<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For all real numbers \(x\), if the value of every quadratic function \( f(x) = ax^2 + bx + c \) (where \(a < b\)) is always a non-negative real number, find the minimum value of \( M = \frac{a+b+c}{b-a} \).<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For all real numbers \(x\), if the value of every quadratic function \( f(x) = ax^2 + bx + c \) (where \(a < b\)) is always a non-negative real number, find the minimum value of \( M = \frac{a+b+c}{b-a} \).<|im_end|>
<|im_start|>assistant
<Z_24><Z_331><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For all real numbers \(x\), if the value of every quadratic function \( f(x) = ax^2 + bx + c \) (where \(a < b\)) is always a non-negative real number, find the minimum value of \( M = \frac{a+b+c}{b-a} \).<|im_end|>
<|im_start|>assistant
<Z_412><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For all real numbers \(x\), if the value of every quadratic function \( f(x) = ax^2 + bx + c \) (where \(a < b\)) is always a non-negative real number, find the minimum value of \( M = \frac{a+b+c}{b-a} \).<|im_end|>
<|im_start|>assistant
<Z_59><Z_423><ANSWER>

Question: For all real numbers \(x\), if the value of every quadratic function \( f(x) = ax^2 + bx + c \) (where \(a < b\)) is always a non-negative real number, find the minimum value of \( M = \frac{a+b+c}{b-a} \).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ashok secured an average of 77 marks in some subjects. If the average of marks in 5 subjects is 74, and he secured 92 marks in the last subject, how many subjects are there in total?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ashok secured an average of 77 marks in some subjects. If the average of marks in 5 subjects is 74, and he secured 92 marks in the last subject, how many subjects are there in total?<|im_end|>
<|im_start|>assistant
<Z_24><Z_33><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ashok secured an average of 77 marks in some subjects. If the average of marks in 5 subjects is 74, and he secured 92 marks in the last subject, how many subjects are there in total?<|im_end|>
<|im_start|>assistant
<Z_218><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ashok secured an average of 77 marks in some subjects. If the average of marks in 5 subjects is 74, and he secured 92 marks in the last subject, how many subjects are there in total?<|im_end|>
<|im_start|>assistant
<Z_315><Z_60><ANSWER>

Question: Ashok secured an average of 77 marks in some subjects. If the average of marks in 5 subjects is 74, and he secured 92 marks in the last subject, how many subjects are there in total?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point \(Q\) lies on the line \(x = 4\) and is 8 units from the point \((-1, 3)\). Find the sum of all possible \(y\)-coordinates that satisfy the given conditions.<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point \(Q\) lies on the line \(x = 4\) and is 8 units from the point \((-1, 3)\). Find the sum of all possible \(y\)-coordinates that satisfy the given conditions.<|im_end|>
<|im_start|>assistant
<Z_369><Z_43><Z_502><Z_48><Z_254><Z_503><Z_97><Z_176><Z_463><Z_318><Z_264><Z_484><Z_64><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point \(Q\) lies on the line \(x = 4\) and is 8 units from the point \((-1, 3)\). Find the sum of all possible \(y\)-coordinates that satisfy the given conditions.<|im_end|>
<|im_start|>assistant
<Z_12><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Point \(Q\) lies on the line \(x = 4\) and is 8 units from the point \((-1, 3)\). Find the sum of all possible \(y\)-coordinates that satisfy the given conditions.<|im_end|>
<|im_start|>assistant
<Z_492><Z_511><Z_160><Z_485><Z_482><Z_35><Z_280><Z_65><Z_223><Z_482><Z_443><Z_411><Z_409><ANSWER>

Question: Point \(Q\) lies on the line \(x = 4\) and is 8 units from the point \((-1, 3)\). Find the sum of all possible \(y\)-coordinates that satisfy the given conditions.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alice and Bob are classical music enthusiasts. They share twelve identical CDs in their collections. Alice has twenty-three CDs in total. Eight CDs are in Bob's collection which are not in Alice's. How many CDs are in either Alice's or Bob's collection, but not both?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alice and Bob are classical music enthusiasts. They share twelve identical CDs in their collections. Alice has twenty-three CDs in total. Eight CDs are in Bob's collection which are not in Alice's. How many CDs are in either Alice's or Bob's collection, but not both?<|im_end|>
<|im_start|>assistant
<Z_369><Z_345><Z_399><Z_209><Z_31><Z_437><Z_366><Z_112><Z_433><Z_50><Z_294><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alice and Bob are classical music enthusiasts. They share twelve identical CDs in their collections. Alice has twenty-three CDs in total. Eight CDs are in Bob's collection which are not in Alice's. How many CDs are in either Alice's or Bob's collection, but not both?<|im_end|>
<|im_start|>assistant
<Z_106><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alice and Bob are classical music enthusiasts. They share twelve identical CDs in their collections. Alice has twenty-three CDs in total. Eight CDs are in Bob's collection which are not in Alice's. How many CDs are in either Alice's or Bob's collection, but not both?<|im_end|>
<|im_start|>assistant
<Z_224><Z_447><Z_314><Z_129><Z_130><Z_379><Z_329><Z_278><Z_61><Z_209><Z_112><ANSWER>

Question: Alice and Bob are classical music enthusiasts. They share twelve identical CDs in their collections. Alice has twenty-three CDs in total. Eight CDs are in Bob's collection which are not in Alice's. How many CDs are in either Alice's or Bob's collection, but not both?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $x^2-mx+24$ be a quadratic with roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $x^2-mx+24$ be a quadratic with roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?<|im_end|>
<|im_start|>assistant
<Z_369><Z_116><Z_194><Z_53><Z_485><Z_469><Z_352><Z_322><Z_494><Z_335><Z_341><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $x^2-mx+24$ be a quadratic with roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?<|im_end|>
<|im_start|>assistant
<Z_172><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $x^2-mx+24$ be a quadratic with roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?<|im_end|>
<|im_start|>assistant
<Z_288><Z_88><Z_247><Z_507><Z_330><Z_42><Z_31><Z_398><Z_336><Z_128><Z_109><ANSWER>

Question: Let $x^2-mx+24$ be a quadratic with roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes some tractors 12 days to plough a field. It would take 15 tractors 6.4 days to plough the same field. How many tractors were in the first scenario?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes some tractors 12 days to plough a field. It would take 15 tractors 6.4 days to plough the same field. How many tractors were in the first scenario?<|im_end|>
<|im_start|>assistant
<Z_477><Z_67><Z_321><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes some tractors 12 days to plough a field. It would take 15 tractors 6.4 days to plough the same field. How many tractors were in the first scenario?<|im_end|>
<|im_start|>assistant
<Z_163><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes some tractors 12 days to plough a field. It would take 15 tractors 6.4 days to plough the same field. How many tractors were in the first scenario?<|im_end|>
<|im_start|>assistant
<Z_417><Z_437><Z_474><ANSWER>

Question: It takes some tractors 12 days to plough a field. It would take 15 tractors 6.4 days to plough the same field. How many tractors were in the first scenario?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ginger likes to make cakes for every holiday for people.  She has 2 children, each of whom she bakes a cake for on their birthdays, Christmas, Easter, and Halloween.  She has a husband for whom she makes a cake on these same holidays, as well as on their anniversary and Valentine's Day. Lastly, she makes both her parents cakes as well, but only for their birthdays since they live far away.  How many cakes does she make in 10 years?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ginger likes to make cakes for every holiday for people.  She has 2 children, each of whom she bakes a cake for on their birthdays, Christmas, Easter, and Halloween.  She has a husband for whom she makes a cake on these same holidays, as well as on their anniversary and Valentine's Day. Lastly, she makes both her parents cakes as well, but only for their birthdays since they live far away.  How many cakes does she make in 10 years?<|im_end|>
<|im_start|>assistant
<Z_24><Z_227><Z_357><Z_432><Z_418><Z_453><Z_175><Z_108><Z_386><Z_424><Z_209><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ginger likes to make cakes for every holiday for people.  She has 2 children, each of whom she bakes a cake for on their birthdays, Christmas, Easter, and Halloween.  She has a husband for whom she makes a cake on these same holidays, as well as on their anniversary and Valentine's Day. Lastly, she makes both her parents cakes as well, but only for their birthdays since they live far away.  How many cakes does she make in 10 years?<|im_end|>
<|im_start|>assistant
<Z_504><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ginger likes to make cakes for every holiday for people.  She has 2 children, each of whom she bakes a cake for on their birthdays, Christmas, Easter, and Halloween.  She has a husband for whom she makes a cake on these same holidays, as well as on their anniversary and Valentine's Day. Lastly, she makes both her parents cakes as well, but only for their birthdays since they live far away.  How many cakes does she make in 10 years?<|im_end|>
<|im_start|>assistant
<Z_363><Z_239><Z_256><Z_49><Z_476><Z_390><Z_453><Z_393><Z_479><Z_252><Z_24><ANSWER>

