## Coin toss

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### Coin toss

by beater » Mon Aug 18, 2008 9:18 am
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.

Guys,
If x - heads and y - tails, based on the information provided in the question, the equation should be: 4+x=y. that is, 4 more heads than y. However, the equation is listed the other way around in OG. x=4+y. I'm not thinking straight for some reason. Could one of you please explain the reason as to why x=4+y is the correct approach . Thanks!

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by pepeprepa » Mon Aug 18, 2008 9:29 am
Just remember it is useful not to confuse you on this thing:
there are 4 more heads than tails
Number of tails=y

4 more heads...take an example if there are 12 tails, how many heads do you have? 12+4=16

16=12+4
x=y+4

The bigger one must not have +4, otherwise it is much bigger than what the reality is.

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### Re: Coin toss

by sudhir3127 » Mon Aug 18, 2008 9:41 am
beater 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.

Guys,
If x - heads and y - tails, based on the information provided in the question, the equation should be: 4+x=y. that is, 4 more heads than y. However, the equation is listed the other way around in OG. x=4+y. I'm not thinking straight for some reason. Could one of you please explain the reason as to why x=4+y is the correct approach . Thanks!
I go with D..

here it is ..

we know from the statement 1 that
h+t =24...........................................1

more more heads than tails from question stem
h = T +4 ............................................2

solve this to get t= 10. thus sufficient...
statement 2 can be written as

3h + t = 52..........................................3

solve 1 and 3 to get t =10 hence sufficient..

As far ur question on why " h= t +4" here what i undestand from it .. hope it helps you as well..

question says " 4 More heads resulted than tails "

assume u can flip the coin a only 6 times..

first flip u get a tail..

ur conditions is ur number of heads shud be 4 more than tails..

hence if theres 1 tails ur heads shud be 5 ( 1 + 4 more than tails)

thus ur heads are 5 and tails are 1

Now ur heads can also be written as 1 + 4

5 = 1 + 4 which is nothing but
H= t+4....

Hope it helps.. do let me know if u have any doubts

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by beater » Mon Aug 18, 2008 9:54 am
pepeprepa - thanks for the wonderful explanation. One quick clarification..

We should be able to solve this problem using this equation, correct? H+4=T? if tails is 1 then heads is 5. It is basically the reverse of what you had proposed. What say? Damn, i cant believe that I'm pulling my hair over this simple equation.. Legendary Member
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by pepeprepa » Mon Aug 18, 2008 10:08 am
I am sorry I don't really understand your triple negative question Do you say that we can solve the question with H+4=T ? Because the right one is H=T+4

If you need, tell us what you don't follow in Sudhir's explanation.

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by hengirl03 » Mon Aug 18, 2008 10:17 am
beater wrote:pepeprepa - thanks for the wonderful explanation. One quick clarification..

We should be able to solve this problem using this equation, correct? H+4=T? if tails is 1 then heads is 5. It is basically the reverse of what you had proposed. What say? Damn, i cant believe that I'm pulling my hair over this simple equation.. I believe that you mean H-4=T. You can't use H+4=T because the problem clearly states that there are 4 more heads than tails.

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by beater » Mon Aug 18, 2008 10:35 am
Thanks!

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### Re: Coin toss

by [email protected] » Sat Nov 27, 2021 7:23 am
beater wrote:
Mon Aug 18, 2008 9:18 am
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.

Given: 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.
Let H = the total number of heads that resulted
Let T = the total number of tails that resulted
So, from the given information we can write: H - T = 4

Target question: What is the value of H?

Statement 1: The player tossed the coin 24 times.
We can write: H + T = 24, which means we now have the following system of equations:
H - T = 4
H + T = 24
Since we have a system of 2 different linear equations with 2 variables, we COULD solve the system for H and T, which means we could answer the target question with certainty [although we would never waste precious time on tests they actually performing the necessary calculations]
Statement 1 is SUFFICIENT

Statement 2: The player received 3 points each time heads resulted and 1 point each time tails resulted, for a total of 52 points
We can write: 3H + 1T = 52, which means we now have the following system of equations:
H - T = 4
3H + 1T = 52
Since we have a system of 2 different linear equations with 2 variables, we COULD solve the system for H and T, which means we could answer the target question with certainty
Statement 2 is SUFFICIENT