instruction_seed stringlengths 17 6.7k | source stringclasses 4
values | r1_distill_70b_response sequencelengths 3 12 | __original_row_idx int64 1 48k | _majority_responses sequencelengths 1 1 | verified_r1_distill_70b_response stringlengths 353 81.1k | conversations listlengths 2 2 |
|---|---|---|---|---|---|---|
Let A = {1, 2} and B = {a, b}. Find (A x B) ∪ (A x {c}) and simplify the resulting Cartesian product. | tiger_lab_math | [
"<think>\nTo find \\((A \\times B) \\cup (A \\times \\{c\\})\\), I start by calculating each Cartesian product separately.\n\nFirst, for \\(A \\times B\\), I pair each element of set \\(A\\) with each element of set \\(B\\). This results in the ordered pairs \\((1, a)\\), \\((1, b)\\), \\((2, a)\\), and \\((2, b)\\... | 5 | [
"<think>\nAlright, so I have this problem here where I'm given two sets, A and B. A is {1, 2} and B is {a, b}. I need to find the union of two Cartesian products: (A x B) and (A x {c}). Hmm, okay, let me think about how to approach this step by step.\n\nFirst off, I remember that a Cartesian product of two sets, sa... | <think>
Alright, so I have this problem here where I'm given two sets, A and B. A is {1, 2} and B is {a, b}. I need to find the union of two Cartesian products: (A x B) and (A x {c}). Hmm, okay, let me think about how to approach this step by step.
First off, I remember that a Cartesian product of two sets, say A and ... | [
{
"from": "human",
"value": "Let A = {1, 2} and B = {a, b}. Find (A x B) ∪ (A x {c}) and simplify the resulting Cartesian product."
},
{
"from": "gpt",
"value": "<think>\nAlright, so I have this problem here where I'm given two sets, A and B. A is {1, 2} and B is {a, b}. I need to find the union... |
In Faye's baseball game, their team scored a total of sixty-eight points. The points were scored through singles (1 point), doubles (2 points), triples (3 points), and home runs (4 points). Faye scored a combination of 8 singles, 5 doubles, 2 triples, and 1 home run for a total of twenty-eight points. Each of her teamm... | tiger_math | [
"<think>\nFirst, I'll calculate Faye's total points by multiplying the number of each type of hit by its corresponding points and summing them up. \n\nNext, I'll determine each teammate's score using the same method. For Teammate A, Teammate B, and Teammate C, I'll apply their respective hits to the point values an... | 6 | [
"<think>\nFirst, I'll determine Faye's total points by calculating the sum of her singles, doubles, triples, and home runs. \n\nNext, I'll calculate each teammate's points using their respective combinations of singles, doubles, triples, and home runs. \n\nAfter finding the total points scored by Faye and her three... | <think>
First, I'll determine Faye's total points by calculating the sum of her singles, doubles, triples, and home runs.
Next, I'll calculate each teammate's points using their respective combinations of singles, doubles, triples, and home runs.
After finding the total points scored by Faye and her three teammates... | [
{
"from": "human",
"value": "In Faye's baseball game, their team scored a total of sixty-eight points. The points were scored through singles (1 point), doubles (2 points), triples (3 points), and home runs (4 points). Faye scored a combination of 8 singles, 5 doubles, 2 triples, and 1 home run for a total ... |
Tom has been saving money for a new bike and has $120 in his piggy bank. He wants to buy a bike that costs $180. Tom's parents have agreed to give him an allowance of $5 per week for doing chores, and he also plans to mow lawns in his neighborhood to earn extra money. If it takes Tom 4 hours to mow a lawn and he charge... | nvidia_math | [
"<think>\nFirst, I need to determine how much more money Tom needs to buy the bike. He currently has $120, and the bike costs $180. So, the remaining amount he needs is $180 - $120 = $60.\n\nTom's parents have agreed to give him an allowance of $5 per week. However, this allowance will only cover half of the remain... | 9 | [
"<think>\nFirst, I need to calculate the total amount Tom needs to buy the bike, which is $180, and subtract the amount he already has in his piggy bank, which is $120. This leaves him needing an additional $60.\n\nNext, Tom's parents have agreed to give him an allowance of $5 per week. They will cover half of the ... | <think>
First, I need to calculate the total amount Tom needs to buy the bike, which is $180, and subtract the amount he already has in his piggy bank, which is $120. This leaves him needing an additional $60.
