<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
At the end of $1997$, the desert area in a certain region was $9\times 10^{5}hm^{2}$ (note: $hm^{2}$ is the unit of area, representing hectares). Geologists started continuous observations from $1998$ to understand the changes in the desert area of this region. The observation results at the end of each year are recorded in the table below:

| Year | Increase in desert area compared to the original area (end of year) |
|------|--------------------------------------------------------------------|
| 1998 | 2000                                                               |
| 1999 | 4000                                                               |
| 2000 | 6001                                                               |
| 2001 | 7999                                                               |
| 2002 | 10001                                                              |

Based on the information provided in the table, estimate the following:
$(1)$ If no measures are taken, approximately how much will the desert area of this region become by the end of $2020$ in $hm^{2}$?
$(2)$ If measures such as afforestation are taken starting from the beginning of $2003$, with an area of $8000hm^{2}$ of desert being transformed each year, but the desert area continues to increase at the original rate, in which year-end will the desert area of this region be less than $8\times 10^{5}hm^{2}$ for the first time?<|im_end|>
<|im_start|>assistant
<Z_5><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
At the end of $1997$, the desert area in a certain region was $9\times 10^{5}hm^{2}$ (note: $hm^{2}$ is the unit of area, representing hectares). Geologists started continuous observations from $1998$ to understand the changes in the desert area of this region. The observation results at the end of each year are recorded in the table below:

| Year | Increase in desert area compared to the original area (end of year) |
|------|--------------------------------------------------------------------|
| 1998 | 2000                                                               |
| 1999 | 4000                                                               |
| 2000 | 6001                                                               |
| 2001 | 7999                                                               |
| 2002 | 10001                                                              |

Based on the information provided in the table, estimate the following:
$(1)$ If no measures are taken, approximately how much will the desert area of this region become by the end of $2020$ in $hm^{2}$?
$(2)$ If measures such as afforestation are taken starting from the beginning of $2003$, with an area of $8000hm^{2}$ of desert being transformed each year, but the desert area continues to increase at the original rate, in which year-end will the desert area of this region be less than $8\times 10^{5}hm^{2}$ for the first time?<|im_end|>
<|im_start|>assistant
<Z_358><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
At the end of $1997$, the desert area in a certain region was $9\times 10^{5}hm^{2}$ (note: $hm^{2}$ is the unit of area, representing hectares). Geologists started continuous observations from $1998$ to understand the changes in the desert area of this region. The observation results at the end of each year are recorded in the table below:

| Year | Increase in desert area compared to the original area (end of year) |
|------|--------------------------------------------------------------------|
| 1998 | 2000                                                               |
| 1999 | 4000                                                               |
| 2000 | 6001                                                               |
| 2001 | 7999                                                               |
| 2002 | 10001                                                              |

Based on the information provided in the table, estimate the following:
$(1)$ If no measures are taken, approximately how much will the desert area of this region become by the end of $2020$ in $hm^{2}$?
$(2)$ If measures such as afforestation are taken starting from the beginning of $2003$, with an area of $8000hm^{2}$ of desert being transformed each year, but the desert area continues to increase at the original rate, in which year-end will the desert area of this region be less than $8\times 10^{5}hm^{2}$ for the first time?<|im_end|>
<|im_start|>assistant
<Z_462><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
At the end of $1997$, the desert area in a certain region was $9\times 10^{5}hm^{2}$ (note: $hm^{2}$ is the unit of area, representing hectares). Geologists started continuous observations from $1998$ to understand the changes in the desert area of this region. The observation results at the end of each year are recorded in the table below:

| Year | Increase in desert area compared to the original area (end of year) |
|------|--------------------------------------------------------------------|
| 1998 | 2000                                                               |
| 1999 | 4000                                                               |
| 2000 | 6001                                                               |
| 2001 | 7999                                                               |
| 2002 | 10001                                                              |

Based on the information provided in the table, estimate the following:
$(1)$ If no measures are taken, approximately how much will the desert area of this region become by the end of $2020$ in $hm^{2}$?
$(2)$ If measures such as afforestation are taken starting from the beginning of $2003$, with an area of $8000hm^{2}$ of desert being transformed each year, but the desert area continues to increase at the original rate, in which year-end will the desert area of this region be less than $8\times 10^{5}hm^{2}$ for the first time?<|im_end|>
<|im_start|>assistant
<Z_7><ANSWER>

Question:
At the end of $1997$, the desert area in a certain region was $9\times 10^{5}hm^{2}$ (note: $hm^{2}$ is the unit of area, representing hectares). Geologists started continuous observations from $1998$ to understand the changes in the desert area of this region. The observation results at the end of each year are recorded in the table below:

| Year | Increase in desert area compared to the original area (end of year) |
|------|--------------------------------------------------------------------|
| 1998 | 2000                                                               |
| 1999 | 4000                                                               |
| 2000 | 6001                                                               |
| 2001 | 7999                                                               |
| 2002 | 10001                                                              |

Based on the information provided in the table, estimate the following:
$(1)$ If no measures are taken, approximately how much will the desert area of this region become by the end of $2020$ in $hm^{2}$?
$(2)$ If measures such as afforestation are taken starting from the beginning of $2003$, with an area of $8000hm^{2}$ of desert being transformed each year, but the desert area continues to increase at the original rate, in which year-end will the desert area of this region be less than $8\times 10^{5}hm^{2}$ for the first time?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the sum of divisors of 3777, which are perfect squares and also prime numbers.<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the sum of divisors of 3777, which are perfect squares and also prime numbers.<|im_end|>
<|im_start|>assistant
<Z_66><Z_277><Z_354><Z_41><Z_453><Z_444><Z_106><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the sum of divisors of 3777, which are perfect squares and also prime numbers.<|im_end|>
<|im_start|>assistant
<Z_0><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the sum of divisors of 3777, which are perfect squares and also prime numbers.<|im_end|>
<|im_start|>assistant
<Z_93><Z_148><Z_377><Z_226><Z_422><Z_104><Z_235><ANSWER>

Question: Find the sum of divisors of 3777, which are perfect squares and also prime numbers.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the base prime representation of the natural number $360$.<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the base prime representation of the natural number $360$.<|im_end|>
<|im_start|>assistant
<Z_176><Z_403><Z_276><Z_118><Z_258><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the base prime representation of the natural number $360$.<|im_end|>
<|im_start|>assistant
<Z_27><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the base prime representation of the natural number $360$.<|im_end|>
<|im_start|>assistant
<Z_430><Z_142><Z_469><Z_306><Z_269><ANSWER>

Question: Determine the base prime representation of the natural number $360$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let  $n \ge 2$  be an integer. Alex writes the numbers  $1, 2, ..., n$  in some order on a circle such that any two neighbours are coprime. Then, for any two numbers that are not comprime, Alex draws a line segment between them. For each such segment  $s$  we denote by  $d_s$  the difference of the numbers written in its extremities and by  $p_s$  the number of all other drawn segments which intersect  $s$  in its interior.
Find the greatest  $n$  for which Alex can write the numbers on the circle such that  $p_s \le |d_s|$ , for each drawn segment  $s$ .<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let  $n \ge 2$  be an integer. Alex writes the numbers  $1, 2, ..., n$  in some order on a circle such that any two neighbours are coprime. Then, for any two numbers that are not comprime, Alex draws a line segment between them. For each such segment  $s$  we denote by  $d_s$  the difference of the numbers written in its extremities and by  $p_s$  the number of all other drawn segments which intersect  $s$  in its interior.
Find the greatest  $n$  for which Alex can write the numbers on the circle such that  $p_s \le |d_s|$ , for each drawn segment  $s$ .<|im_end|>
<|im_start|>assistant
<Z_358><Z_35><Z_185><Z_473><Z_100><Z_354><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let  $n \ge 2$  be an integer. Alex writes the numbers  $1, 2, ..., n$  in some order on a circle such that any two neighbours are coprime. Then, for any two numbers that are not comprime, Alex draws a line segment between them. For each such segment  $s$  we denote by  $d_s$  the difference of the numbers written in its extremities and by  $p_s$  the number of all other drawn segments which intersect  $s$  in its interior.
Find the greatest  $n$  for which Alex can write the numbers on the circle such that  $p_s \le |d_s|$ , for each drawn segment  $s$ .<|im_end|>
<|im_start|>assistant
<Z_13><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let  $n \ge 2$  be an integer. Alex writes the numbers  $1, 2, ..., n$  in some order on a circle such that any two neighbours are coprime. Then, for any two numbers that are not comprime, Alex draws a line segment between them. For each such segment  $s$  we denote by  $d_s$  the difference of the numbers written in its extremities and by  $p_s$  the number of all other drawn segments which intersect  $s$  in its interior.
Find the greatest  $n$  for which Alex can write the numbers on the circle such that  $p_s \le |d_s|$ , for each drawn segment  $s$ .<|im_end|>
<|im_start|>assistant
<Z_46><Z_26><Z_130><Z_452><Z_363><Z_364><ANSWER>