Question: Ginger likes to make cakes for every holiday for people.  She has 2 children, each of whom she bakes a cake for on their birthdays, Christmas, Easter, and Halloween.  She has a husband for whom she makes a cake on these same holidays, as well as on their anniversary and Valentine's Day. Lastly, she makes both her parents cakes as well, but only for their birthdays since they live far away.  How many cakes does she make in 10 years?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Susan, Arthur, Tom and, Bob are siblings. Arthur is 2 years older than Susan, and Tom is 3 years younger than Bob. If Bob is 11 years old, and Susan is 15 years old, how old are all four family members in total?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Susan, Arthur, Tom and, Bob are siblings. Arthur is 2 years older than Susan, and Tom is 3 years younger than Bob. If Bob is 11 years old, and Susan is 15 years old, how old are all four family members in total?<|im_end|>
<|im_start|>assistant
<Z_369><Z_213><Z_386><Z_403><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Susan, Arthur, Tom and, Bob are siblings. Arthur is 2 years older than Susan, and Tom is 3 years younger than Bob. If Bob is 11 years old, and Susan is 15 years old, how old are all four family members in total?<|im_end|>
<|im_start|>assistant
<Z_124><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Susan, Arthur, Tom and, Bob are siblings. Arthur is 2 years older than Susan, and Tom is 3 years younger than Bob. If Bob is 11 years old, and Susan is 15 years old, how old are all four family members in total?<|im_end|>
<|im_start|>assistant
<Z_368><Z_470><Z_210><Z_144><ANSWER>

Question: Susan, Arthur, Tom and, Bob are siblings. Arthur is 2 years older than Susan, and Tom is 3 years younger than Bob. If Bob is 11 years old, and Susan is 15 years old, how old are all four family members in total?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( r(x) \) be a polynomial of degree 7 such that
\[ r(3^n) = \frac{1}{3^n} \] for \( n = 0, 1, 2, \dots, 7 \). Find \( r(0) \).<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( r(x) \) be a polynomial of degree 7 such that
\[ r(3^n) = \frac{1}{3^n} \] for \( n = 0, 1, 2, \dots, 7 \). Find \( r(0) \).<|im_end|>
<|im_start|>assistant
<Z_369><Z_269><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( r(x) \) be a polynomial of degree 7 such that
\[ r(3^n) = \frac{1}{3^n} \] for \( n = 0, 1, 2, \dots, 7 \). Find \( r(0) \).<|im_end|>
<|im_start|>assistant
<Z_167><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( r(x) \) be a polynomial of degree 7 such that
\[ r(3^n) = \frac{1}{3^n} \] for \( n = 0, 1, 2, \dots, 7 \). Find \( r(0) \).<|im_end|>
<|im_start|>assistant
<Z_267><Z_349><ANSWER>

Question:
Let \( r(x) \) be a polynomial of degree 7 such that
\[ r(3^n) = \frac{1}{3^n} \] for \( n = 0, 1, 2, \dots, 7 \). Find \( r(0) \).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For a finite sequence $A=(a_1,a_2,\dots,a_n)$ of numbers, the Cesaro sum of $A$ is defined to be
\[\frac{S_1+\cdots+S_n}{n},\]where $S_k=a_1+\cdots+a_k$ and $1\leq k\leq n$.

If the Cesaro sum of the 99-term sequence $(a_1,\dots,a_{99})$ is 1000,  what is the Cesaro sum of the 100-term sequence $(1,a_1,\dots,a_{99})$?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For a finite sequence $A=(a_1,a_2,\dots,a_n)$ of numbers, the Cesaro sum of $A$ is defined to be
\[\frac{S_1+\cdots+S_n}{n},\]where $S_k=a_1+\cdots+a_k$ and $1\leq k\leq n$.

If the Cesaro sum of the 99-term sequence $(a_1,\dots,a_{99})$ is 1000,  what is the Cesaro sum of the 100-term sequence $(1,a_1,\dots,a_{99})$?<|im_end|>
<|im_start|>assistant
<Z_24><Z_98><Z_108><Z_137><Z_85><Z_478><Z_87><Z_132><Z_130><Z_437><Z_124><Z_491><Z_254><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For a finite sequence $A=(a_1,a_2,\dots,a_n)$ of numbers, the Cesaro sum of $A$ is defined to be
\[\frac{S_1+\cdots+S_n}{n},\]where $S_k=a_1+\cdots+a_k$ and $1\leq k\leq n$.

If the Cesaro sum of the 99-term sequence $(a_1,\dots,a_{99})$ is 1000,  what is the Cesaro sum of the 100-term sequence $(1,a_1,\dots,a_{99})$?<|im_end|>
<|im_start|>assistant
<Z_232><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For a finite sequence $A=(a_1,a_2,\dots,a_n)$ of numbers, the Cesaro sum of $A$ is defined to be
\[\frac{S_1+\cdots+S_n}{n},\]where $S_k=a_1+\cdots+a_k$ and $1\leq k\leq n$.

If the Cesaro sum of the 99-term sequence $(a_1,\dots,a_{99})$ is 1000,  what is the Cesaro sum of the 100-term sequence $(1,a_1,\dots,a_{99})$?<|im_end|>
<|im_start|>assistant
<Z_460><Z_75><Z_205><Z_326><Z_187><Z_358><Z_237><Z_32><Z_200><Z_188><Z_76><Z_61><Z_224><ANSWER>

Question:
For a finite sequence $A=(a_1,a_2,\dots,a_n)$ of numbers, the Cesaro sum of $A$ is defined to be
\[\frac{S_1+\cdots+S_n}{n},\]where $S_k=a_1+\cdots+a_k$ and $1\leq k\leq n$.

If the Cesaro sum of the 99-term sequence $(a_1,\dots,a_{99})$ is 1000,  what is the Cesaro sum of the 100-term sequence $(1,a_1,\dots,a_{99})$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On the day the Ice Palace opened, children made an appointment to go together to escape the summer heat. There is a staircase in front of the Ice Palace, and Alice took 120 seconds to walk 20 steps. Walking at the same speed, Alice took a total of 180 seconds, just enough to finish all the steps. How many steps are there in the staircase to the Ice Palace?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On the day the Ice Palace opened, children made an appointment to go together to escape the summer heat. There is a staircase in front of the Ice Palace, and Alice took 120 seconds to walk 20 steps. Walking at the same speed, Alice took a total of 180 seconds, just enough to finish all the steps. How many steps are there in the staircase to the Ice Palace?<|im_end|>
<|im_start|>assistant
<Z_369><Z_309><Z_214><Z_378><Z_464><Z_108><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On the day the Ice Palace opened, children made an appointment to go together to escape the summer heat. There is a staircase in front of the Ice Palace, and Alice took 120 seconds to walk 20 steps. Walking at the same speed, Alice took a total of 180 seconds, just enough to finish all the steps. How many steps are there in the staircase to the Ice Palace?<|im_end|>
<|im_start|>assistant
<Z_454><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On the day the Ice Palace opened, children made an appointment to go together to escape the summer heat. There is a staircase in front of the Ice Palace, and Alice took 120 seconds to walk 20 steps. Walking at the same speed, Alice took a total of 180 seconds, just enough to finish all the steps. How many steps are there in the staircase to the Ice Palace?<|im_end|>
<|im_start|>assistant
<Z_288><Z_236><Z_439><Z_255><Z_411><Z_511><ANSWER>

Question: On the day the Ice Palace opened, children made an appointment to go together to escape the summer heat. There is a staircase in front of the Ice Palace, and Alice took 120 seconds to walk 20 steps. Walking at the same speed, Alice took a total of 180 seconds, just enough to finish all the steps. How many steps are there in the staircase to the Ice Palace?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Shekar scored 76 in mathematics, 65 in science, 82 in social studies, some marks in English, and 75 in biology. His average marks are 73. What are his marks in English?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Shekar scored 76 in mathematics, 65 in science, 82 in social studies, some marks in English, and 75 in biology. His average marks are 73. What are his marks in English?<|im_end|>
<|im_start|>assistant
<Z_24><Z_196><Z_325><Z_265><Z_114><Z_458><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Shekar scored 76 in mathematics, 65 in science, 82 in social studies, some marks in English, and 75 in biology. His average marks are 73. What are his marks in English?<|im_end|>
<|im_start|>assistant
<Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Shekar scored 76 in mathematics, 65 in science, 82 in social studies, some marks in English, and 75 in biology. His average marks are 73. What are his marks in English?<|im_end|>
<|im_start|>assistant
<Z_277><Z_390><Z_481><Z_191><Z_437><Z_64><ANSWER>

