Last Updated on May 9, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We are given that when a coin was tossed a certain number of times, 4 more heads than tails resulted. If we let H = the number of times heads is tossed and T = the number of times tails is tossed, we can create the following equation:
H = T + 4
We need to determine the value of H.
Statement One Alone:
The player tossed the coin 24 times.
Using the information in statement one we can create the following equation:
T + H = 24
Since H = T + 4, we can substitute T + 4 for H in the equation T + H = 24.
T + T + 4 = 24
2T = 20
T = 10
Since T = 10, H = 10 + 4 = 14.
Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
The player received 3 points each time heads resulted and 1 point each time tails resulted, for a total of 52 points.
Using the information in statement two we can create the following equation:
3H + T = 52
Since H = T + 4, we can substitute T + 4 for H in the equation 3H + T = 52.
3(T + 4) + T = 52
3T + 12 + T = 52
4T = 40
T = 10
Since T = 10, H = 10 + 4 = 14.
Statement two alone is also sufficient to answer the question.
Answer: D
