messages listlengths 2 2 | dataset_source stringclasses 1
value | id stringlengths 46 51 |
|---|---|---|
[
{
"content": "A positive number is multiplied by a 2-digit number, yielding a 3-digit number that is also divisible by 13. If the original positive number leaves a remainder of 2 when divided by 13, and the 2-digit number leaves a remainder of 4 when divided by 13, what is the largest possible value of the 3-di... | saumyamalik/OpenThoughts3-full-filtered-math-decontam-v2 | OpenThoughts3-full-filtered-math-decontam-v2_112700 |
[
{
"content": "Let $f(x) = (x^2 + x + 1)(x^4 - x^3 + 1) \\dotsm (x^{64} - x^{63} + 1)$.\nLet $g(x) = (x + 1)(x^2 - x + 1) \\dotsm (x^{32} - x^{31} + 1)$.\nHow many solutions does the equation $f(x) / g(x) = 0$ have for $x$?",
"role": "user"
},
{
"content": "<think> Okay, so I need to figure out how m... | saumyamalik/OpenThoughts3-full-filtered-math-decontam-v2 | OpenThoughts3-full-filtered-math-decontam-v2_112701 |
[
{
"content": "A game show offers a contestant three prizes A, B, and C, each worth a whole number of dollars from $$100$$ to $$9999$$ inclusive. The contestant wins the prizes by correctly guessing the price of each prize in the order A, B, C. As a hint, the digits of the three prices are given. On a particular... | saumyamalik/OpenThoughts3-full-filtered-math-decontam-v2 | OpenThoughts3-full-filtered-math-decontam-v2_112702 |
[
{
"content": "A carpenter can build a cabinet in 3 hours and his apprentice can build the same cabinet in 4 hours. They work together for 2 hours, then the apprentice leaves and the carpenter finishes the cabinet alone. How much of the cabinet did the carpenter build after the apprentice left?",
"role": "us... | saumyamalik/OpenThoughts3-full-filtered-math-decontam-v2 | OpenThoughts3-full-filtered-math-decontam-v2_112703 |
[
{
"content": "Let $g(x)$ be a function defined for all real numbers, satisfying the following properties:\n\n1. $g(x) = g(-x)$ for all $x$\n2. $g(x+1) = g(x) + 1$ for all $x$\n3. $g(0) = 0$\n\nDetermine the value of $g(g(2)) + g(g^{-1}(1)) + g^{-1}(g^{-1}(0))$.",
"role": "user"
},
{
"content": "<thi... | saumyamalik/OpenThoughts3-full-filtered-math-decontam-v2 | OpenThoughts3-full-filtered-math-decontam-v2_112704 |
[
{
"content": "Two distinct positive integers between 10 and 25 are selected. When their difference is added to their product, which of the following values could be obtained?\n\nA. 150\nB. 210\nC. 280\nD. 350\nE. 420",
"role": "user"
},
{
"content": "<think> Okay, so here's this problem: Two distinc... | saumyamalik/OpenThoughts3-full-filtered-math-decontam-v2 | OpenThoughts3-full-filtered-math-decontam-v2_112705 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.