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In a certain game, a player flips a coin to determine movement. Every
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23 Mar 2021, 05:32
23 Mar 2021, 05:32
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71% (01:59) correct
28% (02:08) wrong based on 21 sessions
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In a certain game, a player flips a coin to determine movement. Every toss of the coin lands with either a head facing up or a tail facing up. If a head is facing up, the player moves forward 10 squares, and if a tail is facing up, he moves backward 13 squares. After flipping the coin 120 times, the player is four squares forward of his starting position. How many of the 120 flips showed a head facing up?
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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Show: :: OA
68
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: In a certain game, a player flips a coin to determine movement. Every
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23 Mar 2021, 08:51
23 Mar 2021, 08:51
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Carcass wrote:
In a certain game, a player flips a coin to determine movement. Every toss of the coin lands with either a head facing up or a tail facing up. If a head is facing up, the player moves forward 10 squares, and if a tail is facing up, he moves backward 13 squares. After flipping the coin 120 times, the player is four squares forward of his starting position. How many of the 120 flips showed a head facing up?
Show: :: OA
68
\(H + T = 120\) ........ (1)
\(10H - 13T = 4\) ........ (2)
Multiplying (1) by \(10\) and subtracting (2) from it:
\(10H + 10T = 1200\) ........ (1)
\(10H - 13T = 4\) ........ (2)
\(23T = 1196\)
\(T = 52\)
So, \(H = 120 - 52 = 68\)
General Discussion
Re: In a certain game, a player flips a coin to determine movement. Every
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23 Mar 2021, 23:59
23 Mar 2021, 23:59
This is a problem of Algebra, so my intuition was to create two different equations
Number of steps taken forward= 10*x where x=Number of times Heads was up
Similarly, the Number of steps taken backward= 13*y where y=Number of times Tails was up
Equation 1:
10*x-13*y = 4............ (since it is given that at the end of 120 total coin flips, he was 4 steps in front of his starting place)
Equation 2:
x + y = 120...........(since there were total 120 flips)
On solving this equation, x comes out to be 68
Hence the number of times Heads was up is 68
Number of steps taken forward= 10*x where x=Number of times Heads was up
Similarly, the Number of steps taken backward= 13*y where y=Number of times Tails was up
Equation 1:
10*x-13*y = 4............ (since it is given that at the end of 120 total coin flips, he was 4 steps in front of his starting place)
Equation 2:
x + y = 120...........(since there were total 120 flips)
On solving this equation, x comes out to be 68
Hence the number of times Heads was up is 68
