Exactly 71 people are standing in a single queue outside a store on black Friday. If these 71 people also include Daniel and Maria, then how many people are standing in front of Maria in the queue?
(1) When counted from the back of the queue, Daniel is at 19th position and there are exactly 7 people between Daniel and Maria.
(2) The number of people in front of Maria in the queue are 18 more than the number of people behind Maria in the queue.
What's the best way to determine whether statement 1 is sufficient? Can any experts help?
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There are 71 people in the queue, including Daniel and Maria. This means that there are 70 people *other* than Daniel and 70 people *other* than Maria. We want to find the number of people in front of Maria.
Statement 1
If Daniel is in the 19th position from the back of the queue, there are 18 people behind him. There are 7 people between Daniel and Maria. However, the statement isn't explicit whether or not Maria is in front of or behind Daniel.
If she's in front of Daniel, then there are 18 people behind Daniel + Daniel + 7 people in front of Daniel = 26 people behind Maria. This means that there are 70-26 = 44 people in front of Maria. But if Maria is behind Daniel, then there are 18 people behind Daniel - 7 people behind Daniel - Maria = 10 people behind Maria. This means that there are 70-10=60 people in front of Maria. Insufficient.
Statement 2
This means that if x is the number of people in front of Maria, the number of people behind Maria is x-18. So x + x - 18 = 70. Solving for x gives 2x = 52, or x = 26. So there are 26 people ahead of Maria in line. Sufficient.
Statement 1
If Daniel is in the 19th position from the back of the queue, there are 18 people behind him. There are 7 people between Daniel and Maria. However, the statement isn't explicit whether or not Maria is in front of or behind Daniel.
If she's in front of Daniel, then there are 18 people behind Daniel + Daniel + 7 people in front of Daniel = 26 people behind Maria. This means that there are 70-26 = 44 people in front of Maria. But if Maria is behind Daniel, then there are 18 people behind Daniel - 7 people behind Daniel - Maria = 10 people behind Maria. This means that there are 70-10=60 people in front of Maria. Insufficient.
Statement 2
This means that if x is the number of people in front of Maria, the number of people behind Maria is x-18. So x + x - 18 = 70. Solving for x gives 2x = 52, or x = 26. So there are 26 people ahead of Maria in line. Sufficient.
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