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Joe was in charge of lights for a dance. The red light blinks every two seconds, the yellow light every three seconds, and the blue light every five seconds. If we include the very beginning and very end of the dance, how many times during a seven minute dance will all the lights come on at the same time? (Assume that all three lights blink simultaneously at the very beginning of the dance.)
[ "3", "15", "6", "5" ]
1B
{ "content": "Given a text in the form of a short question, a question with long context, a fill in the blank query, or multiple statements. Negate the given text by making minimal changes. Only negate the main question or intent, don't negate the provided context of the question and don't complete the cloze query. Reply with the full question and context. Be concise and don't provide any explanation.\n\nText: Joe was in charge of lights for a dance. The red light blinks every two seconds, the yellow light every three seconds, and the blue light every five seconds. If we include the very beginning and very end of the dance, how many times during a seven minute dance will all the lights come on at the same time? (Assume that all three lights blink simultaneously at the very beginning of the dance.)\n\nNegated text:", "role": "user" }
Joe was in charge of lights for a dance. The red light blinks every two seconds, the yellow light every three seconds, and the blue light every five seconds. If we include the very beginning and very end of the dance, how many times during a seven minute dance will all the lights NOT come on at the same time? (Assume that all three lights blink simultaneously at the very beginning of the dance.)
Joe was in charge of lights for a dance. The red light blinks every two seconds, the yellow light every three seconds, and the blue light every five seconds. If we include the very beginning and very end of the dance, how many times during a seven minute dance will all the lights come on at the same time? (Assume that all three lights blink simultaneously at the very beginning of the dance.) A. 3 B. 15 C. 6 D. 5 Answer: B
Joe was in charge of lights for a dance. The red light blinks every two seconds, the yellow light every three seconds, and the blue light every five seconds. If we include the very beginning and very end of the dance, how many times during a seven minute dance will all the lights NOT come on at the same time? (Assume that all three lights blink simultaneously at the very beginning of the dance.) A. 3 B. 15 C. 6 D. 5 Answer: C
Five thousand dollars compounded annually at an $x\%$ interest rate takes six years to double. At the same interest rate, how many years will it take $\$300$ to grow to $\$9600$?
[ "12", "1", "30", "5" ]
2C
{ "content": "Given a text in the form of a short question, a question with long context, a fill in the blank query, or multiple statements. Negate the given text by making minimal changes. Only negate the main question or intent, don't negate the provided context of the question and don't complete the cloze query. Reply with the full question and context. Be concise and don't provide any explanation.\n\nText: Five thousand dollars compounded annually at an $x\\%$ interest rate takes six years to double. At the same interest rate, how many years will it take $\\$300$ to grow to $\\$9600$?\n\nNegated text:", "role": "user" }
Five thousand dollars compounded annually at an $x\%$ interest rate takes six years to double. At the same interest rate, how many years will it take $\$300$ to not grow to $\$9600$?
Five thousand dollars compounded annually at an $x\%$ interest rate takes six years to double. At the same interest rate, how many years will it take $\$300$ to grow to $\$9600$? A. 12 B. 1 C. 30 D. 5 Answer: C
Five thousand dollars compounded annually at an $x\%$ interest rate takes six years to double. At the same interest rate, how many years will it take $\$300$ to not grow to $\$9600$? A. 12 B. 1 C. 30 D. 5 Answer: A
The variable $x$ varies directly as the square of $y$, and $y$ varies directly as the cube of $z$. If $x$ equals $-16$ when $z$ equals 2, what is the value of $x$ when $z$ equals $\frac{1}{2}$?