Question:
Let  $n \ge 2$  be an integer. Alex writes the numbers  $1, 2, ..., n$  in some order on a circle such that any two neighbours are coprime. Then, for any two numbers that are not comprime, Alex draws a line segment between them. For each such segment  $s$  we denote by  $d_s$  the difference of the numbers written in its extremities and by  $p_s$  the number of all other drawn segments which intersect  $s$  in its interior.
Find the greatest  $n$  for which Alex can write the numbers on the circle such that  $p_s \le |d_s|$ , for each drawn segment  $s$ .


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Compute the number of two digit positive integers that are divisible by both of their digits. For example,  $36$  is one of these two digit positive integers because it is divisible by both  $3$  and  $6$ .

*2021 CCA Math Bonanza Lightning Round #2.4*<|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
Compute the number of two digit positive integers that are divisible by both of their digits. For example,  $36$  is one of these two digit positive integers because it is divisible by both  $3$  and  $6$ .

*2021 CCA Math Bonanza Lightning Round #2.4*<|im_end|>
<|im_start|>assistant
<Z_195><Z_93><Z_41><Z_488><Z_127><Z_310><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Compute the number of two digit positive integers that are divisible by both of their digits. For example,  $36$  is one of these two digit positive integers because it is divisible by both  $3$  and  $6$ .

*2021 CCA Math Bonanza Lightning Round #2.4*<|im_end|>
<|im_start|>assistant
<Z_213><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Compute the number of two digit positive integers that are divisible by both of their digits. For example,  $36$  is one of these two digit positive integers because it is divisible by both  $3$  and  $6$ .

*2021 CCA Math Bonanza Lightning Round #2.4*<|im_end|>
<|im_start|>assistant
<Z_414><Z_112><Z_119><Z_431><Z_506><Z_269><ANSWER>

Question:
Compute the number of two digit positive integers that are divisible by both of their digits. For example,  $36$  is one of these two digit positive integers because it is divisible by both  $3$  and  $6$ .

*2021 CCA Math Bonanza Lightning Round #2.4*


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A day can be evenly divided into 86,400 seconds; hence it can also be divided into various periods based on different lengths of time. How many ways are there to divide a day into $n$ periods of $m$ minutes, where $n$ and $m$ are positive integers and the product of $n$ and $m$ equals 1440 minutes?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A day can be evenly divided into 86,400 seconds; hence it can also be divided into various periods based on different lengths of time. How many ways are there to divide a day into $n$ periods of $m$ minutes, where $n$ and $m$ are positive integers and the product of $n$ and $m$ equals 1440 minutes?<|im_end|>
<|im_start|>assistant
<Z_5><Z_323><Z_187><Z_383><Z_233><Z_334><Z_65><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A day can be evenly divided into 86,400 seconds; hence it can also be divided into various periods based on different lengths of time. How many ways are there to divide a day into $n$ periods of $m$ minutes, where $n$ and $m$ are positive integers and the product of $n$ and $m$ equals 1440 minutes?<|im_end|>
<|im_start|>assistant
<Z_254><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A day can be evenly divided into 86,400 seconds; hence it can also be divided into various periods based on different lengths of time. How many ways are there to divide a day into $n$ periods of $m$ minutes, where $n$ and $m$ are positive integers and the product of $n$ and $m$ equals 1440 minutes?<|im_end|>
<|im_start|>assistant
<Z_107><Z_175><Z_488><Z_314><Z_328><Z_398><Z_333><ANSWER>

Question: A day can be evenly divided into 86,400 seconds; hence it can also be divided into various periods based on different lengths of time. How many ways are there to divide a day into $n$ periods of $m$ minutes, where $n$ and $m$ are positive integers and the product of $n$ and $m$ equals 1440 minutes?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence $\{a_n\}$ with the sum of the first $n$ terms denoted as $S_n$, $a_1 \neq 0$, a constant $\lambda > 0$, and $\lambda a_1 a_n = S_1 + S_n$ holds for all positive integers $n$.
$(1)$ Find the general formula for the sequence $\{a_n\}$.
$(2)$ Suppose $a_1 > 0$ and $\lambda = 100$, for what value of $n$ is the sum of the first $n$ terms of the sequence $\{\lg \frac{1}{a_n}\}$ maximized?<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence $\{a_n\}$ with the sum of the first $n$ terms denoted as $S_n$, $a_1 \neq 0$, a constant $\lambda > 0$, and $\lambda a_1 a_n = S_1 + S_n$ holds for all positive integers $n$.
$(1)$ Find the general formula for the sequence $\{a_n\}$.
$(2)$ Suppose $a_1 > 0$ and $\lambda = 100$, for what value of $n$ is the sum of the first $n$ terms of the sequence $\{\lg \frac{1}{a_n}\}$ maximized?<|im_end|>
<|im_start|>assistant
<Z_358><Z_326><Z_223><Z_275><Z_92><Z_340><Z_364><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence $\{a_n\}$ with the sum of the first $n$ terms denoted as $S_n$, $a_1 \neq 0$, a constant $\lambda > 0$, and $\lambda a_1 a_n = S_1 + S_n$ holds for all positive integers $n$.
$(1)$ Find the general formula for the sequence $\{a_n\}$.
$(2)$ Suppose $a_1 > 0$ and $\lambda = 100$, for what value of $n$ is the sum of the first $n$ terms of the sequence $\{\lg \frac{1}{a_n}\}$ maximized?<|im_end|>
<|im_start|>assistant
<Z_157><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence $\{a_n\}$ with the sum of the first $n$ terms denoted as $S_n$, $a_1 \neq 0$, a constant $\lambda > 0$, and $\lambda a_1 a_n = S_1 + S_n$ holds for all positive integers $n$.
$(1)$ Find the general formula for the sequence $\{a_n\}$.
$(2)$ Suppose $a_1 > 0$ and $\lambda = 100$, for what value of $n$ is the sum of the first $n$ terms of the sequence $\{\lg \frac{1}{a_n}\}$ maximized?<|im_end|>
<|im_start|>assistant
<Z_173><Z_400><Z_507><Z_280><Z_83><Z_146><Z_377><ANSWER>