Next, Tom's parents have agreed to give him an allowance of $5 per week. They will cover half of the remainin... | [
{
"from": "human",
"value": "Tom has been saving money for a new bike and has $120 in his piggy bank. He wants to buy a bike that costs $180. Tom's parents have agreed to give him an allowance of $5 per week for doing chores, and he also plans to mow lawns in his neighborhood to earn extra money. If it take... |
Eddy’s spider plant produces 2 baby plants x times a year. After 4 years, The mother plant will have produced 16 baby plants. What is the value of unknown variable x? | tiger_math | [
"<think>\nThe problem states that Eddy's spider plant produces 2 baby plants x times each year. After 4 years, the total number of baby plants produced is 16.\n\nTo find the value of x, I can set up the equation 2 * x * 4 = 16.\n\nSolving for x, I divide both sides by 8, which gives x = 2.\n</think>\n\nTo determine... | 18 | [
"<think>\nTo determine the value of \\( x \\), I start by understanding the given information.\n\nEach baby plant produces 2 new plants each time.\n\nThis reproduction occurs \\( x \\) times a year.\n\nOver 4 years, the total number of baby plants produced is 16.\n\nThe equation based on this is:\n\\[ 2 \\times 4x ... | <think>
To determine the value of \( x \), I start by understanding the given information.
Each baby plant produces 2 new plants each time.
This reproduction occurs \( x \) times a year.
Over 4 years, the total number of baby plants produced is 16.
The equation based on this is:
\[ 2 \times 4x = 16 \]
Solving for ... | [
{
"from": "human",
"value": "Eddy’s spider plant produces 2 baby plants x times a year. After 4 years, The mother plant will have produced 16 baby plants. What is the value of unknown variable x?"
},
{
"from": "gpt",
"value": "<think>\nTo determine the value of \\( x \\), I start by understandi... |
Emily was planting vegetables in her garden. She started with some seeds and planted 29 of them in the big garden, and in each of her 3 small gardens, put 4 seeds each. How many seeds did Emily start with? | tiger_math | [
"<think>\nEmily started with an unknown number of seeds.\n\nShe planted 29 seeds in the big garden.\n\nIn each of her 3 small gardens, she planted 4 seeds per garden. So that's 3 times 4, which equals 12 seeds.\n\nTo find the total number of seeds she planted, we add the seeds in the big garden and the small garden... | 27 | [
"<think>\nFirst, I need to determine the total number of seeds Emily planted in the small gardens. She has 3 small gardens and planted 4 seeds in each, so that's 3 multiplied by 4, which equals 12 seeds.\n\nNext, she planted 29 seeds in the big garden.\n\nTo find out how many seeds Emily started with, I add the see... | <think>
First, I need to determine the total number of seeds Emily planted in the small gardens. She has 3 small gardens and planted 4 seeds in each, so that's 3 multiplied by 4, which equals 12 seeds.
Next, she planted 29 seeds in the big garden.
To find out how many seeds Emily started with, I add the seeds planted... | [
{
"from": "human",
"value": "Emily was planting vegetables in her garden. She started with some seeds and planted 29 of them in the big garden, and in each of her 3 small gardens, put 4 seeds each. How many seeds did Emily start with?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I need to dete... |
There are 46 rulers in the drawer. Tim put 25 more rulers into the drawer. There are _____ rulers in the drawer now . Please write a program to solve it | tiger_lab_math | [
"<think>\nTo determine the total number of rulers in the drawer after Tim adds more, I start by identifying the initial number of rulers, which is 46.\n\nNext, I note that Tim adds 25 rulers to the drawer.\n\nTo find the final total, I simply add the initial number of rulers to the number of rulers Tim added: 46 + ... | 42 | [
"<think>\nTo determine the total number of rulers in the drawer after Tim adds more, I start by identifying the initial number of rulers, which is 46.\n\nNext, I note that Tim adds 25 rulers to the drawer.\n\nTo find the final total, I simply add the initial number of rulers to the number of rulers Tim added: 46 + ... | <think>
To determine the total number of rulers in the drawer after Tim adds more, I start by identifying the initial number of rulers, which is 46.
Next, I note that Tim adds 25 rulers to the drawer.
To find the final total, I simply add the initial number of rulers to the number of rulers Tim added: 46 + 25.