Question: Shekar scored 76 in mathematics, 65 in science, 82 in social studies, some marks in English, and 75 in biology. His average marks are 73. What are his marks in English?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Frank was reading through some books. Each book had 249 pages and it took Frank 3 days to finish each book. How many pages did he read per day?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Frank was reading through some books. Each book had 249 pages and it took Frank 3 days to finish each book. How many pages did he read per day?<|im_end|>
<|im_start|>assistant
<Z_24><Z_371><Z_102><Z_73><Z_416><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Frank was reading through some books. Each book had 249 pages and it took Frank 3 days to finish each book. How many pages did he read per day?<|im_end|>
<|im_start|>assistant
<Z_4><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Frank was reading through some books. Each book had 249 pages and it took Frank 3 days to finish each book. How many pages did he read per day?<|im_end|>
<|im_start|>assistant
<Z_318><Z_62><Z_360><Z_66><Z_433><ANSWER>

Question: Frank was reading through some books. Each book had 249 pages and it took Frank 3 days to finish each book. How many pages did he read per day?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John takes three different types of pills each with a different schedule. He takes pill A every 6 hours, pill B every 8 hours, and pill C every 12 hours. How many pills of each type does he take in a week?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John takes three different types of pills each with a different schedule. He takes pill A every 6 hours, pill B every 8 hours, and pill C every 12 hours. How many pills of each type does he take in a week?<|im_end|>
<|im_start|>assistant
<Z_369><Z_135><Z_312><Z_443><Z_434><Z_294><Z_240><Z_273><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John takes three different types of pills each with a different schedule. He takes pill A every 6 hours, pill B every 8 hours, and pill C every 12 hours. How many pills of each type does he take in a week?<|im_end|>
<|im_start|>assistant
<Z_246><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John takes three different types of pills each with a different schedule. He takes pill A every 6 hours, pill B every 8 hours, and pill C every 12 hours. How many pills of each type does he take in a week?<|im_end|>
<|im_start|>assistant
<Z_35><Z_335><Z_337><Z_476><Z_346><Z_459><Z_47><Z_440><ANSWER>

Question: John takes three different types of pills each with a different schedule. He takes pill A every 6 hours, pill B every 8 hours, and pill C every 12 hours. How many pills of each type does he take in a week?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $3^x + 3^x + 3^x + 3^x = 2187$, find the value of $(x+2)(x-2)$.<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $3^x + 3^x + 3^x + 3^x = 2187$, find the value of $(x+2)(x-2)$.<|im_end|>
<|im_start|>assistant
<Z_24><Z_437><Z_244><Z_453><Z_227><Z_454><Z_491><Z_98><Z_99><Z_251><Z_220><Z_304><Z_151><Z_447><Z_296><Z_362><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $3^x + 3^x + 3^x + 3^x = 2187$, find the value of $(x+2)(x-2)$.<|im_end|>
<|im_start|>assistant
<Z_98><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $3^x + 3^x + 3^x + 3^x = 2187$, find the value of $(x+2)(x-2)$.<|im_end|>
<|im_start|>assistant
<Z_105><Z_162><Z_280><Z_30><Z_123><Z_28><Z_76><Z_365><Z_57><Z_246><Z_505><Z_229><Z_427><Z_127><Z_9><Z_457><ANSWER>

Question: Given that $3^x + 3^x + 3^x + 3^x = 2187$, find the value of $(x+2)(x-2)$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by a certain percent. The actual attendance was 64 percent of the projected attendance. What was the actual percent decrease in attendance?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by a certain percent. The actual attendance was 64 percent of the projected attendance. What was the actual percent decrease in attendance?<|im_end|>
<|im_start|>assistant
<Z_24><Z_175><Z_224><Z_274><Z_322><Z_391><Z_304><Z_253><Z_294><Z_201><Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by a certain percent. The actual attendance was 64 percent of the projected attendance. What was the actual percent decrease in attendance?<|im_end|>
<|im_start|>assistant
<Z_219><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by a certain percent. The actual attendance was 64 percent of the projected attendance. What was the actual percent decrease in attendance?<|im_end|>
<|im_start|>assistant
<Z_379><Z_328><Z_57><Z_222><Z_108><Z_81><Z_356><Z_177><Z_74><Z_401><Z_264><ANSWER>

Question: The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by a certain percent. The actual attendance was 64 percent of the projected attendance. What was the actual percent decrease in attendance?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Barbara collects two types of ancient coins, type A and type B. She has 18 coins in total. She finds out that 8 of these coins, which are all of type A, are worth 24 dollars in total. Additionally, she has confirmed that 6 of the type B coins total up to 21 dollars. If Barbara has 12 coins of type A, how much is her entire collection worth?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Barbara collects two types of ancient coins, type A and type B. She has 18 coins in total. She finds out that 8 of these coins, which are all of type A, are worth 24 dollars in total. Additionally, she has confirmed that 6 of the type B coins total up to 21 dollars. If Barbara has 12 coins of type A, how much is her entire collection worth?<|im_end|>
<|im_start|>assistant
<Z_477><Z_87><Z_101><Z_252><Z_106><Z_60><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Barbara collects two types of ancient coins, type A and type B. She has 18 coins in total. She finds out that 8 of these coins, which are all of type A, are worth 24 dollars in total. Additionally, she has confirmed that 6 of the type B coins total up to 21 dollars. If Barbara has 12 coins of type A, how much is her entire collection worth?<|im_end|>
<|im_start|>assistant
<Z_507><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Barbara collects two types of ancient coins, type A and type B. She has 18 coins in total. She finds out that 8 of these coins, which are all of type A, are worth 24 dollars in total. Additionally, she has confirmed that 6 of the type B coins total up to 21 dollars. If Barbara has 12 coins of type A, how much is her entire collection worth?<|im_end|>
<|im_start|>assistant
<Z_160><Z_38><Z_318><Z_164><Z_407><Z_1><ANSWER>

Question: Barbara collects two types of ancient coins, type A and type B. She has 18 coins in total. She finds out that 8 of these coins, which are all of type A, are worth 24 dollars in total. Additionally, she has confirmed that 6 of the type B coins total up to 21 dollars. If Barbara has 12 coins of type A, how much is her entire collection worth?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \(a\), \(b\), and \(c\) be the roots of the equation \(x^3 - 15x^2 + 22x - 8 = 0.\) Calculate the value of \((2+a)(2+b)(2+c).\)<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \(a\), \(b\), and \(c\) be the roots of the equation \(x^3 - 15x^2 + 22x - 8 = 0.\) Calculate the value of \((2+a)(2+b)(2+c).\)<|im_end|>
<|im_start|>assistant
<Z_369><Z_214><Z_502><Z_254><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \(a\), \(b\), and \(c\) be the roots of the equation \(x^3 - 15x^2 + 22x - 8 = 0.\) Calculate the value of \((2+a)(2+b)(2+c).\)<|im_end|>
<|im_start|>assistant
<Z_312><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \(a\), \(b\), and \(c\) be the roots of the equation \(x^3 - 15x^2 + 22x - 8 = 0.\) Calculate the value of \((2+a)(2+b)(2+c).\)<|im_end|>
<|im_start|>assistant
<Z_26><Z_119><Z_419><Z_381><ANSWER>

Question: Let \(a\), \(b\), and \(c\) be the roots of the equation \(x^3 - 15x^2 + 22x - 8 = 0.\) Calculate the value of \((2+a)(2+b)(2+c).\)


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Olya wrote fractions of the form  $1 / n$  on cards, where  $n$  is all possible divisors the numbers  $6^{100}$  (including the unit and the number itself). These cards she laid out in some order. After that, she wrote down the number on the first card, then the sum of the numbers on the first and second cards, then the sum of the numbers on the first three cards, etc., finally, the sum of the numbers on all the cards. Every amount Olya recorded on the board in the form of irreducible fraction. What is the least different denominators could be on the numbers on the board?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Olya wrote fractions of the form  $1 / n$  on cards, where  $n$  is all possible divisors the numbers  $6^{100}$  (including the unit and the number itself). These cards she laid out in some order. After that, she wrote down the number on the first card, then the sum of the numbers on the first and second cards, then the sum of the numbers on the first three cards, etc., finally, the sum of the numbers on all the cards. Every amount Olya recorded on the board in the form of irreducible fraction. What is the least different denominators could be on the numbers on the board?<|im_end|>
<|im_start|>assistant
<Z_477><Z_209><Z_253><Z_422><Z_229><Z_350><Z_253><Z_305><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Olya wrote fractions of the form  $1 / n$  on cards, where  $n$  is all possible divisors the numbers  $6^{100}$  (including the unit and the number itself). These cards she laid out in some order. After that, she wrote down the number on the first card, then the sum of the numbers on the first and second cards, then the sum of the numbers on the first three cards, etc., finally, the sum of the numbers on all the cards. Every amount Olya recorded on the board in the form of irreducible fraction. What is the least different denominators could be on the numbers on the board?<|im_end|>
<|im_start|>assistant
<Z_428><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Olya wrote fractions of the form  $1 / n$  on cards, where  $n$  is all possible divisors the numbers  $6^{100}$  (including the unit and the number itself). These cards she laid out in some order. After that, she wrote down the number on the first card, then the sum of the numbers on the first and second cards, then the sum of the numbers on the first three cards, etc., finally, the sum of the numbers on all the cards. Every amount Olya recorded on the board in the form of irreducible fraction. What is the least different denominators could be on the numbers on the board?<|im_end|>
<|im_start|>assistant
<Z_208><Z_423><Z_94><Z_202><Z_224><Z_350><Z_419><Z_125><ANSWER>