Question:
Given a sequence $\{a_n\}$ with the sum of the first $n$ terms denoted as $S_n$, $a_1 \neq 0$, a constant $\lambda > 0$, and $\lambda a_1 a_n = S_1 + S_n$ holds for all positive integers $n$.
$(1)$ Find the general formula for the sequence $\{a_n\}$.
$(2)$ Suppose $a_1 > 0$ and $\lambda = 100$, for what value of $n$ is the sum of the first $n$ terms of the sequence $\{\lg \frac{1}{a_n}\}$ maximized?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A metallic sheet is of rectangular shape with a length of 48 m and a certain width. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, and the volume of the box is 5120 m³, what is the width of the metallic sheet?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A metallic sheet is of rectangular shape with a length of 48 m and a certain width. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, and the volume of the box is 5120 m³, what is the width of the metallic sheet?<|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
A metallic sheet is of rectangular shape with a length of 48 m and a certain width. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, and the volume of the box is 5120 m³, what is the width of the metallic sheet?<|im_end|>
<|im_start|>assistant
<Z_224><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A metallic sheet is of rectangular shape with a length of 48 m and a certain width. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, and the volume of the box is 5120 m³, what is the width of the metallic sheet?<|im_end|>
<|im_start|>assistant
<Z_234><ANSWER>

Question: A metallic sheet is of rectangular shape with a length of 48 m and a certain width. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, and the volume of the box is 5120 m³, what is the width of the metallic sheet?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A jogger running at 9 kmph alongside a railway track is 230 metres ahead of the engine of a 120 metre long train running at a certain speed in the same direction. The train passes the jogger in 35 seconds. What is the speed of the train?<|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
A jogger running at 9 kmph alongside a railway track is 230 metres ahead of the engine of a 120 metre long train running at a certain speed in the same direction. The train passes the jogger in 35 seconds. What is the speed of the train?<|im_end|>
<|im_start|>assistant
<Z_5><Z_463><Z_332><Z_294><Z_102><Z_408><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A jogger running at 9 kmph alongside a railway track is 230 metres ahead of the engine of a 120 metre long train running at a certain speed in the same direction. The train passes the jogger in 35 seconds. What is the speed of the train?<|im_end|>
<|im_start|>assistant
<Z_161><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A jogger running at 9 kmph alongside a railway track is 230 metres ahead of the engine of a 120 metre long train running at a certain speed in the same direction. The train passes the jogger in 35 seconds. What is the speed of the train?<|im_end|>
<|im_start|>assistant
<Z_28><Z_76><Z_157><Z_94><Z_251><Z_355><ANSWER>

Question: A jogger running at 9 kmph alongside a railway track is 230 metres ahead of the engine of a 120 metre long train running at a certain speed in the same direction. The train passes the jogger in 35 seconds. What is the speed of the train?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Helen the hippo and her friends are preparing for thanksgiving at Helen's house. Helen baked 519 chocolate chip cookies and 300 raisin cookies yesterday. And she baked 280 raisin cookies and some chocolate chip cookies this morning. Helen baked 20 more raisin cookies yesterday compared to today. How many chocolate chip cookies did Helen bake today?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Helen the hippo and her friends are preparing for thanksgiving at Helen's house. Helen baked 519 chocolate chip cookies and 300 raisin cookies yesterday. And she baked 280 raisin cookies and some chocolate chip cookies this morning. Helen baked 20 more raisin cookies yesterday compared to today. How many chocolate chip cookies did Helen bake today?<|im_end|>
<|im_start|>assistant
<Z_358><Z_504><Z_32><Z_293><Z_91><Z_476><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Helen the hippo and her friends are preparing for thanksgiving at Helen's house. Helen baked 519 chocolate chip cookies and 300 raisin cookies yesterday. And she baked 280 raisin cookies and some chocolate chip cookies this morning. Helen baked 20 more raisin cookies yesterday compared to today. How many chocolate chip cookies did Helen bake today?<|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
Helen the hippo and her friends are preparing for thanksgiving at Helen's house. Helen baked 519 chocolate chip cookies and 300 raisin cookies yesterday. And she baked 280 raisin cookies and some chocolate chip cookies this morning. Helen baked 20 more raisin cookies yesterday compared to today. How many chocolate chip cookies did Helen bake today?<|im_end|>
<|im_start|>assistant
<Z_434><Z_221><Z_129><Z_282><Z_370><Z_193><ANSWER>

Question: Helen the hippo and her friends are preparing for thanksgiving at Helen's house. Helen baked 519 chocolate chip cookies and 300 raisin cookies yesterday. And she baked 280 raisin cookies and some chocolate chip cookies this morning. Helen baked 20 more raisin cookies yesterday compared to today. How many chocolate chip cookies did Helen bake today?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a jar, the number of white balls to red balls is in the ratio of $5:3$. If adding 15 more white balls to the jar makes the total number of balls 50, how many red balls are there?<|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
In a jar, the number of white balls to red balls is in the ratio of $5:3$. If adding 15 more white balls to the jar makes the total number of balls 50, how many red balls are there?<|im_end|>
<|im_start|>assistant
<Z_5><Z_304><Z_122><Z_294><Z_383><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a jar, the number of white balls to red balls is in the ratio of $5:3$. If adding 15 more white balls to the jar makes the total number of balls 50, how many red balls are there?<|im_end|>
<|im_start|>assistant
<Z_481><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a jar, the number of white balls to red balls is in the ratio of $5:3$. If adding 15 more white balls to the jar makes the total number of balls 50, how many red balls are there?<|im_end|>
<|im_start|>assistant
<Z_249><Z_149><Z_65><Z_228><Z_33><ANSWER>

Question: In a jar, the number of white balls to red balls is in the ratio of $5:3$. If adding 15 more white balls to the jar makes the total number of balls 50, how many red balls are there?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $A\,568\,B72$ is divisible by $9$, where $A$ and $B$ each represent a single digit, what is the sum of all possible values of the sum $A+B$?<|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
If $A\,568\,B72$ is divisible by $9$, where $A$ and $B$ each represent a single digit, what is the sum of all possible values of the sum $A+B$?<|im_end|>
<|im_start|>assistant
<Z_72><Z_214><Z_253><Z_509><Z_107><Z_337><Z_238><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $A\,568\,B72$ is divisible by $9$, where $A$ and $B$ each represent a single digit, what is the sum of all possible values of the sum $A+B$?<|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
If $A\,568\,B72$ is divisible by $9$, where $A$ and $B$ each represent a single digit, what is the sum of all possible values of the sum $A+B$?<|im_end|>
<|im_start|>assistant
<Z_484><Z_242><Z_12><Z_83><Z_396><Z_204><Z_481><ANSWER>

Question: If $A\,568\,B72$ is divisible by $9$, where $A$ and $B$ each represent a single digit, what is the sum of all possible values of the sum $A+B$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest prime whose digits sum to $23$?<|im_end|>
<|im_start|>assistant
<Z_195><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 prime whose digits sum to $23$?<|im_end|>
<|im_start|>assistant
<Z_195><Z_418><Z_167><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 prime whose digits sum to $23$?<|im_end|>
<|im_start|>assistant
<Z_184><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 prime whose digits sum to $23$?<|im_end|>
<|im_start|>assistant
<Z_422><Z_185><Z_451><ANSWER>

Question: What is the smallest prime whose digits sum to $23$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dan has some violet balloons. Tim has 7 times more violet balloons than Dan. Tim has 203 violet balloons. How many violet balloons does Dan have?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dan has some violet balloons. Tim has 7 times more violet balloons than Dan. Tim has 203 violet balloons. How many violet balloons does Dan have?<|im_end|>
<|im_start|>assistant
<Z_5><Z_172><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dan has some violet balloons. Tim has 7 times more violet balloons than Dan. Tim has 203 violet balloons. How many violet balloons does Dan have?<|im_end|>
<|im_start|>assistant
<Z_308><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Dan has some violet balloons. Tim has 7 times more violet balloons than Dan. Tim has 203 violet balloons. How many violet balloons does Dan have?<|im_end|>
<|im_start|>assistant
<Z_351><Z_30><ANSWER>

