instruction:
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.
question:
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.
answer:
B


question:
There are \(n\) students in a chemistry class, and only \(s\) of them are seniors. If \(j\) juniors are added to the class, what percent of the students in the class will not be seniors?
(A)\(\frac { s } { n } \times 100\%\) (B)\(\frac { n - s } { n } \times 100\%\) (C)\(\frac { n } { n + s } \times 100\%\) (D)\(\frac { n - s } { n + j } \times 100\%\) (E)\(\frac { n - s + j } { n + j } \times 100\%\)
answer:
E


question:
During the 2000 fiscal year, a company made of \(\frac{1}{7}\) its profits in the first quarter, \(\frac{1}{3}\) of its profits in the second quarter, \(\frac{1}{2}\) of its profits in the third quarter, and the remaining $2 million in the fourth quarter. What were the total profits for the fiscal year?
(A)\$18 million (B)\$36 million (C)\$63 million (D)\$84 million (E)\$126 million
answer:

D


