TASK DEFINITION: You are given a mathematical question described with an open-ended vocabulary. Questions in this task involve real-world situations, describing a mathematical problem. You are also given 4 or 5 answer options (associated with "A", "B", "C", "D", "E"). Do not generate anything else apart from one of the following characters: 'A', 'B, 'C', 'D', 'E'. LaTeX mathematical format (the standard way to express mathematical expressions in the typesetting software known as LaTeX) is used to express equations. Each question is solvable with high school math knowledge. Give only one answer for each question.
PROBLEM: A bicyclist riding at 12 miles an hour for 2 hours travels twice the distance a hiker travels walking at 4 miles an hour for how many hours?
(A)2 (B)3 (C)4 (D)5 (E)6

SOLUTION: B

PROBLEM: Fruit 1 is an apple. Fruit 5 is the same as fruit 2. Fruit 2 is an orange. Fruit 6 is a banana. Fruit 3 is not an apple. Fruit 7 is not a banana. Fruit 4 is the same as fruit 1. If a bag contains 20 pieces of fruit of three types (apples, oranges, bananas), and 7 pieces of fruit are chosen according to the rules above, which of the following must be true?
(A)Only one apple is drawn. (B)Only one orange is drawn. (C)Two apples are drawn. (D)At least two bananas are drawn. (E)At least two apples are drawn.

SOLUTION: E

PROBLEM: Ahmed rolled an eight-sided polygon six times. Each face of the polygon has a number from 1-8 painted on it. No two numbers are repeated. Each roll yields one number face up. The first roll yields an even number. The second roll yields an odd number. The third roll yields the number 5. The fourth roll yields a number smaller than 4. The fifth roll yields the same number as the fourth roll. The sixth roll yields a number smaller than the fifth roll. Which of the following must be true?
(A)Ahmed could have rolled a 5 three times. (B)Ahmed could have rolled a 2 more frequently than he could have rolled any other numbers. (C)Ahmed rolled more odd numbers than even numbers. (D)Ahmed rolled a 3 at least once. (E)Ahmed rolled a 1 on four rolls.

SOLUTION:
B