Question: Dan has some violet balloons. Tim has 7 times more violet balloons than Dan. Tim has 203 violet balloons. How many violet balloons does Dan have?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $y$ is a multiple of $30492$, what is the greatest common divisor of $g(y)=(3y+4)(8y+3)(11y+5)(y+11)$ and $y$?<|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
Given that $y$ is a multiple of $30492$, what is the greatest common divisor of $g(y)=(3y+4)(8y+3)(11y+5)(y+11)$ and $y$?<|im_end|>
<|im_start|>assistant
<Z_176><Z_500><Z_269><Z_223><Z_484><Z_271><Z_446><Z_409><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $y$ is a multiple of $30492$, what is the greatest common divisor of $g(y)=(3y+4)(8y+3)(11y+5)(y+11)$ and $y$?<|im_end|>
<|im_start|>assistant
<Z_488><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $y$ is a multiple of $30492$, what is the greatest common divisor of $g(y)=(3y+4)(8y+3)(11y+5)(y+11)$ and $y$?<|im_end|>
<|im_start|>assistant
<Z_259><Z_62><Z_350><Z_134><Z_351><Z_291><Z_116><Z_95><ANSWER>

Question: Given that $y$ is a multiple of $30492$, what is the greatest common divisor of $g(y)=(3y+4)(8y+3)(11y+5)(y+11)$ and $y$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Hayden eats 1 oz of mixed nuts as an evening snack. He buys the bulk bag of mixed nuts that cost $25.00 a bag and holds 40 oz of mixed nuts. There is currently a $5.00 coupon for this item. How much will each serving of nuts cost, in cents, after the coupon is applied?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Hayden eats 1 oz of mixed nuts as an evening snack. He buys the bulk bag of mixed nuts that cost $25.00 a bag and holds 40 oz of mixed nuts. There is currently a $5.00 coupon for this item. How much will each serving of nuts cost, in cents, after the coupon is applied?<|im_end|>
<|im_start|>assistant
<Z_176><Z_287><Z_504><Z_409><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Hayden eats 1 oz of mixed nuts as an evening snack. He buys the bulk bag of mixed nuts that cost $25.00 a bag and holds 40 oz of mixed nuts. There is currently a $5.00 coupon for this item. How much will each serving of nuts cost, in cents, after the coupon is applied?<|im_end|>
<|im_start|>assistant
<Z_360><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Hayden eats 1 oz of mixed nuts as an evening snack. He buys the bulk bag of mixed nuts that cost $25.00 a bag and holds 40 oz of mixed nuts. There is currently a $5.00 coupon for this item. How much will each serving of nuts cost, in cents, after the coupon is applied?<|im_end|>
<|im_start|>assistant
<Z_48><Z_53><Z_451><Z_94><ANSWER>

Question: Hayden eats 1 oz of mixed nuts as an evening snack. He buys the bulk bag of mixed nuts that cost $25.00 a bag and holds 40 oz of mixed nuts. There is currently a $5.00 coupon for this item. How much will each serving of nuts cost, in cents, after the coupon is applied?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the number of trailing zeroes in 2019!.<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the number of trailing zeroes in 2019!.<|im_end|>
<|im_start|>assistant
<Z_66><Z_281><Z_355><Z_318><Z_238><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the number of trailing zeroes in 2019!.<|im_end|>
<|im_start|>assistant
<Z_398><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Calculate the number of trailing zeroes in 2019!.<|im_end|>
<|im_start|>assistant
<Z_66><Z_193><Z_359><Z_261><Z_118><ANSWER>

Question: Calculate the number of trailing zeroes in 2019!.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jeanne wants to ride the Ferris wheel, the roller coaster, and the bumper cars. The Ferris wheel costs a certain number of tickets, the roller coaster costs 4 tickets, and the bumper cars cost 4 tickets. Jeanne has 5 tickets and needs to buy 8 more tickets. How many tickets does the Ferris wheel cost?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jeanne wants to ride the Ferris wheel, the roller coaster, and the bumper cars. The Ferris wheel costs a certain number of tickets, the roller coaster costs 4 tickets, and the bumper cars cost 4 tickets. Jeanne has 5 tickets and needs to buy 8 more tickets. How many tickets does the Ferris wheel cost?<|im_end|>
<|im_start|>assistant
<Z_195><Z_412><Z_255><Z_251><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jeanne wants to ride the Ferris wheel, the roller coaster, and the bumper cars. The Ferris wheel costs a certain number of tickets, the roller coaster costs 4 tickets, and the bumper cars cost 4 tickets. Jeanne has 5 tickets and needs to buy 8 more tickets. How many tickets does the Ferris wheel cost?<|im_end|>
<|im_start|>assistant
<Z_465><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jeanne wants to ride the Ferris wheel, the roller coaster, and the bumper cars. The Ferris wheel costs a certain number of tickets, the roller coaster costs 4 tickets, and the bumper cars cost 4 tickets. Jeanne has 5 tickets and needs to buy 8 more tickets. How many tickets does the Ferris wheel cost?<|im_end|>
<|im_start|>assistant
<Z_90><Z_126><Z_380><Z_411><ANSWER>

Question: Jeanne wants to ride the Ferris wheel, the roller coaster, and the bumper cars. The Ferris wheel costs a certain number of tickets, the roller coaster costs 4 tickets, and the bumper cars cost 4 tickets. Jeanne has 5 tickets and needs to buy 8 more tickets. How many tickets does the Ferris wheel cost?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
We will say that a number has the form $\overline{a b a}$ if its first and third digits are the same; the second digit does not have to be different. For example, 101 and 222 have this form, while 220 and 123 do not. Similarly, let's define the form $\overline{\overline{b a b c}}$. How many numbers of the form $\overline{a b a b c}$ are divisible by 5?<|im_end|>
<|im_start|>assistant
<Z_5><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
We will say that a number has the form $\overline{a b a}$ if its first and third digits are the same; the second digit does not have to be different. For example, 101 and 222 have this form, while 220 and 123 do not. Similarly, let's define the form $\overline{\overline{b a b c}}$. How many numbers of the form $\overline{a b a b c}$ are divisible by 5?<|im_end|>
<|im_start|>assistant
<Z_72><Z_384><Z_477><Z_68><Z_214><Z_255><Z_500><Z_126><Z_180><Z_233><Z_106><Z_485><Z_463><Z_200><Z_252><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
We will say that a number has the form $\overline{a b a}$ if its first and third digits are the same; the second digit does not have to be different. For example, 101 and 222 have this form, while 220 and 123 do not. Similarly, let's define the form $\overline{\overline{b a b c}}$. How many numbers of the form $\overline{a b a b c}$ are divisible by 5?<|im_end|>
<|im_start|>assistant
<Z_27><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
We will say that a number has the form $\overline{a b a}$ if its first and third digits are the same; the second digit does not have to be different. For example, 101 and 222 have this form, while 220 and 123 do not. Similarly, let's define the form $\overline{\overline{b a b c}}$. How many numbers of the form $\overline{a b a b c}$ are divisible by 5?<|im_end|>
<|im_start|>assistant
<Z_207><Z_481><Z_171><Z_297><Z_126><Z_226><Z_251><Z_411><Z_296><Z_408><Z_302><Z_14><Z_342><Z_265><Z_344><ANSWER>

Question: We will say that a number has the form $\overline{a b a}$ if its first and third digits are the same; the second digit does not have to be different. For example, 101 and 222 have this form, while 220 and 123 do not. Similarly, let's define the form $\overline{\overline{b a b c}}$. How many numbers of the form $\overline{a b a b c}$ are divisible by 5?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Maddie bought some packs of white T-shirts and 4 packs of blue T-shirts for her basketball team. The white T-shirts come in packs of 5, and the blue T-shirts come in packs of 3. Each T-shirt cost $3. Maddie spent $66 in all. How many packs of white T-shirts did Maddie buy?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Maddie bought some packs of white T-shirts and 4 packs of blue T-shirts for her basketball team. The white T-shirts come in packs of 5, and the blue T-shirts come in packs of 3. Each T-shirt cost $3. Maddie spent $66 in all. How many packs of white T-shirts did Maddie buy?<|im_end|>
<|im_start|>assistant
<Z_195><Z_181><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Maddie bought some packs of white T-shirts and 4 packs of blue T-shirts for her basketball team. The white T-shirts come in packs of 5, and the blue T-shirts come in packs of 3. Each T-shirt cost $3. Maddie spent $66 in all. How many packs of white T-shirts did Maddie buy?<|im_end|>
<|im_start|>assistant
<Z_333><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Maddie bought some packs of white T-shirts and 4 packs of blue T-shirts for her basketball team. The white T-shirts come in packs of 5, and the blue T-shirts come in packs of 3. Each T-shirt cost $3. Maddie spent $66 in all. How many packs of white T-shirts did Maddie buy?<|im_end|>
<|im_start|>assistant
<Z_447><Z_511><ANSWER>

