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: 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
a

Problem: set s consists of integers { 7, 8, 10, 12, 13 }. if integer n is included in the set, the average ( arithmetic mean ) of set s will increase by 10 %. what is the value of integer n ?
Options: a. 10, b. 12, c. 16, d. 22, e. 24
c

Problem: tabby is training for a triathlon. she swims at a speed of 1 mile per hour. she runs at a speed of 7 miles per hour. she wants to figure out her average speed for these two events. what is the correct answer for her ?
Options: a. 8 mph, b. 5.25 mph, c. 3.5 mph, d. 4 mph, e. 0.5 mph

d