Question: Olya wrote fractions of the form  $1 / n$  on cards, where  $n$  is all possible divisors the numbers  $6^{100}$  (including the unit and the number itself). These cards she laid out in some order. After that, she wrote down the number on the first card, then the sum of the numbers on the first and second cards, then the sum of the numbers on the first three cards, etc., finally, the sum of the numbers on all the cards. Every amount Olya recorded on the board in the form of irreducible fraction. What is the least different denominators could be on the numbers on the board?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find all positive integers \( k \) such that for any positive numbers \( a, b, c \) satisfying the inequality
\[ k(ab + bc + ca) > 5(a^2 + b^2 + c^2), \]
there must exist a triangle with side lengths \( a \), \( b \), and \( c \).<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find all positive integers \( k \) such that for any positive numbers \( a, b, c \) satisfying the inequality
\[ k(ab + bc + ca) > 5(a^2 + b^2 + c^2), \]
there must exist a triangle with side lengths \( a \), \( b \), and \( c \).<|im_end|>
<|im_start|>assistant
<Z_369><Z_334><Z_465><Z_414><Z_329><Z_425><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find all positive integers \( k \) such that for any positive numbers \( a, b, c \) satisfying the inequality
\[ k(ab + bc + ca) > 5(a^2 + b^2 + c^2), \]
there must exist a triangle with side lengths \( a \), \( b \), and \( c \).<|im_end|>
<|im_start|>assistant
<Z_214><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find all positive integers \( k \) such that for any positive numbers \( a, b, c \) satisfying the inequality
\[ k(ab + bc + ca) > 5(a^2 + b^2 + c^2), \]
there must exist a triangle with side lengths \( a \), \( b \), and \( c \).<|im_end|>
<|im_start|>assistant
<Z_237><Z_35><Z_268><Z_100><Z_347><Z_122><ANSWER>

Question:
Find all positive integers \( k \) such that for any positive numbers \( a, b, c \) satisfying the inequality
\[ k(ab + bc + ca) > 5(a^2 + b^2 + c^2), \]
there must exist a triangle with side lengths \( a \), \( b \), and \( c \).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 9 pencils and 4 rulers in the drawer . Sally took 4 pencils out of the drawer . How many pencils are there now ? <|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 9 pencils and 4 rulers in the drawer . Sally took 4 pencils out of the drawer . How many pencils are there now ? <|im_end|>
<|im_start|>assistant
<Z_24><Z_470><Z_376><Z_58><Z_318><Z_378><Z_204><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 9 pencils and 4 rulers in the drawer . Sally took 4 pencils out of the drawer . How many pencils are there now ? <|im_end|>
<|im_start|>assistant
<Z_270><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 9 pencils and 4 rulers in the drawer . Sally took 4 pencils out of the drawer . How many pencils are there now ? <|im_end|>
<|im_start|>assistant
<Z_114><Z_486><Z_499><Z_50><Z_469><Z_123><Z_129><ANSWER>

Question: There are 9 pencils and 4 rulers in the drawer . Sally took 4 pencils out of the drawer . How many pencils are there now ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three pirates divided the diamonds they collected during the day: Bill and Sam got twelve each, and the rest went to John, who did not know how to count. At night, Bill stole one diamond from Sam, Sam stole one diamond from John, and John stole one diamond from Bill. As a result, the average mass of Bill's diamonds decreased by one carat, the average mass of Sam's diamonds decreased by two carats, but the average mass of John's diamonds increased by four carats. How many diamonds did John receive?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three pirates divided the diamonds they collected during the day: Bill and Sam got twelve each, and the rest went to John, who did not know how to count. At night, Bill stole one diamond from Sam, Sam stole one diamond from John, and John stole one diamond from Bill. As a result, the average mass of Bill's diamonds decreased by one carat, the average mass of Sam's diamonds decreased by two carats, but the average mass of John's diamonds increased by four carats. How many diamonds did John receive?<|im_end|>
<|im_start|>assistant
<Z_369><Z_393><Z_352><Z_33><Z_255><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three pirates divided the diamonds they collected during the day: Bill and Sam got twelve each, and the rest went to John, who did not know how to count. At night, Bill stole one diamond from Sam, Sam stole one diamond from John, and John stole one diamond from Bill. As a result, the average mass of Bill's diamonds decreased by one carat, the average mass of Sam's diamonds decreased by two carats, but the average mass of John's diamonds increased by four carats. How many diamonds did John receive?<|im_end|>
<|im_start|>assistant
<Z_362><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three pirates divided the diamonds they collected during the day: Bill and Sam got twelve each, and the rest went to John, who did not know how to count. At night, Bill stole one diamond from Sam, Sam stole one diamond from John, and John stole one diamond from Bill. As a result, the average mass of Bill's diamonds decreased by one carat, the average mass of Sam's diamonds decreased by two carats, but the average mass of John's diamonds increased by four carats. How many diamonds did John receive?<|im_end|>
<|im_start|>assistant
<Z_470><Z_227><Z_225><Z_250><Z_144><ANSWER>

Question: Three pirates divided the diamonds they collected during the day: Bill and Sam got twelve each, and the rest went to John, who did not know how to count. At night, Bill stole one diamond from Sam, Sam stole one diamond from John, and John stole one diamond from Bill. As a result, the average mass of Bill's diamonds decreased by one carat, the average mass of Sam's diamonds decreased by two carats, but the average mass of John's diamonds increased by four carats. How many diamonds did John receive?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of the numbers 45 and $y$ is 37. What is the positive difference between 45 and $y$?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of the numbers 45 and $y$ is 37. What is the positive difference between 45 and $y$?<|im_end|>
<|im_start|>assistant
<Z_24><Z_200><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of the numbers 45 and $y$ is 37. What is the positive difference between 45 and $y$?<|im_end|>
<|im_start|>assistant
<Z_419><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of the numbers 45 and $y$ is 37. What is the positive difference between 45 and $y$?<|im_end|>
<|im_start|>assistant
<Z_9><Z_188><ANSWER>

Question: The average of the numbers 45 and $y$ is 37. What is the positive difference between 45 and $y$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A rectangular array of chairs is an arrangement of the chairs in rows and columns such that each row contains the same number of chairs as every other row and each column contains the same number of chairs as every other column.  If there must be at least two chairs in every row and column and all of the chairs in the room must be included, how many arrays are possible in a classroom containing $36$ chairs? Note that $12$ rows of $3$ chairs is different from $3$ rows of $12$ chairs.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A rectangular array of chairs is an arrangement of the chairs in rows and columns such that each row contains the same number of chairs as every other row and each column contains the same number of chairs as every other column.  If there must be at least two chairs in every row and column and all of the chairs in the room must be included, how many arrays are possible in a classroom containing $36$ chairs? Note that $12$ rows of $3$ chairs is different from $3$ rows of $12$ chairs.<|im_end|>
<|im_start|>assistant
<Z_369><Z_334><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A rectangular array of chairs is an arrangement of the chairs in rows and columns such that each row contains the same number of chairs as every other row and each column contains the same number of chairs as every other column.  If there must be at least two chairs in every row and column and all of the chairs in the room must be included, how many arrays are possible in a classroom containing $36$ chairs? Note that $12$ rows of $3$ chairs is different from $3$ rows of $12$ chairs.<|im_end|>
<|im_start|>assistant
<Z_432><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A rectangular array of chairs is an arrangement of the chairs in rows and columns such that each row contains the same number of chairs as every other row and each column contains the same number of chairs as every other column.  If there must be at least two chairs in every row and column and all of the chairs in the room must be included, how many arrays are possible in a classroom containing $36$ chairs? Note that $12$ rows of $3$ chairs is different from $3$ rows of $12$ chairs.<|im_end|>
<|im_start|>assistant
<Z_52><Z_139><ANSWER>

