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: what is the smallest number which, when increased by 7, is divisible by 8, 11, and 24 ?
Options: a. 264, b. 257, c. 269, d. 270, e. 282
b

Problem: two positive integers differ by 4, and sum of their reciprocals is 2. then one of the numbers is
Options: a. a. 3, b. 2, c. c. 5, d. d. 21, e. e. 28
b

Problem: if a is a positive integer, and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 4, what is the units x digit of ( a + 2 ) ^ 2 ?
Options: a. 1, b. 3, c. 5, d. 6, e. c. 14

a