Question: Maddie bought some packs of white T-shirts and 4 packs of blue T-shirts for her basketball team. The white T-shirts come in packs of 5, and the blue T-shirts come in packs of 3. Each T-shirt cost $3. Maddie spent $66 in all. How many packs of white T-shirts did Maddie buy?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A and B enter into a partnership. A contributed Rs. 5000 for 8 months and B contributed Rs. 6000 for 5 months. They made a total profit of Rs. 8400. What is A's share in the total profit?<|im_end|>
<|im_start|>assistant
<Z_5><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A and B enter into a partnership. A contributed Rs. 5000 for 8 months and B contributed Rs. 6000 for 5 months. They made a total profit of Rs. 8400. What is A's share in the total profit?<|im_end|>
<|im_start|>assistant
<Z_5><Z_272><Z_132><Z_44><Z_493><Z_473><Z_326><Z_54><Z_484><Z_238><Z_400><Z_76><Z_465><Z_435><Z_141><Z_391><Z_293><Z_398><Z_481><Z_76><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A and B enter into a partnership. A contributed Rs. 5000 for 8 months and B contributed Rs. 6000 for 5 months. They made a total profit of Rs. 8400. What is A's share in the total profit?<|im_end|>
<|im_start|>assistant
<Z_44><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A and B enter into a partnership. A contributed Rs. 5000 for 8 months and B contributed Rs. 6000 for 5 months. They made a total profit of Rs. 8400. What is A's share in the total profit?<|im_end|>
<|im_start|>assistant
<Z_323><Z_348><Z_10><Z_503><Z_35><Z_325><Z_367><Z_433><Z_100><Z_430><Z_340><Z_206><Z_351><Z_494><Z_60><Z_273><Z_493><Z_130><Z_474><Z_312><ANSWER>

Question: A and B enter into a partnership. A contributed Rs. 5000 for 8 months and B contributed Rs. 6000 for 5 months. They made a total profit of Rs. 8400. What is A's share in the total profit?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The line $y = 5$ intersects the graph of $y = 2x^2 + 3x - 2$ at points $C$ and $D$. The distance between $C$ and $D$ can be written as $\frac{\sqrt{p}}{q}$, where $p$ and $q$ are positive integers that do not share any factors other than one. Find the value of $p - q$.<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The line $y = 5$ intersects the graph of $y = 2x^2 + 3x - 2$ at points $C$ and $D$. The distance between $C$ and $D$ can be written as $\frac{\sqrt{p}}{q}$, where $p$ and $q$ are positive integers that do not share any factors other than one. Find the value of $p - q$.<|im_end|>
<|im_start|>assistant
<Z_176><Z_436><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The line $y = 5$ intersects the graph of $y = 2x^2 + 3x - 2$ at points $C$ and $D$. The distance between $C$ and $D$ can be written as $\frac{\sqrt{p}}{q}$, where $p$ and $q$ are positive integers that do not share any factors other than one. Find the value of $p - q$.<|im_end|>
<|im_start|>assistant
<Z_155><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The line $y = 5$ intersects the graph of $y = 2x^2 + 3x - 2$ at points $C$ and $D$. The distance between $C$ and $D$ can be written as $\frac{\sqrt{p}}{q}$, where $p$ and $q$ are positive integers that do not share any factors other than one. Find the value of $p - q$.<|im_end|>
<|im_start|>assistant
<Z_111><Z_275><ANSWER>

Question: The line $y = 5$ intersects the graph of $y = 2x^2 + 3x - 2$ at points $C$ and $D$. The distance between $C$ and $D$ can be written as $\frac{\sqrt{p}}{q}$, where $p$ and $q$ are positive integers that do not share any factors other than one. Find the value of $p - q$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On a track for remote-controlled racing cars, racing car A completes the track in 28 seconds, while racing car B completes it in 24 seconds. If they both start at the same time, after how many seconds will they be side by side again?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On a track for remote-controlled racing cars, racing car A completes the track in 28 seconds, while racing car B completes it in 24 seconds. If they both start at the same time, after how many seconds will they be side by side again?<|im_end|>
<|im_start|>assistant
<Z_5><Z_444><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On a track for remote-controlled racing cars, racing car A completes the track in 28 seconds, while racing car B completes it in 24 seconds. If they both start at the same time, after how many seconds will they be side by side again?<|im_end|>
<|im_start|>assistant
<Z_360><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On a track for remote-controlled racing cars, racing car A completes the track in 28 seconds, while racing car B completes it in 24 seconds. If they both start at the same time, after how many seconds will they be side by side again?<|im_end|>
<|im_start|>assistant
<Z_467><Z_484><ANSWER>

Question: On a track for remote-controlled racing cars, racing car A completes the track in 28 seconds, while racing car B completes it in 24 seconds. If they both start at the same time, after how many seconds will they be side by side again?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the amount of Water formed on combining 2 moles of Hydrochloric acid and some moles of Sodium bicarbonate. The amount of water formed is 36. How many moles of Sodium bicarbonate were combined?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the amount of Water formed on combining 2 moles of Hydrochloric acid and some moles of Sodium bicarbonate. The amount of water formed is 36. How many moles of Sodium bicarbonate were combined?<|im_end|>
<|im_start|>assistant
<Z_195><Z_233><Z_270><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the amount of Water formed on combining 2 moles of Hydrochloric acid and some moles of Sodium bicarbonate. The amount of water formed is 36. How many moles of Sodium bicarbonate were combined?<|im_end|>
<|im_start|>assistant
<Z_48><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the amount of Water formed on combining 2 moles of Hydrochloric acid and some moles of Sodium bicarbonate. The amount of water formed is 36. How many moles of Sodium bicarbonate were combined?<|im_end|>
<|im_start|>assistant
<Z_208><Z_62><Z_18><ANSWER>

Question: Find the amount of Water formed on combining 2 moles of Hydrochloric acid and some moles of Sodium bicarbonate. The amount of water formed is 36. How many moles of Sodium bicarbonate were combined?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
in a class of 40 students , 10 did not opt for math . 15 did not opt for science and 2 did not opt for either . how many students of the class opted for both math and science ?<|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
in a class of 40 students , 10 did not opt for math . 15 did not opt for science and 2 did not opt for either . how many students of the class opted for both math and science ?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
in a class of 40 students , 10 did not opt for math . 15 did not opt for science and 2 did not opt for either . how many students of the class opted for both math and science ?<|im_end|>
<|im_start|>assistant
<Z_86><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
in a class of 40 students , 10 did not opt for math . 15 did not opt for science and 2 did not opt for either . how many students of the class opted for both math and science ?<|im_end|>
<|im_start|>assistant
<Z_285><ANSWER>

Question: in a class of 40 students , 10 did not opt for math . 15 did not opt for science and 2 did not opt for either . how many students of the class opted for both math and science ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many ways can 7 people sit around a round table? (Two seatings are considered the same if one is a rotation of the other.)<|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
In how many ways can 7 people sit around a round table? (Two seatings are considered the same if one is a rotation of the other.)<|im_end|>
<|im_start|>assistant
<Z_66><Z_59><Z_200><Z_252><Z_92><Z_79><Z_366><Z_301><Z_333><Z_90><Z_254><Z_462><Z_409><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many ways can 7 people sit around a round table? (Two seatings are considered the same if one is a rotation of the other.)<|im_end|>
<|im_start|>assistant
<Z_377><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many ways can 7 people sit around a round table? (Two seatings are considered the same if one is a rotation of the other.)<|im_end|>
<|im_start|>assistant
<Z_146><Z_175><Z_247><Z_509><Z_47><Z_156><Z_314><Z_126><Z_494><Z_234><Z_7><Z_406><Z_332><ANSWER>

Question: In how many ways can 7 people sit around a round table? (Two seatings are considered the same if one is a rotation of the other.)