Question: A rectangular array of chairs is an arrangement of the chairs in rows and columns such that each row contains the same number of chairs as every other row and each column contains the same number of chairs as every other column.  If there must be at least two chairs in every row and column and all of the chairs in the room must be included, how many arrays are possible in a classroom containing $36$ chairs? Note that $12$ rows of $3$ chairs is different from $3$ rows of $12$ chairs.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A lent Rs. 5000 to B for some years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is 10%. For how many years did A lend money to B?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A lent Rs. 5000 to B for some years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is 10%. For how many years did A lend money to B?<|im_end|>
<|im_start|>assistant
<Z_369><Z_146><Z_427><Z_220><Z_386><Z_394><Z_223><Z_341><Z_346><Z_348><Z_158><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A lent Rs. 5000 to B for some years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is 10%. For how many years did A lend money to B?<|im_end|>
<|im_start|>assistant
<Z_39><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A lent Rs. 5000 to B for some years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is 10%. For how many years did A lend money to B?<|im_end|>
<|im_start|>assistant
<Z_181><Z_431><Z_255><Z_346><Z_493><Z_227><Z_39><Z_53><Z_217><Z_310><Z_329><ANSWER>

Question: A lent Rs. 5000 to B for some years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is 10%. For how many years did A lend money to B?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Five friends meet every weekend. Each weekend, three of them cook and the other two handle shopping for ingredients. How many different ways are there for them to choose who cooks and who shops?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Five friends meet every weekend. Each weekend, three of them cook and the other two handle shopping for ingredients. How many different ways are there for them to choose who cooks and who shops?<|im_end|>
<|im_start|>assistant
<Z_24><Z_69><Z_368><Z_388><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Five friends meet every weekend. Each weekend, three of them cook and the other two handle shopping for ingredients. How many different ways are there for them to choose who cooks and who shops?<|im_end|>
<|im_start|>assistant
<Z_432><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Five friends meet every weekend. Each weekend, three of them cook and the other two handle shopping for ingredients. How many different ways are there for them to choose who cooks and who shops?<|im_end|>
<|im_start|>assistant
<Z_424><Z_205><Z_281><Z_425><ANSWER>

Question: Five friends meet every weekend. Each weekend, three of them cook and the other two handle shopping for ingredients. How many different ways are there for them to choose who cooks and who shops?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two stations A and B are 200 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two stations A and B are 200 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?<|im_end|>
<|im_start|>assistant
<Z_477><Z_68><Z_188><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two stations A and B are 200 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?<|im_end|>
<|im_start|>assistant
<Z_403><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two stations A and B are 200 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?<|im_end|>
<|im_start|>assistant
<Z_83><Z_114><Z_209><ANSWER>

Question: Two stations A and B are 200 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A restaurant served some slices of pie during lunch and 5 during dinner today. It served 8 of them yesterday. The restaurant served 12 slices of pie today. How many slices of pie were served during lunch today?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A restaurant served some slices of pie during lunch and 5 during dinner today. It served 8 of them yesterday. The restaurant served 12 slices of pie today. How many slices of pie were served during lunch today?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A restaurant served some slices of pie during lunch and 5 during dinner today. It served 8 of them yesterday. The restaurant served 12 slices of pie today. How many slices of pie were served during lunch today?<|im_end|>
<|im_start|>assistant
<Z_153><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A restaurant served some slices of pie during lunch and 5 during dinner today. It served 8 of them yesterday. The restaurant served 12 slices of pie today. How many slices of pie were served during lunch today?<|im_end|>
<|im_start|>assistant
<Z_442><ANSWER>

Question: A restaurant served some slices of pie during lunch and 5 during dinner today. It served 8 of them yesterday. The restaurant served 12 slices of pie today. How many slices of pie were served during lunch today?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest four-digit number that is divisible by $25$?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest four-digit number that is divisible by $25$?<|im_end|>
<|im_start|>assistant
<Z_477><Z_92><Z_419><Z_415><Z_96><Z_483><Z_420><Z_54><Z_141><Z_36><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest four-digit number that is divisible by $25$?<|im_end|>
<|im_start|>assistant
<Z_300><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest four-digit number that is divisible by $25$?<|im_end|>
<|im_start|>assistant
<Z_57><Z_332><Z_57><Z_456><Z_262><Z_507><Z_280><Z_384><Z_259><Z_322><ANSWER>

Question: What is the smallest four-digit number that is divisible by $25$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A $200\times 420\times 480$ rectangular solid is made by gluing together $1\times 1\times 1$ cubes. An internal diagonal of this solid passes through the interiors of how many of the $1\times 1\times 1$ cubes?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A $200\times 420\times 480$ rectangular solid is made by gluing together $1\times 1\times 1$ cubes. An internal diagonal of this solid passes through the interiors of how many of the $1\times 1\times 1$ cubes?<|im_end|>
<|im_start|>assistant
<Z_24><Z_183><Z_213><Z_209><Z_425><Z_232><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A $200\times 420\times 480$ rectangular solid is made by gluing together $1\times 1\times 1$ cubes. An internal diagonal of this solid passes through the interiors of how many of the $1\times 1\times 1$ cubes?<|im_end|>
<|im_start|>assistant
<Z_159><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A $200\times 420\times 480$ rectangular solid is made by gluing together $1\times 1\times 1$ cubes. An internal diagonal of this solid passes through the interiors of how many of the $1\times 1\times 1$ cubes?<|im_end|>
<|im_start|>assistant
<Z_15><Z_129><Z_389><Z_65><Z_472><Z_323><ANSWER>

Question: A $200\times 420\times 480$ rectangular solid is made by gluing together $1\times 1\times 1$ cubes. An internal diagonal of this solid passes through the interiors of how many of the $1\times 1\times 1$ cubes?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a store, there are 9 headphones, 13 computer mice, and 5 keyboards for sale. Besides these, there are also 4 sets of "keyboard and mouse" and 5 sets of "headphones and mouse." How many ways can you buy three items: headphones, a keyboard, and a mouse? Answer: 646.<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a store, there are 9 headphones, 13 computer mice, and 5 keyboards for sale. Besides these, there are also 4 sets of "keyboard and mouse" and 5 sets of "headphones and mouse." How many ways can you buy three items: headphones, a keyboard, and a mouse? Answer: 646.<|im_end|>
<|im_start|>assistant
<Z_369><Z_345><Z_50><Z_219><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a store, there are 9 headphones, 13 computer mice, and 5 keyboards for sale. Besides these, there are also 4 sets of "keyboard and mouse" and 5 sets of "headphones and mouse." How many ways can you buy three items: headphones, a keyboard, and a mouse? Answer: 646.<|im_end|>
<|im_start|>assistant
<Z_278><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a store, there are 9 headphones, 13 computer mice, and 5 keyboards for sale. Besides these, there are also 4 sets of "keyboard and mouse" and 5 sets of "headphones and mouse." How many ways can you buy three items: headphones, a keyboard, and a mouse? Answer: 646.<|im_end|>
<|im_start|>assistant
<Z_251><Z_289><Z_296><Z_47><ANSWER>

Question: In a store, there are 9 headphones, 13 computer mice, and 5 keyboards for sale. Besides these, there are also 4 sets of "keyboard and mouse" and 5 sets of "headphones and mouse." How many ways can you buy three items: headphones, a keyboard, and a mouse? Answer: 646.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sum of the present age of Henry and Jill is 33. Their present ages are such that 6 years ago, Henry was twice the age of Jill. What is Jill's present age?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sum of the present age of Henry and Jill is 33. Their present ages are such that 6 years ago, Henry was twice the age of Jill. What is Jill's present age?<|im_end|>
<|im_start|>assistant
<Z_369><Z_89><Z_273><Z_460><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sum of the present age of Henry and Jill is 33. Their present ages are such that 6 years ago, Henry was twice the age of Jill. What is Jill's present age?<|im_end|>
<|im_start|>assistant
<Z_212><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sum of the present age of Henry and Jill is 33. Their present ages are such that 6 years ago, Henry was twice the age of Jill. What is Jill's present age?<|im_end|>
<|im_start|>assistant
<Z_440><Z_205><Z_2><Z_502><ANSWER>

