probability

[gmatnmein2010]

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.

[ajith]

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 H may be the no of times he received heads and T be the number of times he received tails
H -T = 4

1) H+T = 24

Value of H & T can be found out , Sufficient

2) 3H+T =52

4H = 56
H= 14, T=10

[spoiler]Value of H & T can be found out , Sufficient

Hence D[/spoiler]

[thephoenix]

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.

IMO D

LET NO. OF TAILS=X----> NO. OF HEADS=X+4.

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

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

[Stuart@KaplanGMAT]

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's attack this using the most powerful data sufficiency tool in the known universe: the number of equations vs number of unknowns rule!

Here's the rule:

To solve a system with n variables, one requires n distinct, linear, equations.

From the stem:

2 variables (h, t)
1 equation (4 more heads than tails)

What do we need? 1 more linear equation.

(1) exact sum of heads and tails... that's certainly an equation - sufficient!

(2) 3h + 1t = 52... that's certainly another equation - sufficient!

Each statement is sufficient alone, choose (D).

The better you understand this rule, and the more often you apply it, the fewer actual calculations you'll need to do when solving DS questions.

Remember, in DS we don't care what the answer is, we only care if we can determine the exact answer!