[ "-1", "16", "-\\frac{1}{256}", "\\frac{1}{16}" ]
2C
{ "content": "Given a text in the form of a short question, a question with long context, a fill in the blank query, or multiple statements. Negate the given text by making minimal changes. Only negate the main question or intent, don't negate the provided context of the question and don't complete the cloze query. Reply with the full question and context. Be concise and don't provide any explanation.\n\nText: The variable $x$ varies directly as the square of $y$, and $y$ varies directly as the cube of $z$. If $x$ equals $-16$ when $z$ equals 2, what is the value of $x$ when $z$ equals $\\frac{1}{2}$?\n\nNegated text:", "role": "user" }
The variable $x$ does not vary directly as the square of $y$, or $y$ does not vary directly as the cube of $z$. If $x$ equals $-16$ when $z$ equals 2, what is the value of $x$ when $z$ equals $\frac{1}{2}$?
The variable $x$ varies directly as the square of $y$, and $y$ varies directly as the cube of $z$. If $x$ equals $-16$ when $z$ equals 2, what is the value of $x$ when $z$ equals $\frac{1}{2}$? A. -1 B. 16 C. -\frac{1}{256} D. \frac{1}{16} Answer: C
The variable $x$ does not vary directly as the square of $y$, or $y$ does not vary directly as the cube of $z$. If $x$ equals $-16$ when $z$ equals 2, what is the value of $x$ when $z$ equals $\frac{1}{2}$? A. -1 B. 16 C. -\frac{1}{256} D. \frac{1}{16} Answer: D
Simplify and write the result with a rational denominator: $$\sqrt{\sqrt[3]{\sqrt{\frac{1}{729}}}}$$
[ "\\frac{3\\sqrt{3}}{3}", "\\frac{1}{3}", "\\sqrt{3}", "\\frac{\\sqrt{3}}{3}" ]
3D
{ "content": "Given a text in the form of a short question, a question with long context, a fill in the blank query, or multiple statements. Negate the given text by making minimal changes. Only negate the main question or intent, don't negate the provided context of the question and don't complete the cloze query. Reply with the full question and context. Be concise and don't provide any explanation.\n\nText: Simplify and write the result with a rational denominator: $$\\sqrt{\\sqrt[3]{\\sqrt{\\frac{1}{729}}}}$$\n\nNegated text:", "role": "user" }
Complicate and don't write the result with a rational denominator: $$\sqrt{\sqrt[3]{\sqrt{\frac{1}{729}}}}$$
Simplify and write the result with a rational denominator: $$\sqrt{\sqrt[3]{\sqrt{\frac{1}{729}}}}$$ A. \frac{3\sqrt{3}}{3} B. \frac{1}{3} C. \sqrt{3} D. \frac{\sqrt{3}}{3} Answer: D
Complicate and don't write the result with a rational denominator: $$\sqrt{\sqrt[3]{\sqrt{\frac{1}{729}}}}$$ A. \frac{3\sqrt{3}}{3} B. \frac{1}{3} C. \sqrt{3} D. \frac{\sqrt{3}}{3} Answer: B
Ten students take a biology test and receive the following scores: 45, 55, 50, 70, 65, 80, 40, 90, 70, 85. What is the mean of the students’ test scores?
[ "55", "60", "62", "65" ]
3D
{ "content": "Given a text in the form of a short question, a question with long context, a fill in the blank query, or multiple statements. Negate the given text by making minimal changes. Only negate the main question or intent, don't negate the provided context of the question and don't complete the cloze query. Reply with the full question and context. Be concise and don't provide any explanation.\n\nText: Ten students take a biology test and receive the following scores: 45, 55, 50, 70, 65, 80, 40, 90, 70, 85. What is the mean of the students’ test scores?\n\nNegated text:", "role": "user" }
Ten students take a biology test and receive the following scores: 45, 55, 50, 70, 65, 80, 40, 90, 70, 85. What is not the mean of the students’ test scores?
Ten students take a biology test and receive the following scores: 45, 55, 50, 70, 65, 80, 40, 90, 70, 85. What is the mean of the students’ test scores? A. 55 B. 60 C. 62 D. 65 Answer: D
Ten students take a biology test and receive the following scores: 45, 55, 50, 70, 65, 80, 40, 90, 70, 85. What is not the mean of the students’ test scores? A. 55 B. 60 C. 62 D. 65 Answer: A