TASK DEFINITION: Given a math problem with context and a question and 5 answer choices, the task is to provide the correct answer choice based on the problem. You must choose one of the given answer choices by letter: a, b, c, d, or e; anything else is invalid.
PROBLEM: Problem: if ( x - 10 ) ( y - 5 ) ( z - 2 ) = 1000 then what is the least value of x + y + z ? if x, y, z are all integer no.
Options: a. 7, b. 8, c. 9, d. 10, e. 11

SOLUTION: a

PROBLEM: Problem: a certain roller coaster has 6 cars, and a passenger is equally likely to ride in any 1 of the 6 cars each time that passenger rides the roller coaster. if a certain passenger is to ride the roller coaster 6 times, what is the probability that the passenger will ride in each of the 6 cars ?
Options: a. 3 / 1944, b. 1 / 96, c. 2 / 96, d. 1 / 1944, e. 1

SOLUTION: a

PROBLEM: Problem: there are 22 kids in a classroom. 12 kids are wearing socks and 8 are wearing shoes. 6 kids are wearing both. how many are bare feet ?
Options: a. 10, b. 2, c. 4, d. 5, e. 8

SOLUTION:
e