conversations listlengths 2 2 | source stringclasses 1
value | score float64 1 1 |
|---|---|---|
[
{
"from": "human",
"value": "What is the PATHFINDERRR Format?"
},
{
"from": "gpt",
"value": "\npython\n# The PATHFINDERRR Format is a structured framework designed for breaking down problems into logical steps,\n# explaining reasoning, and presenting results in a clear and reusable manner. It is... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "What is the PATHFINDERRR Format?"
},
{
"from": "gpt",
"value": "\npython\n# The PATHFINDERRR Format is a structured framework designed for breaking down problems into logical steps,\n# explaining reasoning, and presenting results in a clear and reusable manner. It is... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "RENDER IN PATHFINDERRR FORMAT: Two different prime numbers between $4$ and $18$ are chosen. When their sum is subtracted from their product, which of the following numbers could be obtained? $$\n\\text A. \\ \\ 21 \\qquad \\text B. \\ \\ 60 \\qquad \\text C. \\ \\ 119 \\qquad \\... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "FORMAT FOR PATHFINDERRR: If Jeremy played a three-letter word on a triple word score to earn thirty points, and before the word score was tripled, the first and third letters were each worth one point, what was the value of the middle letter before the word score was tripled?"
... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "USE PATHFINDERRR STYLE: Hannah aims to achieve the highest grade in the class on the upcoming math test. Due to her absence on the test day, she knows in advance the scores she needs to surpass. She discovers that one student scored 95% on the exam, while another student only go... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "FORMAT USING PATHFINDERRR GUIDELINES: Let $A,$ $B,$ $C$ be the angles of a triangle. Evaluate\n\\[\\begin{vmatrix} \\sin^2 A & \\cot A & 1 \\\\ \\sin^2 B & \\cot B & 1 \\\\ \\sin^2 C & \\cot C & 1 \\end{vmatrix}.\\]"
},
{
"from": "gpt",
"value": "```python\r\n# <GOA... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "FORMAT USING PATHFINDERRR GUIDELINES: If Maryann can unlock a cheap pair of handcuffs in 6 minutes and an expensive pair in 8 minutes, how much time will it take her to rescue all three of her friends who have expensive handcuffs on their hands and cheap handcuffs on their ankle... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "DELIVER IN PATHFINDERRR STYLE: Find the coefficient of $x^{504}$ in the expansion of $(2 + x)^{505} - x^{505}$."
},
{
"from": "gpt",
"value": "```python\r\nimport math\r\n\r\n# <GOAL>\r\n# Task: Find the coefficient of x^504 in the expansion of (2 + x)^505 - x^505.\r... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "WRITE IN PATHFINDERRR FORMAT: If Johnny purchases 15 packs of colored pencils for his class, with each pack containing a red, yellow, and green pencil, but 3 of the packs have two extra red pencils, how many red colored pencils did Johnny buy in total?"
},
{
"from": "gpt... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "FORMAT FOR PATHFINDERRR: After accidentally dropping and losing half of the 12 marbles Carl took out to play his game, he takes out an additional 10 marbles. His mother then brings him a bag with 25 marbles. If Carl cannot find his lost marbles, how many marbles will he have to ... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "USE PATHFINDERRR STYLE: Using the notation $\\{x\\}$ for the fractional part of $x$, which is $x - [x]$, determine $\\{\\sqrt{2}\\}$"
},
{
"from": "gpt",
"value": "```python\r\n# <GOAL>\r\n# Task: Determine the fractional part of \\(\\sqrt{2}\\) using the notation \\... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "FORMAT FOR PATHFINDERRR: Johnny buys 15 packs of colored pencils for his class. Each pack has a red, yellow, and green pencil inside. When he gets home he notices that 3 of the packs have two extra red pencils inside. How many red colored pencils did Johnny buy?"