Question: The sum of the present age of Henry and Jill is 33. Their present ages are such that 6 years ago, Henry was twice the age of Jill. What is Jill's present age?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A group of researchers are studying a colony of penguins. Their results show that the size doubled in the first year they watched the colony, then tripled in the next year. This year, however, harsh conditions meant the colony only gained 129 penguins. The colony has 1077 penguins in it now. Each penguin eats one and a half fish every day. How many fish did the whole colony catch per day to eat at the beginning of the first year?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A group of researchers are studying a colony of penguins. Their results show that the size doubled in the first year they watched the colony, then tripled in the next year. This year, however, harsh conditions meant the colony only gained 129 penguins. The colony has 1077 penguins in it now. Each penguin eats one and a half fish every day. How many fish did the whole colony catch per day to eat at the beginning of the first year?<|im_end|>
<|im_start|>assistant
<Z_24><Z_157><Z_58><Z_219><Z_68><Z_201><Z_158><Z_82><Z_105><Z_391><Z_433><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A group of researchers are studying a colony of penguins. Their results show that the size doubled in the first year they watched the colony, then tripled in the next year. This year, however, harsh conditions meant the colony only gained 129 penguins. The colony has 1077 penguins in it now. Each penguin eats one and a half fish every day. How many fish did the whole colony catch per day to eat at the beginning of the first year?<|im_end|>
<|im_start|>assistant
<Z_405><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A group of researchers are studying a colony of penguins. Their results show that the size doubled in the first year they watched the colony, then tripled in the next year. This year, however, harsh conditions meant the colony only gained 129 penguins. The colony has 1077 penguins in it now. Each penguin eats one and a half fish every day. How many fish did the whole colony catch per day to eat at the beginning of the first year?<|im_end|>
<|im_start|>assistant
<Z_490><Z_361><Z_51><Z_227><Z_206><Z_255><Z_372><Z_507><Z_112><Z_426><Z_211><ANSWER>

Question: A group of researchers are studying a colony of penguins. Their results show that the size doubled in the first year they watched the colony, then tripled in the next year. This year, however, harsh conditions meant the colony only gained 129 penguins. The colony has 1077 penguins in it now. Each penguin eats one and a half fish every day. How many fish did the whole colony catch per day to eat at the beginning of the first year?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given $m^{2}-2m-1=0$, then the value of $m^2+\frac{1}{m^2}$ is ______.<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given $m^{2}-2m-1=0$, then the value of $m^2+\frac{1}{m^2}$ is ______.<|im_end|>
<|im_start|>assistant
<Z_24><Z_67><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given $m^{2}-2m-1=0$, then the value of $m^2+\frac{1}{m^2}$ is ______.<|im_end|>
<|im_start|>assistant
<Z_395><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given $m^{2}-2m-1=0$, then the value of $m^2+\frac{1}{m^2}$ is ______.<|im_end|>
<|im_start|>assistant
<Z_194><Z_123><ANSWER>

Question: Given $m^{2}-2m-1=0$, then the value of $m^2+\frac{1}{m^2}$ is ______.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of $c$ if $-x^2+cx-8 < 0$ only when $x \in (-\infty, 2) \cup (6, \infty)$?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of $c$ if $-x^2+cx-8 < 0$ only when $x \in (-\infty, 2) \cup (6, \infty)$?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of $c$ if $-x^2+cx-8 < 0$ only when $x \in (-\infty, 2) \cup (6, \infty)$?<|im_end|>
<|im_start|>assistant
<Z_179><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of $c$ if $-x^2+cx-8 < 0$ only when $x \in (-\infty, 2) \cup (6, \infty)$?<|im_end|>
<|im_start|>assistant
<Z_511><ANSWER>

Question: What is the value of $c$ if $-x^2+cx-8 < 0$ only when $x \in (-\infty, 2) \cup (6, \infty)$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The salary of a typist was at first raised by 10% and then the same was reduced by 5%. The original salary was Rs. 4000.0000000000005. What is the typist's current salary?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The salary of a typist was at first raised by 10% and then the same was reduced by 5%. The original salary was Rs. 4000.0000000000005. What is the typist's current salary?<|im_end|>
<|im_start|>assistant
<Z_24><Z_146><Z_194><Z_113><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The salary of a typist was at first raised by 10% and then the same was reduced by 5%. The original salary was Rs. 4000.0000000000005. What is the typist's current salary?<|im_end|>
<|im_start|>assistant
<Z_115><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The salary of a typist was at first raised by 10% and then the same was reduced by 5%. The original salary was Rs. 4000.0000000000005. What is the typist's current salary?<|im_end|>
<|im_start|>assistant
<Z_59><Z_227><Z_127><Z_343><ANSWER>

Question: The salary of a typist was at first raised by 10% and then the same was reduced by 5%. The original salary was Rs. 4000.0000000000005. What is the typist's current salary?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence $\{a_n\}$ that satisfies the condition $$a_1 + a_2 + \ldots + a_n = n^3$$, find the value of $a_6 + a_7 + a_8 + a_9$.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence $\{a_n\}$ that satisfies the condition $$a_1 + a_2 + \ldots + a_n = n^3$$, find the value of $a_6 + a_7 + a_8 + a_9$.<|im_end|>
<|im_start|>assistant
<Z_477><Z_228><Z_55><Z_494><Z_159><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence $\{a_n\}$ that satisfies the condition $$a_1 + a_2 + \ldots + a_n = n^3$$, find the value of $a_6 + a_7 + a_8 + a_9$.<|im_end|>
<|im_start|>assistant
<Z_11><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence $\{a_n\}$ that satisfies the condition $$a_1 + a_2 + \ldots + a_n = n^3$$, find the value of $a_6 + a_7 + a_8 + a_9$.<|im_end|>
<|im_start|>assistant
<Z_193><Z_156><Z_420><Z_347><Z_382><ANSWER>

Question: Given a sequence $\{a_n\}$ that satisfies the condition $$a_1 + a_2 + \ldots + a_n = n^3$$, find the value of $a_6 + a_7 + a_8 + a_9$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The construction site required ants to complete several tasks. To carry heavy construction materials, they employed 413 red ants, 487 black ants, and 360 yellow ants. For digging tunnels, 356 red ants, 518 black ants, and 250 green ants were needed. Additionally, 25% of the black ants that carried materials also helped in gathering food. Lastly, for assembling structures, they hired 298 red ants, 392 black ants, and 200 blue ants. What is the total number of ants that were employed for all tasks?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The construction site required ants to complete several tasks. To carry heavy construction materials, they employed 413 red ants, 487 black ants, and 360 yellow ants. For digging tunnels, 356 red ants, 518 black ants, and 250 green ants were needed. Additionally, 25% of the black ants that carried materials also helped in gathering food. Lastly, for assembling structures, they hired 298 red ants, 392 black ants, and 200 blue ants. What is the total number of ants that were employed for all tasks?<|im_end|>
<|im_start|>assistant
<Z_477><Z_77><Z_403><Z_289><Z_151><Z_215><Z_138><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The construction site required ants to complete several tasks. To carry heavy construction materials, they employed 413 red ants, 487 black ants, and 360 yellow ants. For digging tunnels, 356 red ants, 518 black ants, and 250 green ants were needed. Additionally, 25% of the black ants that carried materials also helped in gathering food. Lastly, for assembling structures, they hired 298 red ants, 392 black ants, and 200 blue ants. What is the total number of ants that were employed for all tasks?<|im_end|>
<|im_start|>assistant
<Z_121><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The construction site required ants to complete several tasks. To carry heavy construction materials, they employed 413 red ants, 487 black ants, and 360 yellow ants. For digging tunnels, 356 red ants, 518 black ants, and 250 green ants were needed. Additionally, 25% of the black ants that carried materials also helped in gathering food. Lastly, for assembling structures, they hired 298 red ants, 392 black ants, and 200 blue ants. What is the total number of ants that were employed for all tasks?<|im_end|>
<|im_start|>assistant
<Z_259><Z_312><Z_22><Z_228><Z_151><Z_381><Z_159><ANSWER>

Question: The construction site required ants to complete several tasks. To carry heavy construction materials, they employed 413 red ants, 487 black ants, and 360 yellow ants. For digging tunnels, 356 red ants, 518 black ants, and 250 green ants were needed. Additionally, 25% of the black ants that carried materials also helped in gathering food. Lastly, for assembling structures, they hired 298 red ants, 392 black ants, and 200 blue ants. What is the total number of ants that were employed for all tasks?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $x + \frac{1}{x} = 3,$ then compute the value of
\[(x - 3)^2 + \frac{16}{(x - 3)^2}.\]<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $x + \frac{1}{x} = 3,$ then compute the value of
\[(x - 3)^2 + \frac{16}{(x - 3)^2}.\]<|im_end|>
<|im_start|>assistant
<Z_24><Z_49><Z_485><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $x + \frac{1}{x} = 3,$ then compute the value of
\[(x - 3)^2 + \frac{16}{(x - 3)^2}.\]<|im_end|>
<|im_start|>assistant
<Z_316><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $x + \frac{1}{x} = 3,$ then compute the value of
\[(x - 3)^2 + \frac{16}{(x - 3)^2}.\]<|im_end|>
<|im_start|>assistant
<Z_190><Z_484><Z_141><ANSWER>