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 4 bookstores that subscribed to a total of 400 "Mathematical and Physical World" magazines. Each bookstore subscribed to at least 98 and at most 101 magazines. How many different ways can they subscribe to these magazines?<|im_end|>
<|im_start|>assistant
<Z_5><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 4 bookstores that subscribed to a total of 400 "Mathematical and Physical World" magazines. Each bookstore subscribed to at least 98 and at most 101 magazines. How many different ways can they subscribe to these magazines?<|im_end|>
<|im_start|>assistant
<Z_358><Z_334><Z_505><Z_418><Z_432><Z_81><Z_391><Z_254><Z_446><Z_250><Z_125><Z_187><Z_354><Z_180><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 4 bookstores that subscribed to a total of 400 "Mathematical and Physical World" magazines. Each bookstore subscribed to at least 98 and at most 101 magazines. How many different ways can they subscribe to these magazines?<|im_end|>
<|im_start|>assistant
<Z_449><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 4 bookstores that subscribed to a total of 400 "Mathematical and Physical World" magazines. Each bookstore subscribed to at least 98 and at most 101 magazines. How many different ways can they subscribe to these magazines?<|im_end|>
<|im_start|>assistant
<Z_82><Z_468><Z_297><Z_330><Z_86><Z_269><Z_442><Z_12><Z_199><Z_337><Z_296><Z_340><Z_73><Z_202><ANSWER>

Question: There are 4 bookstores that subscribed to a total of 400 "Mathematical and Physical World" magazines. Each bookstore subscribed to at least 98 and at most 101 magazines. How many different ways can they subscribe to these magazines?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
excluding stoppages , the speed of a train is 48 kmph and including stoppages it is 36 kmph . of how many minutes does the train stop per hour ?<|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
excluding stoppages , the speed of a train is 48 kmph and including stoppages it is 36 kmph . of how many minutes does the train stop per hour ?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
excluding stoppages , the speed of a train is 48 kmph and including stoppages it is 36 kmph . of how many minutes does the train stop per hour ?<|im_end|>
<|im_start|>assistant
<Z_483><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
excluding stoppages , the speed of a train is 48 kmph and including stoppages it is 36 kmph . of how many minutes does the train stop per hour ?<|im_end|>
<|im_start|>assistant
<Z_43><ANSWER>

Question: excluding stoppages , the speed of a train is 48 kmph and including stoppages it is 36 kmph . of how many minutes does the train stop per hour ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \(L\) denote the L.C.M. of \(1, 2, \ldots, 20\). How many positive factors of \(L\) are divisible by exactly 18 of the 20 numbers \(1, 2, \ldots, 20\)?<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \(L\) denote the L.C.M. of \(1, 2, \ldots, 20\). How many positive factors of \(L\) are divisible by exactly 18 of the 20 numbers \(1, 2, \ldots, 20\)?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \(L\) denote the L.C.M. of \(1, 2, \ldots, 20\). How many positive factors of \(L\) are divisible by exactly 18 of the 20 numbers \(1, 2, \ldots, 20\)?<|im_end|>
<|im_start|>assistant
<Z_484><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \(L\) denote the L.C.M. of \(1, 2, \ldots, 20\). How many positive factors of \(L\) are divisible by exactly 18 of the 20 numbers \(1, 2, \ldots, 20\)?<|im_end|>
<|im_start|>assistant
<Z_267><ANSWER>

Question: Let \(L\) denote the L.C.M. of \(1, 2, \ldots, 20\). How many positive factors of \(L\) are divisible by exactly 18 of the 20 numbers \(1, 2, \ldots, 20\)?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The student population at one high school consists of freshmen, sophomores, juniors, and seniors.  There are 25 percent more freshmen than juniors, 10 percent fewer sophomores than freshmen, and 20 percent of the students are seniors. If there are 144 sophomores, how many students attend the school?<|im_end|>
<|im_start|>assistant
<Z_5><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The student population at one high school consists of freshmen, sophomores, juniors, and seniors.  There are 25 percent more freshmen than juniors, 10 percent fewer sophomores than freshmen, and 20 percent of the students are seniors. If there are 144 sophomores, how many students attend the school?<|im_end|>
<|im_start|>assistant
<Z_5><Z_449><Z_334><Z_48><Z_135><Z_95><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The student population at one high school consists of freshmen, sophomores, juniors, and seniors.  There are 25 percent more freshmen than juniors, 10 percent fewer sophomores than freshmen, and 20 percent of the students are seniors. If there are 144 sophomores, how many students attend the school?<|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
The student population at one high school consists of freshmen, sophomores, juniors, and seniors.  There are 25 percent more freshmen than juniors, 10 percent fewer sophomores than freshmen, and 20 percent of the students are seniors. If there are 144 sophomores, how many students attend the school?<|im_end|>
<|im_start|>assistant
<Z_34><Z_186><Z_230><Z_257><Z_456><Z_260><ANSWER>

Question: The student population at one high school consists of freshmen, sophomores, juniors, and seniors.  There are 25 percent more freshmen than juniors, 10 percent fewer sophomores than freshmen, and 20 percent of the students are seniors. If there are 144 sophomores, how many students attend the school?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The hyperbola $$\frac {x^{2}}{n} - y^{2} = 1$$ (where $n > 1$) has two foci $F_{1}$ and $F_{2}$. A point $P$ is on the hyperbola and satisfies $|PF_{1}| + |PF_{2}| = 2\sqrt{n + 2}$. The area of $\triangle PF_{1}F_{2}$ is \_\_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The hyperbola $$\frac {x^{2}}{n} - y^{2} = 1$$ (where $n > 1$) has two foci $F_{1}$ and $F_{2}$. A point $P$ is on the hyperbola and satisfies $|PF_{1}| + |PF_{2}| = 2\sqrt{n + 2}$. The area of $\triangle PF_{1}F_{2}$ is \_\_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_5><Z_473><Z_380><Z_301><Z_445><Z_503><Z_233><Z_177><Z_398><Z_172><Z_180><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The hyperbola $$\frac {x^{2}}{n} - y^{2} = 1$$ (where $n > 1$) has two foci $F_{1}$ and $F_{2}$. A point $P$ is on the hyperbola and satisfies $|PF_{1}| + |PF_{2}| = 2\sqrt{n + 2}$. The area of $\triangle PF_{1}F_{2}$ is \_\_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_239><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The hyperbola $$\frac {x^{2}}{n} - y^{2} = 1$$ (where $n > 1$) has two foci $F_{1}$ and $F_{2}$. A point $P$ is on the hyperbola and satisfies $|PF_{1}| + |PF_{2}| = 2\sqrt{n + 2}$. The area of $\triangle PF_{1}F_{2}$ is \_\_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_430><Z_240><Z_209><Z_424><Z_206><Z_410><Z_264><Z_267><Z_86><Z_510><Z_14><ANSWER>