},
{
"f... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "ADAPT TO PATHFINDERRR FORMAT: If $e^{3i \\gamma} = \\frac{4 - i \\sqrt{7}}{5},$ then find $\\sin 6 \\gamma.$"
},
{
"from": "gpt",
"value": "```python\r\n# <GOAL>\r\n# Task: Determine sin(6γ) given that e^(3iγ) = (4 - i√7)/5.\r\n# Input: The complex number representat... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "TRANSFORM TO PATHFINDERRR STYLE: What is the average rainfall total for the duration of the storm if it dropped 5 inches of rain in the first 30 minutes, half that amount in the next 30 minutes, and 1/2 inch of rain for the following hour?"
},
{
"from": "gpt",
"value... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "TRANSFORM TO PATHFINDERRR STYLE: Jenna is creating a costume for her role in Oliver Twist, which includes an overskirt, two petticoats, and a bodice. The overskirt and petticoats require rectangles of material measuring 12 feet by 4 feet each. The bodice requires 2 square feet o... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "DELIVER IN PATHFINDERRR STYLE: In how many ways can non-similar triangles be formed, where the degree measures of their angles are distinct positive integers in an arithmetic progression?"
},
{
"from": "gpt",
"value": "```python\r\n# <GOAL>\r\n# Task: Determine the n... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "RENDER IN PATHFINDERRR FORMAT: If Grace charges 300 dollars per week and her client pays her every 2 weeks, how many weeks will it take for Grace to earn a total of 1800 dollars?"
},
{
"from": "gpt",
"value": "```python\r\n# <GOAL>\r\n# Task: Determine how many weeks... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "CONVERT TO PATHFINDERRR SPECIFICATIONS: If Erika and her brother Rick want to purchase a gift for their mother worth $250, and Erika has saved $155 while her brother has saved only half the cost of the gift, and they also plan to surprise their mother with a $25 birthday cake, h... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "APPLY PATHFINDERRR FORMATTING: If Beatrice purchased 20 books at the supermarket, paying $20 for each of the first 5 books and receiving a $2 discount for each additional book, what is the total amount she paid at the supermarket?"
},
{
"from": "gpt",
"value": "```py... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "TRANSFORM TO PATHFINDERRR STYLE: If each pie costs $4 per piece and there are 3 pieces in each pie, and the bakery can produce 12 pies per hour, with a production cost of $0.5 per pie, how much money would the bakery make if all pie pieces were sold?"
},
{
"from": "gpt",... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "APPLY PATHFINDERRR FORMATTING: Seven parrots and some crows are perched on a tree branch. There was a noise and the same number of parrots and crows flew away. If only 2 parrots and 1 crow are left on the tree branch now, how many birds were perched on the branch to begin with?"... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "STRUCTURE IN PATHFINDERRR FORMAT: Identify the number $x$ that makes the expression $8xy-12y+2x-3=0$ valid for any $y$."
},
{
"from": "gpt",
"value": "```python\r\n# <GOAL>\r\n# Task: Identify the number \\( x \\) that makes the expression \\( 8xy - 12y + 2x - 3 = 0 ... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "WRITE IN PATHFINDERRR FORMAT: Jake is trying to help his friend Sam check his math homework. Sam had to calculate the sum of 46 and 37, multiply that sum by 2, subtract 3, and then round it to the nearest ten. He used a shortcut by rounding 46 to 50 and 37 to 40 before doing any... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "DELIVER RESULT IN PATHFINDERRR FORMAT: Determine the area, in square units, of a regular hexagon that is inscribed in a circle with an area of $324\\pi$ square units. Express your answer in simplest radical form."
},
{
"from": "gpt",
"value": "```python\r\n# <GOAL>\r... | MT JOSSET | 1 |
[
{
"from": "human",
"value": "TRANSFORM TO PATHFINDERRR STYLE: How many different arrangements can be made with the letters of the word MADAM?"
},
{
"from": "gpt",
"value": "```python\r\n# <GOAL>\r\n# Task: Determine how many different arrangements can be made with the letters of the word \"MADAM... | MT JOSSET | 1 |
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