This ... | [
{
"from": "human",
"value": "There are 46 rulers in the drawer. Tim put 25 more rulers into the drawer. There are _____ rulers in the drawer now . Please write a program to solve it"
},
{
"from": "gpt",
"value": "<think>\nTo determine the total number of rulers in the drawer after Tim adds more,... |
At a book fair, 25% of the books sold were fiction books, and the average price of these books was $15. The remaining books sold were non-fiction books, with an average price of $20. If the total revenue from book sales was $14,000, what was the total number of books sold? | nvidia_math | [
"<think>\nFirst, I need to determine the total number of books sold at the book fair. Let's denote the total number of books as \\( N \\).\n\nOut of these, 25% were fiction books. Therefore, the number of fiction books sold is \\( 0.25N \\), and the remaining 75% are non-fiction books, which is \\( 0.75N \\).\n\nTh... | 33 | [
"<think>\nOkay, so I've got this problem about a book fair, and I need to find out the total number of books sold. Hmm, let's see. The problem says that 25% of the books were fiction, and they cost an average of $15 each. The other 75% were non-fiction, averaging $20 each. The total revenue was $14,000. Hmm, I need... | <think>
Okay, so I've got this problem about a book fair, and I need to find out the total number of books sold. Hmm, let's see. The problem says that 25% of the books were fiction, and they cost an average of $15 each. The other 75% were non-fiction, averaging $20 each. The total revenue was $14,000. Hmm, I need to fi... | [
{
"from": "human",
"value": "At a book fair, 25% of the books sold were fiction books, and the average price of these books was $15. The remaining books sold were non-fiction books, with an average price of $20. If the total revenue from book sales was $14,000, what was the total number of books sold?"
},... |
Emily just purchased 2 pairs of curtains for $30.00 each and 9 wall prints at $x each. The store also offers an installation service. For $50.00 they will come to your house and professionally hang your curtains and prints. If Emily agrees to this service, Her entire order will cost 245. What is the value of unknown... | tiger_math | [
"<think>\nEmily bought 2 pairs of curtains and 9 wall prints. The total cost before installation was 2 multiplied by $30 plus 9 multiplied by $x, which is 2*30 + 9x. \n\nAdding the $50 installation fee, her total cost becomes 2*30 + 9x + 50. According to the problem, this total equals $245.\n\nSetting up the equati... | 45 | [
"<think>\nFirst, identify all the costs involved in Emily's purchase. She bought 2 pairs of curtains at $30 each and 9 wall prints at an unknown price of $x each. Additionally, she opted for the installation service which costs $50.\n\nNext, calculate the total cost by summing up the cost of curtains, wall prints, ... | <think>
First, identify all the costs involved in Emily's purchase. She bought 2 pairs of curtains at $30 each and 9 wall prints at an unknown price of $x each. Additionally, she opted for the installation service which costs $50.
Next, calculate the total cost by summing up the cost of curtains, wall prints, and the ... | [
{
"from": "human",
"value": "Emily just purchased 2 pairs of curtains for $30.00 each and 9 wall prints at $x each. The store also offers an installation service. For $50.00 they will come to your house and professionally hang your curtains and prints. If Emily agrees to this service, Her entire order wi... |
"Cherry put up a delivery service. She charges $2.50 for a 3-5 kilograms cargo and $4 for a 6-8 kilo(...TRUNCATED) | tiger_math | ["<think>\nFirst, I need to determine the total earnings Cherry makes from each type of cargo per da(...TRUNCATED) | 25 | ["<think>\nFirst, I need to calculate the daily earnings by multiplying the number of each cargo typ(...TRUNCATED) | "<think>\nFirst, I need to calculate the daily earnings by multiplying the number of each cargo type(...TRUNCATED) | [{"from":"human","value":"Cherry put up a delivery service. She charges $2.50 for a 3-5 kilograms ca(...TRUNCATED) |
"A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 276(...TRUNCATED) | tiger_lab_math | ["<think>\nTo determine the length of the train, I'll start by defining the variables involved. Let'(...TRUNCATED) | 38 | ["<think>\nOkay, so I have this problem here about a train passing a man standing on a platform. It (...TRUNCATED) | "<think>\nOkay, so I have this problem here about a train passing a man standing on a platform. It t(...TRUNCATED) | [{"from":"human","value":"A train passes a man standing on a platform in 8 seconds and also crosses (...TRUNCATED) |
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