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 greatest positive integer e such that 3 ^ e is a factor of 9 ^ 10 ?
Options: a. e = 5, b. e = 9, c. e = 10, d. e = 20, e. 30
d

Problem: ray writes a two digit number. he sees that the number exceeds 4 times the sum of its digits by 3. if the number is increased by 18, the result is the same as the number formed by reversing the digits. find the number.
Options: a. 2, b. 5, c. 6, d. 7, e. 8
b

Problem: the length of a rectangle is increased by 40 % while its width is halved. what is the % change in area ?
Options: ['a. 25 %', 'b. 30 %', 'c. 50 %', 'd. 65 %', 'e. 70 %']
b