Question: The hyperbola $$\frac {x^{2}}{n} - y^{2} = 1$$ (where $n > 1$) has two foci $F_{1}$ and $F_{2}$. A point $P$ is on the hyperbola and satisfies $|PF_{1}| + |PF_{2}| = 2\sqrt{n + 2}$. The area of $\triangle PF_{1}F_{2}$ is \_\_\_\_\_\_.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The number of positive integer pairs  $(a,b)$  that have  $a$  dividing  $b$  and  $b$  dividing  $2013^{2014}$  can be written as  $2013n+k$ , where  $n$  and  $k$  are integers and  $0\leq k<2013$ .  What is  $k$ ?  Recall  $2013=3\cdot 11\cdot 61$ .<|im_end|>
<|im_start|>assistant
<Z_5><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The number of positive integer pairs  $(a,b)$  that have  $a$  dividing  $b$  and  $b$  dividing  $2013^{2014}$  can be written as  $2013n+k$ , where  $n$  and  $k$  are integers and  $0\leq k<2013$ .  What is  $k$ ?  Recall  $2013=3\cdot 11\cdot 61$ .<|im_end|>
<|im_start|>assistant
<Z_66><Z_502><Z_278><Z_358><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The number of positive integer pairs  $(a,b)$  that have  $a$  dividing  $b$  and  $b$  dividing  $2013^{2014}$  can be written as  $2013n+k$ , where  $n$  and  $k$  are integers and  $0\leq k<2013$ .  What is  $k$ ?  Recall  $2013=3\cdot 11\cdot 61$ .<|im_end|>
<|im_start|>assistant
<Z_509><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The number of positive integer pairs  $(a,b)$  that have  $a$  dividing  $b$  and  $b$  dividing  $2013^{2014}$  can be written as  $2013n+k$ , where  $n$  and  $k$  are integers and  $0\leq k<2013$ .  What is  $k$ ?  Recall  $2013=3\cdot 11\cdot 61$ .<|im_end|>
<|im_start|>assistant
<Z_215><Z_299><Z_176><Z_148><ANSWER>

Question: The number of positive integer pairs  $(a,b)$  that have  $a$  dividing  $b$  and  $b$  dividing  $2013^{2014}$  can be written as  $2013n+k$ , where  $n$  and  $k$  are integers and  $0\leq k<2013$ .  What is  $k$ ?  Recall  $2013=3\cdot 11\cdot 61$ .


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x) = x - 1 - a \ln x$.

(1) If $a=2$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(4, f(4))$.

(2) Discuss the minimum value of $f(x)$ for $a \in \mathbb{R}$ and find the value of $a$ such that $f(x) \geqslant 0$.

(3) Let $m$ be an integer, and for any positive integer $n$, $(1+\frac{1}{2})(1+\frac{1}{2^{2}}) \ldots (1+\frac{1}{2^{n}}) < m$. Find the minimum value of $m$.<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x) = x - 1 - a \ln x$.

(1) If $a=2$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(4, f(4))$.

(2) Discuss the minimum value of $f(x)$ for $a \in \mathbb{R}$ and find the value of $a$ such that $f(x) \geqslant 0$.

(3) Let $m$ be an integer, and for any positive integer $n$, $(1+\frac{1}{2})(1+\frac{1}{2^{2}}) \ldots (1+\frac{1}{2^{n}}) < m$. Find the minimum value of $m$.<|im_end|>
<|im_start|>assistant
<Z_5><Z_135><Z_452><Z_417><Z_338><Z_204><Z_256><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x) = x - 1 - a \ln x$.

(1) If $a=2$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(4, f(4))$.

(2) Discuss the minimum value of $f(x)$ for $a \in \mathbb{R}$ and find the value of $a$ such that $f(x) \geqslant 0$.

(3) Let $m$ be an integer, and for any positive integer $n$, $(1+\frac{1}{2})(1+\frac{1}{2^{2}}) \ldots (1+\frac{1}{2^{n}}) < m$. Find the minimum value of $m$.<|im_end|>
<|im_start|>assistant
<Z_456><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x) = x - 1 - a \ln x$.

(1) If $a=2$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(4, f(4))$.

(2) Discuss the minimum value of $f(x)$ for $a \in \mathbb{R}$ and find the value of $a$ such that $f(x) \geqslant 0$.

(3) Let $m$ be an integer, and for any positive integer $n$, $(1+\frac{1}{2})(1+\frac{1}{2^{2}}) \ldots (1+\frac{1}{2^{n}}) < m$. Find the minimum value of $m$.<|im_end|>
<|im_start|>assistant
<Z_16><Z_25><Z_402><Z_200><Z_212><Z_39><Z_1><ANSWER>

Question:
Given the function $f(x) = x - 1 - a \ln x$.

(1) If $a=2$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(4, f(4))$.

(2) Discuss the minimum value of $f(x)$ for $a \in \mathbb{R}$ and find the value of $a$ such that $f(x) \geqslant 0$.

(3) Let $m$ be an integer, and for any positive integer $n$, $(1+\frac{1}{2})(1+\frac{1}{2^{2}}) \ldots (1+\frac{1}{2^{n}}) < m$. Find the minimum value of $m$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If a two-digit number divisible by 5 cannot be divisible by 3 nor 4, its 97 times is an even number, and the tens digit is not less than 6, what is this two-digit number?<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If a two-digit number divisible by 5 cannot be divisible by 3 nor 4, its 97 times is an even number, and the tens digit is not less than 6, what is this two-digit number?<|im_end|>
<|im_start|>assistant
<Z_5><Z_421><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If a two-digit number divisible by 5 cannot be divisible by 3 nor 4, its 97 times is an even number, and the tens digit is not less than 6, what is this two-digit number?<|im_end|>
<|im_start|>assistant
<Z_482><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If a two-digit number divisible by 5 cannot be divisible by 3 nor 4, its 97 times is an even number, and the tens digit is not less than 6, what is this two-digit number?<|im_end|>
<|im_start|>assistant
<Z_202><Z_497><ANSWER>

Question: If a two-digit number divisible by 5 cannot be divisible by 3 nor 4, its 97 times is an even number, and the tens digit is not less than 6, what is this two-digit number?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $m = 2^{12} \cdot 3^{15} \cdot 5^{9}$, how many of the natural-number factors of $m$ are multiples of 300?<|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
If $m = 2^{12} \cdot 3^{15} \cdot 5^{9}$, how many of the natural-number factors of $m$ are multiples of 300?<|im_end|>
<|im_start|>assistant
<Z_66><Z_498><Z_88><Z_146><Z_289><Z_461><Z_449><Z_233><Z_183><Z_228><Z_446><Z_494><Z_147><Z_311><Z_159><Z_48><Z_157><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $m = 2^{12} \cdot 3^{15} \cdot 5^{9}$, how many of the natural-number factors of $m$ are multiples of 300?<|im_end|>
<|im_start|>assistant
<Z_215><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $m = 2^{12} \cdot 3^{15} \cdot 5^{9}$, how many of the natural-number factors of $m$ are multiples of 300?<|im_end|>
<|im_start|>assistant
<Z_332><Z_455><Z_125><Z_311><Z_78><Z_485><Z_393><Z_0><Z_259><Z_303><Z_206><Z_31><Z_135><Z_120><Z_209><Z_143><Z_222><ANSWER>

Question: If $m = 2^{12} \cdot 3^{15} \cdot 5^{9}$, how many of the natural-number factors of $m$ are multiples of 300?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Workers at a campaign office have 3000 fliers to send out. They send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon. How many fliers are left for the next day?<|im_end|>
<|im_start|>assistant
<Z_5><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Workers at a campaign office have 3000 fliers to send out. They send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon. How many fliers are left for the next day?<|im_end|>
<|im_start|>assistant
<Z_5><Z_139><Z_336><Z_318><Z_325><Z_450><Z_277><Z_157><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Workers at a campaign office have 3000 fliers to send out. They send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon. How many fliers are left for the next day?<|im_end|>
<|im_start|>assistant
<Z_269><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Workers at a campaign office have 3000 fliers to send out. They send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon. How many fliers are left for the next day?<|im_end|>
<|im_start|>assistant
<Z_40><Z_277><Z_140><Z_62><Z_316><Z_445><Z_509><Z_34><ANSWER>