Question:
If $x + \frac{1}{x} = 3,$ then compute the value of
\[(x - 3)^2 + \frac{16}{(x - 3)^2}.\]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kendra has 4 packs of pens. Tony has 2 packs of pens. There are 3 pens in each pack. Kendra and Tony decide to keep some pens each and give the remaining pens to their friends one pen per friend. They give pens to 14 friends. How many pens do Kendra and Tony keep each?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kendra has 4 packs of pens. Tony has 2 packs of pens. There are 3 pens in each pack. Kendra and Tony decide to keep some pens each and give the remaining pens to their friends one pen per friend. They give pens to 14 friends. How many pens do Kendra and Tony keep each?<|im_end|>
<|im_start|>assistant
<Z_369><Z_255><Z_245><Z_140><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kendra has 4 packs of pens. Tony has 2 packs of pens. There are 3 pens in each pack. Kendra and Tony decide to keep some pens each and give the remaining pens to their friends one pen per friend. They give pens to 14 friends. How many pens do Kendra and Tony keep each?<|im_end|>
<|im_start|>assistant
<Z_275><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kendra has 4 packs of pens. Tony has 2 packs of pens. There are 3 pens in each pack. Kendra and Tony decide to keep some pens each and give the remaining pens to their friends one pen per friend. They give pens to 14 friends. How many pens do Kendra and Tony keep each?<|im_end|>
<|im_start|>assistant
<Z_68><Z_498><Z_4><Z_261><ANSWER>

Question: Kendra has 4 packs of pens. Tony has 2 packs of pens. There are 3 pens in each pack. Kendra and Tony decide to keep some pens each and give the remaining pens to their friends one pen per friend. They give pens to 14 friends. How many pens do Kendra and Tony keep each?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of 5 quantities is a certain number. The average of 3 of them is 4. The average of the remaining 2 numbers is 19. What is the average of all 5 quantities?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of 5 quantities is a certain number. The average of 3 of them is 4. The average of the remaining 2 numbers is 19. What is the average of all 5 quantities?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of 5 quantities is a certain number. The average of 3 of them is 4. The average of the remaining 2 numbers is 19. What is the average of all 5 quantities?<|im_end|>
<|im_start|>assistant
<Z_52><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of 5 quantities is a certain number. The average of 3 of them is 4. The average of the remaining 2 numbers is 19. What is the average of all 5 quantities?<|im_end|>
<|im_start|>assistant
<Z_212><ANSWER>

Question: The average of 5 quantities is a certain number. The average of 3 of them is 4. The average of the remaining 2 numbers is 19. What is the average of all 5 quantities?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an opaque bag, there are $10$ red balls, $2$ yellow balls, and $8$ blue balls, all of which are identical except for their colors.
$(1)$ Find the probability of drawing a red ball from the bag;
$(2)$ Now, some red balls are removed from the bag and an equal number of yellow balls are added. After thorough mixing, the probability of drawing a yellow ball from the bag is $\frac{2}{5}$. How many red balls were removed?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an opaque bag, there are $10$ red balls, $2$ yellow balls, and $8$ blue balls, all of which are identical except for their colors.
$(1)$ Find the probability of drawing a red ball from the bag;
$(2)$ Now, some red balls are removed from the bag and an equal number of yellow balls are added. After thorough mixing, the probability of drawing a yellow ball from the bag is $\frac{2}{5}$. How many red balls were removed?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an opaque bag, there are $10$ red balls, $2$ yellow balls, and $8$ blue balls, all of which are identical except for their colors.
$(1)$ Find the probability of drawing a red ball from the bag;
$(2)$ Now, some red balls are removed from the bag and an equal number of yellow balls are added. After thorough mixing, the probability of drawing a yellow ball from the bag is $\frac{2}{5}$. How many red balls were removed?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an opaque bag, there are $10$ red balls, $2$ yellow balls, and $8$ blue balls, all of which are identical except for their colors.
$(1)$ Find the probability of drawing a red ball from the bag;
$(2)$ Now, some red balls are removed from the bag and an equal number of yellow balls are added. After thorough mixing, the probability of drawing a yellow ball from the bag is $\frac{2}{5}$. How many red balls were removed?<|im_end|>
<|im_start|>assistant
<Z_483><ANSWER>

Question:
In an opaque bag, there are $10$ red balls, $2$ yellow balls, and $8$ blue balls, all of which are identical except for their colors.
$(1)$ Find the probability of drawing a red ball from the bag;
$(2)$ Now, some red balls are removed from the bag and an equal number of yellow balls are added. After thorough mixing, the probability of drawing a yellow ball from the bag is $\frac{2}{5}$. How many red balls were removed?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A function $f$ from the integers to the integers is defined as follows:
\[f(n) = \left\{
\begin{array}{cl}
n + 5 & \text{if $n$ is odd}, \\
n - 2 & \text{if $n$ is even}.
\end{array}
\right.\]
Suppose $k$ is odd and $f(f(f(k))) = 35.$  Find $k.$<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A function $f$ from the integers to the integers is defined as follows:
\[f(n) = \left\{
\begin{array}{cl}
n + 5 & \text{if $n$ is odd}, \\
n - 2 & \text{if $n$ is even}.
\end{array}
\right.\]
Suppose $k$ is odd and $f(f(f(k))) = 35.$  Find $k.$<|im_end|>
<|im_start|>assistant
<Z_24><Z_194><Z_98><Z_195><Z_425><Z_128><Z_322><Z_274><Z_467><Z_341><Z_502><Z_135><Z_436><Z_39><Z_377><Z_488><Z_151><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A function $f$ from the integers to the integers is defined as follows:
\[f(n) = \left\{
\begin{array}{cl}
n + 5 & \text{if $n$ is odd}, \\
n - 2 & \text{if $n$ is even}.
\end{array}
\right.\]
Suppose $k$ is odd and $f(f(f(k))) = 35.$  Find $k.$<|im_end|>
<|im_start|>assistant
<Z_403><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A function $f$ from the integers to the integers is defined as follows:
\[f(n) = \left\{
\begin{array}{cl}
n + 5 & \text{if $n$ is odd}, \\
n - 2 & \text{if $n$ is even}.
\end{array}
\right.\]
Suppose $k$ is odd and $f(f(f(k))) = 35.$  Find $k.$<|im_end|>
<|im_start|>assistant
<Z_431><Z_474><Z_488><Z_440><Z_498><Z_280><Z_346><Z_365><Z_355><Z_253><Z_117><Z_414><Z_158><Z_396><Z_431><Z_502><Z_478><ANSWER>

Question:
A function $f$ from the integers to the integers is defined as follows:
\[f(n) = \left\{
\begin{array}{cl}
n + 5 & \text{if $n$ is odd}, \\
n - 2 & \text{if $n$ is even}.
\end{array}
\right.\]
Suppose $k$ is odd and $f(f(f(k))) = 35.$  Find $k.$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sara has some red flowers and 24 yellow flowers. She wants to make bouquets with the same number of each color flower in each bouquet. The greatest number of bouquets she can make is 8. How many red flowers does Sara have?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sara has some red flowers and 24 yellow flowers. She wants to make bouquets with the same number of each color flower in each bouquet. The greatest number of bouquets she can make is 8. How many red flowers does Sara have?<|im_end|>
<|im_start|>assistant
<Z_477><Z_112><Z_150><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sara has some red flowers and 24 yellow flowers. She wants to make bouquets with the same number of each color flower in each bouquet. The greatest number of bouquets she can make is 8. How many red flowers does Sara have?<|im_end|>
<|im_start|>assistant
<Z_229><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sara has some red flowers and 24 yellow flowers. She wants to make bouquets with the same number of each color flower in each bouquet. The greatest number of bouquets she can make is 8. How many red flowers does Sara have?<|im_end|>
<|im_start|>assistant
<Z_307><Z_97><Z_418><ANSWER>

Question: Sara has some red flowers and 24 yellow flowers. She wants to make bouquets with the same number of each color flower in each bouquet. The greatest number of bouquets she can make is 8. How many red flowers does Sara have?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On Thursday, Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3 of the transactions that Anthony handled, and Jade handled a certain number of more transactions than Cal. Jade handled 82 transactions. How many more transactions did Jade handle compared to Cal?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On Thursday, Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3 of the transactions that Anthony handled, and Jade handled a certain number of more transactions than Cal. Jade handled 82 transactions. How many more transactions did Jade handle compared to Cal?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On Thursday, Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3 of the transactions that Anthony handled, and Jade handled a certain number of more transactions than Cal. Jade handled 82 transactions. How many more transactions did Jade handle compared to Cal?<|im_end|>
<|im_start|>assistant
<Z_132><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On Thursday, Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3 of the transactions that Anthony handled, and Jade handled a certain number of more transactions than Cal. Jade handled 82 transactions. How many more transactions did Jade handle compared to Cal?<|im_end|>
<|im_start|>assistant
<Z_393><ANSWER>

