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OG - 142 DS question

by GaneshMalkar » Sat Jun 08, 2013 8:49 pm
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.

OA - D

statement (2) explanation confused me :(

The question says h=t+4, Here everything is in terms of heads and tails and no points involved.

Statement (2) states about points ie 3h + t = 52

How we can equate two equations which are in terms of different quantities? I may sound little bit foolish but that was the first doubt which cropped in :(
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by vivekchandrams » Sun Jun 09, 2013 12:40 am
Hi Ganesh,

The two equations can be equated. Here's why:

h=t+4.
h-no:of heads
t-no:of tails.

3*h+1*t=52.

h-no:of heads
t-no:of tails.

The equations can be equated because they just tell us the relation between 2 quantities. The equations might be different in terms of what the represent but what we need is the relation between h and t.

Hope it answers
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by aaggar7 » Sun Jun 09, 2013 5:01 am
Let number of times coin is tossed = N

Tail appears = T times

Head appears = T + 4

So, T + (T + 4) =N --(1)

1) N = 24 ,sufficient as we can get value of T by putting N = 24 in (1).

2) 3 points for head so 3 (T+4)
1 point for tail T

3(T+4)+1(T) = 52
sufficient to find the value of T.

Hence D.

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by Brent@GMATPrepNow » Sun Jun 09, 2013 5:49 am
GaneshMalkar 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.
Target question: How many times did heads result?

Let H = # of heads
Let T = # of tails

Rephrased target question: What is the value of H

Given: 4 more heads than tails resulted.
In other words, H = T + 4
Rearrange to get H - T = 4

Statement 1: The player tossed the coin 24 times.
So, the # of heads plus the number of tails = 24
In other words, H + T = 24
Since we also know that H - T = 4, we now have a system of two different linear equations which we could solve for H (if we were so inclined).
Since we can answer the target question with certainty, 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.
In other words, 3H + 1T = 52
Since we also know that H - T = 4, we now have a system of two different linear equations which we could solve for H (if we were so inclined).
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent
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by GaneshMalkar » Mon Jun 10, 2013 4:21 am
Thanks Sir for your reply... I got how the problem was solved the only doubt was "How we can equate two equations which are in different terms?"

From all reply it seems we can do that until and unless the assumed variables assumed are in same form.

Thanks Sir...

Brent@GMATPrepNow wrote:
GaneshMalkar 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.
Target question: How many times did heads result?

Let H = # of heads
Let T = # of tails

Rephrased target question: What is the value of H

Given: 4 more heads than tails resulted.
In other words, H = T + 4
Rearrange to get H - T = 4

Statement 1: The player tossed the coin 24 times.
So, the # of heads plus the number of tails = 24
In other words, H + T = 24
Since we also know that H - T = 4, we now have a system of two different linear equations which we could solve for H (if we were so inclined).
Since we can answer the target question with certainty, 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.
In other words, 3H + 1T = 52
Since we also know that H - T = 4, we now have a system of two different linear equations which we could solve for H (if we were so inclined).
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent
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by Brent@GMATPrepNow » Mon Jun 10, 2013 4:59 am
GaneshMalkar wrote:Thanks Sir for your reply... I got how the problem was solved the only doubt was "How we can equate two equations which are in different terms?"

From all reply it seems we can do that until and unless the assumed variables assumed are in same form.
I'm not entirely sure what you mean by "different terms." Do you mean variables?
The equation we derived from the given information (H - T = 4) as well as the two equations we derived from statements 1 and 2 (H + T = 24 and 3H + 1T = 52) are all in terms of H and T.
At the outset, we let H = # of heads and T = # of tails. So, the two variables are always the same.


Or are you asking how to solve systems of equations?
If so, let's solve the system:
H - T = 4
3H + T = 52

One way to solve this system is to add the equations.
H + 3H = 4H
(-T) + T = 0
4 + 52 = 56

So, when we add the two equations, we get: 4H = 56
This means that H = 14
If H = 14, we can conclude that T = 10

I hope that helps.

Cheers,
Brent
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by GaneshMalkar » Tue Jun 11, 2013 9:38 am
Sir I meant to say that first equation is the "no of heads and tails" and second equation was "no of points alloted to each move"...I was confused in whether we can equate the two equations of which one is # of heads and tails and in second one we gave weight[in terms of points] to each move.

Brent@GMATPrepNow wrote:
GaneshMalkar wrote:Thanks Sir for your reply... I got how the problem was solved the only doubt was "How we can equate two equations which are in different terms?"

From all reply it seems we can do that until and unless the assumed variables assumed are in same form.
I'm not entirely sure what you mean by "different terms." Do you mean variables?
The equation we derived from the given information (H - T = 4) as well as the two equations we derived from statements 1 and 2 (H + T = 24 and 3H + 1T = 52) are all in terms of H and T.
At the outset, we let H = # of heads and T = # of tails. So, the two variables are always the same.


Or are you asking how to solve systems of equations?
If so, let's solve the system:
H - T = 4
3H + T = 52

One way to solve this system is to add the equations.
H + 3H = 4H
(-T) + T = 0
4 + 52 = 56

So, when we add the two equations, we get: 4H = 56
This means that H = 14
If H = 14, we can conclude that T = 10

I hope that helps.

Cheers,
Brent
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by Brent@GMATPrepNow » Tue Jun 11, 2013 9:44 am
GaneshMalkar wrote:Sir I meant to say that first equation is the "no of heads and tails" and second equation was "no of points alloted to each move"
Thanks for that clarification.

It's important to note that, in both cases, T and H represent the number of heads and tails.

So, if the player received 3 points for each head, then the total points for the heads will be 3H (3 times the number of heads).
For example, if the player gets 8 heads, then the number of points he/she receives = (3)(8) = 24

Similarly, if the player received 1 point for each tail, then the total points for the heads will be 1T.
For example, if the player gets 11 tails, then the number of points he/she receives = (1)(11) = 11

So, we're using the number of heads and tails to help us calculate the number of points the player received.

Cheers,
Brent
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