resulted. Heads or tails resulted each time the player tossed the coin. How many times did heads result?

(1) The player tossed the coin 24 times.
(2) The player received 3 points each time heads resulted and 1 point each time tails resulted, for a total of 52 points.

OPEN DISCUSSION OF THIS QUESTION IS HERE: when-a-player-in-a-certain-game-tossed-a-coin-a-number-of-144143.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Feb 2014, 06:26, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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15 Jan 2008, 11:04
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netcaesar wrote:
When a player in a certain game tossed a coin a number of times, 4 more heads than tails resulted. Heads or tails resulted each time the player tossed the coin. How many times did heads result?
1) The player tossed the coin 24 times
2) The player received 3 points each time heads resulted and 1 point each time tails resulted, for a total of 52 points.

1:2x+4=24 --> 2x=20 --> x=10 so he tossed the heads x+4--> 14 times.

2: we are given another ratio but this doesnt change anything.

x + 3(x+4)=52 --> 4x+12=52 --> 4x=40 --> x=10 again 14 times is the answer.

D
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27 Jan 2008, 17:37
D

x+y=24 and x=y+4, where x=# heads, y=# tails

stat 1: y+4+y=24 --> y=10, x=14. suff.

stat 2: 3x+y=52 --> 3y+12+y=52 --> 4y=40 -->y=10, x=14. suff.
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27 Jan 2008, 22:40
netcaesar wrote:
When a player in a certain game tossed a coin a number of times, 4 more heads than tails resulted. Heads or tails resulted each time the player tossed the coin. How many times did heads result?
1) The player tossed the coin 24 times
2) The player received 3 points each time heads resulted and 1 point each time tails resulted, for a total of 52 points.

T+(4+T) = 24

T = 10

H = (4+T) = 14

from (ii)

T +3*(4+T) = 52

T = 10

H = 14

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27 Sep 2009, 06:46
When a player in a certain game tossed a coin a number of times, 4 more heads than tails resulted. Heads or tails resulted each time the player tossed the coin. How many times did heads result?
1) The player tossed the coin 24 times
2) The player received 3 points each time heads resulted and 1 point each time tails resulted, for a total of 52 points.

Soln:
1) The player tossed the coin 24 times
Total number of heads = H
Total number of tails = T
H + T = 24
H - T = 4
Solving both equations we get H = 14
Statement 1 alone is sufficient.

2) The player received 3 points each time heads resulted and 1 point each time tails resulted, for a total of 52 points.
Total number of heads = H
Total number of tails = T
3H + T = 52
H - T = 4
Solving these two equations we get H = 14
Statement 2 alone is sufficient.

Thus D.
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14 Feb 2010, 14:46
netcaesar wrote:
When a player in a certain game tossed a coin a number of times, 4 more heads than tails resulted. Heads or tails resulted each time the player tossed the coin. How many times did heads result?
1) The player tossed the coin 24 times
2) The player received 3 points each time heads resulted and 1 point each time tails resulted, for a total of 52 points.

let total of tosses be n
no of tails T
no of Heads H = T + 4
Also n = H + T = 2T + 4

S1: n = 24... Therefore SUFF.... as 24 = 2T + 4 gives T = 10...& H = 14

S2: 3H + T = 52 ... 3T + 12 + T = 52 ...gives T = 10 & H = 14. SUFF...

D..
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14 Feb 2010, 22:59
1) The player tossed the coin 24 times
2) The player received 3 points each time heads resulted and 1 point each time tails resulted, for a total of 52 points.

given for certain number of times 4 more heads than tails

1) if coin is tossed 24 times then h=14 and t=10

so 1 is sufficient

2)3x+x-4=52
4x=56
so x=14

so my choice is D
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14 Feb 2010, 23:17
netcaesar wrote:
When a player in a certain game tossed a coin a number of times, 4 more heads than tails resulted. Heads or tails resulted each time the player tossed the coin. How many times did heads result?
1) The player tossed the coin 24 times
2) The player received 3 points each time heads resulted and 1 point each time tails resulted, for a total of 52 points.

x - Number of tails

1) x+x+4 = 24 can solve for x. Sufficient
2) 3(x+4) + x = 52 can solve for x. Sufficient

Hence D.

Is this really a 700 - plus questions as mentioned by the tag???
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16 Oct 2010, 05:31
probability sucks...don't have much command on it...
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Re: When a player in a certain game tossed a coin a number of [#permalink]

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24 Feb 2014, 06:05
Hi,
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MGMAT 2 640 (V48/Q31)

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Re: When a player in a certain game tossed a coin a number of ti [#permalink]

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24 Feb 2014, 06:27
Expert's post
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When a player in a certain game tossed a coin a number of times, 4 more heads than tails resulted. Heads or tails resulted each time the player tossed the coin. How many times did heads result?

Given: H-4=T.
Question: T=?

(1) The player tossed the coin 24 times. H+(H-4)=24. We can find H. Sufficient.

(2) The player received 3 points each time heads resulted and 1 point each time tails resulted, for a total of 52 points. 3H+1*(H-4)=52. The same here: we can find H. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: when-a-player-in-a-certain-game-tossed-a-coin-a-number-of-144143.html
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Re: When a player in a certain game tossed a coin a number of ti   [#permalink] 24 Feb 2014, 06:27
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