Question: On Thursday, Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3 of the transactions that Anthony handled, and Jade handled a certain number of more transactions than Cal. Jade handled 82 transactions. How many more transactions did Jade handle compared to Cal?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Bob rolls a fair eight-sided die each morning. If Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal. If he rolls a 1, then he rolls again. In a non-leap year, what is the expected number of times Bob will roll his die?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Bob rolls a fair eight-sided die each morning. If Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal. If he rolls a 1, then he rolls again. In a non-leap year, what is the expected number of times Bob will roll his die?<|im_end|>
<|im_start|>assistant
<Z_24><Z_494><Z_460><Z_309><Z_244><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Bob rolls a fair eight-sided die each morning. If Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal. If he rolls a 1, then he rolls again. In a non-leap year, what is the expected number of times Bob will roll his die?<|im_end|>
<|im_start|>assistant
<Z_165><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Bob rolls a fair eight-sided die each morning. If Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal. If he rolls a 1, then he rolls again. In a non-leap year, what is the expected number of times Bob will roll his die?<|im_end|>
<|im_start|>assistant
<Z_43><Z_179><Z_454><Z_419><Z_479><ANSWER>

Question: Bob rolls a fair eight-sided die each morning. If Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal. If he rolls a 1, then he rolls again. In a non-leap year, what is the expected number of times Bob will roll his die?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a choir, members are arranged in rectangular formations. When arranged in 10 rows, there are 4 positions unoccupied. When arranged in 11 rows, there are 5 positions unoccupied. How many members are in the choir if the total number of members is between 200 and 300?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a choir, members are arranged in rectangular formations. When arranged in 10 rows, there are 4 positions unoccupied. When arranged in 11 rows, there are 5 positions unoccupied. How many members are in the choir if the total number of members is between 200 and 300?<|im_end|>
<|im_start|>assistant
<Z_477><Z_125><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a choir, members are arranged in rectangular formations. When arranged in 10 rows, there are 4 positions unoccupied. When arranged in 11 rows, there are 5 positions unoccupied. How many members are in the choir if the total number of members is between 200 and 300?<|im_end|>
<|im_start|>assistant
<Z_192><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a choir, members are arranged in rectangular formations. When arranged in 10 rows, there are 4 positions unoccupied. When arranged in 11 rows, there are 5 positions unoccupied. How many members are in the choir if the total number of members is between 200 and 300?<|im_end|>
<|im_start|>assistant
<Z_174><Z_106><ANSWER>

Question: In a choir, members are arranged in rectangular formations. When arranged in 10 rows, there are 4 positions unoccupied. When arranged in 11 rows, there are 5 positions unoccupied. How many members are in the choir if the total number of members is between 200 and 300?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of two 2-digit positive integers is equal to the decimal number obtained by writing one of the two-digit integers before the decimal point and the other two-digit integer after the decimal point, with the integer after the decimal point being a multiple of 25. What is the larger of the two integers?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of two 2-digit positive integers is equal to the decimal number obtained by writing one of the two-digit integers before the decimal point and the other two-digit integer after the decimal point, with the integer after the decimal point being a multiple of 25. What is the larger of the two integers?<|im_end|>
<|im_start|>assistant
<Z_477><Z_125><Z_255><Z_405><Z_494><Z_64><Z_463><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of two 2-digit positive integers is equal to the decimal number obtained by writing one of the two-digit integers before the decimal point and the other two-digit integer after the decimal point, with the integer after the decimal point being a multiple of 25. What is the larger of the two integers?<|im_end|>
<|im_start|>assistant
<Z_186><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average of two 2-digit positive integers is equal to the decimal number obtained by writing one of the two-digit integers before the decimal point and the other two-digit integer after the decimal point, with the integer after the decimal point being a multiple of 25. What is the larger of the two integers?<|im_end|>
<|im_start|>assistant
<Z_228><Z_33><Z_395><Z_391><Z_122><Z_91><Z_55><ANSWER>

Question: The average of two 2-digit positive integers is equal to the decimal number obtained by writing one of the two-digit integers before the decimal point and the other two-digit integer after the decimal point, with the integer after the decimal point being a multiple of 25. What is the larger of the two integers?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two arithmetic sequences $C$ and $D$ both begin with 50. Sequence $C$ has a common difference of 12 and is increasing, while sequence $D$ has a common difference of 8 and is decreasing. What is the absolute value of the difference between the 31st term of sequence $C$ and the 31st term of sequence $D$?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two arithmetic sequences $C$ and $D$ both begin with 50. Sequence $C$ has a common difference of 12 and is increasing, while sequence $D$ has a common difference of 8 and is decreasing. What is the absolute value of the difference between the 31st term of sequence $C$ and the 31st term of sequence $D$?<|im_end|>
<|im_start|>assistant
<Z_477><Z_169><Z_289><Z_425><Z_99><Z_425><Z_101><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two arithmetic sequences $C$ and $D$ both begin with 50. Sequence $C$ has a common difference of 12 and is increasing, while sequence $D$ has a common difference of 8 and is decreasing. What is the absolute value of the difference between the 31st term of sequence $C$ and the 31st term of sequence $D$?<|im_end|>
<|im_start|>assistant
<Z_248><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two arithmetic sequences $C$ and $D$ both begin with 50. Sequence $C$ has a common difference of 12 and is increasing, while sequence $D$ has a common difference of 8 and is decreasing. What is the absolute value of the difference between the 31st term of sequence $C$ and the 31st term of sequence $D$?<|im_end|>
<|im_start|>assistant
<Z_355><Z_376><Z_98><Z_80><Z_337><Z_414><Z_399><ANSWER>

Question: Two arithmetic sequences $C$ and $D$ both begin with 50. Sequence $C$ has a common difference of 12 and is increasing, while sequence $D$ has a common difference of 8 and is decreasing. What is the absolute value of the difference between the 31st term of sequence $C$ and the 31st term of sequence $D$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $p$ and $q$ are odd integers, how many terms in the expansion of $(p+q)^8$ are odd?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $p$ and $q$ are odd integers, how many terms in the expansion of $(p+q)^8$ are odd?<|im_end|>
<|im_start|>assistant
<Z_24><Z_41><Z_102><Z_330><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $p$ and $q$ are odd integers, how many terms in the expansion of $(p+q)^8$ are odd?<|im_end|>
<|im_start|>assistant
<Z_147><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $p$ and $q$ are odd integers, how many terms in the expansion of $(p+q)^8$ are odd?<|im_end|>
<|im_start|>assistant
<Z_455><Z_172><Z_488><Z_66><ANSWER>

Question: If $p$ and $q$ are odd integers, how many terms in the expansion of $(p+q)^8$ are odd?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the focal length of the hyperbola $\frac{x^{2}}{m^{2}+12} - \frac{y^{2}}{4-m^{2}} = 1$.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the focal length of the hyperbola $\frac{x^{2}}{m^{2}+12} - \frac{y^{2}}{4-m^{2}} = 1$.<|im_end|>
<|im_start|>assistant
<Z_369><Z_71><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the focal length of the hyperbola $\frac{x^{2}}{m^{2}+12} - \frac{y^{2}}{4-m^{2}} = 1$.<|im_end|>
<|im_start|>assistant
<Z_499><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the focal length of the hyperbola $\frac{x^{2}}{m^{2}+12} - \frac{y^{2}}{4-m^{2}} = 1$.<|im_end|>
<|im_start|>assistant
<Z_253><Z_5><ANSWER>

Question: Find the focal length of the hyperbola $\frac{x^{2}}{m^{2}+12} - \frac{y^{2}}{4-m^{2}} = 1$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Adam has some magnets. He gave away a third of the magnets, and he still had half as many magnets as Peter. Peter has 24 magnets. How many magnets did Adam have initially?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Adam has some magnets. He gave away a third of the magnets, and he still had half as many magnets as Peter. Peter has 24 magnets. How many magnets did Adam have initially?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Adam has some magnets. He gave away a third of the magnets, and he still had half as many magnets as Peter. Peter has 24 magnets. How many magnets did Adam have initially?<|im_end|>
<|im_start|>assistant
<Z_198><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Adam has some magnets. He gave away a third of the magnets, and he still had half as many magnets as Peter. Peter has 24 magnets. How many magnets did Adam have initially?<|im_end|>
<|im_start|>assistant
<Z_80><ANSWER>

Question: Adam has some magnets. He gave away a third of the magnets, and he still had half as many magnets as Peter. Peter has 24 magnets. How many magnets did Adam have initially?