Question: Workers at a campaign office have 3000 fliers to send out. They send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon. How many fliers are left for the next day?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $(x + y)^2 = 64$ and $xy = 12$, what is $(x - y)^2$?<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $(x + y)^2 = 64$ and $xy = 12$, what is $(x - y)^2$?<|im_end|>
<|im_start|>assistant
<Z_176><Z_352><Z_65><Z_310><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $(x + y)^2 = 64$ and $xy = 12$, what is $(x - y)^2$?<|im_end|>
<|im_start|>assistant
<Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $(x + y)^2 = 64$ and $xy = 12$, what is $(x - y)^2$?<|im_end|>
<|im_start|>assistant
<Z_210><Z_27><Z_322><Z_507><ANSWER>

Question: If $(x + y)^2 = 64$ and $xy = 12$, what is $(x - y)^2$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When $\sqrt[3]{8000}$ is simplified, the result is $c\sqrt[3]{d}$, where $c$ and $d$ are positive integers and $d$ is as small as possible. What is $c+d$?<|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
When $\sqrt[3]{8000}$ is simplified, the result is $c\sqrt[3]{d}$, where $c$ and $d$ are positive integers and $d$ is as small as possible. What is $c+d$?<|im_end|>
<|im_start|>assistant
<Z_195><Z_98><Z_156><Z_503><Z_404><Z_478><Z_256><Z_456><Z_155><Z_76><Z_294><Z_453><Z_77><Z_213><Z_409><Z_284><Z_305><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When $\sqrt[3]{8000}$ is simplified, the result is $c\sqrt[3]{d}$, where $c$ and $d$ are positive integers and $d$ is as small as possible. What is $c+d$?<|im_end|>
<|im_start|>assistant
<Z_430><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When $\sqrt[3]{8000}$ is simplified, the result is $c\sqrt[3]{d}$, where $c$ and $d$ are positive integers and $d$ is as small as possible. What is $c+d$?<|im_end|>
<|im_start|>assistant
<Z_133><Z_201><Z_261><Z_362><Z_495><Z_352><Z_26><Z_323><Z_496><Z_174><Z_12><Z_408><Z_390><Z_506><Z_284><Z_415><Z_119><ANSWER>

Question: When $\sqrt[3]{8000}$ is simplified, the result is $c\sqrt[3]{d}$, where $c$ and $d$ are positive integers and $d$ is as small as possible. What is $c+d$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes 15 mink skins to make a coat. Andy buys 30 minks and each mink has 6 babies, but half the total minks are set free by activists. How many coats can Andy make?<|im_end|>
<|im_start|>assistant
<Z_5><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes 15 mink skins to make a coat. Andy buys 30 minks and each mink has 6 babies, but half the total minks are set free by activists. How many coats can Andy make?<|im_end|>
<|im_start|>assistant
<Z_66><Z_96><Z_510><Z_233><Z_383><Z_386><Z_177><Z_278><Z_465><Z_251><Z_310><Z_232><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes 15 mink skins to make a coat. Andy buys 30 minks and each mink has 6 babies, but half the total minks are set free by activists. How many coats can Andy make?<|im_end|>
<|im_start|>assistant
<Z_490><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes 15 mink skins to make a coat. Andy buys 30 minks and each mink has 6 babies, but half the total minks are set free by activists. How many coats can Andy make?<|im_end|>
<|im_start|>assistant
<Z_482><Z_132><Z_223><Z_110><Z_22><Z_273><Z_162><Z_134><Z_45><Z_81><Z_377><Z_301><ANSWER>

Question: It takes 15 mink skins to make a coat. Andy buys 30 minks and each mink has 6 babies, but half the total minks are set free by activists. How many coats can Andy make?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average age of some men increases by 4 years when two women are included in place of two men of ages 36 and 32 years. The average age of the women is 52. How many men were there initially?<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average age of some men increases by 4 years when two women are included in place of two men of ages 36 and 32 years. The average age of the women is 52. How many men were there initially?<|im_end|>
<|im_start|>assistant
<Z_176><Z_96><Z_366><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average age of some men increases by 4 years when two women are included in place of two men of ages 36 and 32 years. The average age of the women is 52. How many men were there initially?<|im_end|>
<|im_start|>assistant
<Z_456><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average age of some men increases by 4 years when two women are included in place of two men of ages 36 and 32 years. The average age of the women is 52. How many men were there initially?<|im_end|>
<|im_start|>assistant
<Z_72><Z_135><Z_62><ANSWER>

Question: The average age of some men increases by 4 years when two women are included in place of two men of ages 36 and 32 years. The average age of the women is 52. How many men were there initially?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If (18 ^ a) * (some number ^ (3a - 1)) = (2 ^ 6) (3 ^ b) and a and b are positive integers, and the value of a is 6, what is the base of the second exponent?<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If (18 ^ a) * (some number ^ (3a - 1)) = (2 ^ 6) (3 ^ b) and a and b are positive integers, and the value of a is 6, what is the base of the second exponent?<|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
If (18 ^ a) * (some number ^ (3a - 1)) = (2 ^ 6) (3 ^ b) and a and b are positive integers, and the value of a is 6, what is the base of the second exponent?<|im_end|>
<|im_start|>assistant
<Z_305><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If (18 ^ a) * (some number ^ (3a - 1)) = (2 ^ 6) (3 ^ b) and a and b are positive integers, and the value of a is 6, what is the base of the second exponent?<|im_end|>
<|im_start|>assistant
<Z_87><ANSWER>

Question: If (18 ^ a) * (some number ^ (3a - 1)) = (2 ^ 6) (3 ^ b) and a and b are positive integers, and the value of a is 6, what is the base of the second exponent?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Forty slips are placed into a hat, each bearing a number 1 through 8, with each number entered on five slips. Four slips are drawn from the hat at random and without replacement. Let $p'$ be the probability that all four slips bear the same number. Let $q'$ be the probability that two of the slips bear a number $a$ and the other two bear a number $b\ne a$. What is the value of $q'/p'$?<|im_end|>
<|im_start|>assistant
<Z_195><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Forty slips are placed into a hat, each bearing a number 1 through 8, with each number entered on five slips. Four slips are drawn from the hat at random and without replacement. Let $p'$ be the probability that all four slips bear the same number. Let $q'$ be the probability that two of the slips bear a number $a$ and the other two bear a number $b\ne a$. What is the value of $q'/p'$?<|im_end|>
<|im_start|>assistant
<Z_195><Z_338><Z_425><Z_113><Z_382><Z_257><Z_319><Z_95><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Forty slips are placed into a hat, each bearing a number 1 through 8, with each number entered on five slips. Four slips are drawn from the hat at random and without replacement. Let $p'$ be the probability that all four slips bear the same number. Let $q'$ be the probability that two of the slips bear a number $a$ and the other two bear a number $b\ne a$. What is the value of $q'/p'$?<|im_end|>
<|im_start|>assistant
<Z_399><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Forty slips are placed into a hat, each bearing a number 1 through 8, with each number entered on five slips. Four slips are drawn from the hat at random and without replacement. Let $p'$ be the probability that all four slips bear the same number. Let $q'$ be the probability that two of the slips bear a number $a$ and the other two bear a number $b\ne a$. What is the value of $q'/p'$?<|im_end|>
<|im_start|>assistant
<Z_256><Z_57><Z_310><Z_339><Z_123><Z_245><Z_329><Z_87><ANSWER>

Question: Forty slips are placed into a hat, each bearing a number 1 through 8, with each number entered on five slips. Four slips are drawn from the hat at random and without replacement. Let $p'$ be the probability that all four slips bear the same number. Let $q'$ be the probability that two of the slips bear a number $a$ and the other two bear a number $b\ne a$. What is the value of $q'/p'$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In convex quadrilateral $PQRS$, side $\overline{RS}$ is perpendicular to diagonal $\overline{PQ}$, side $\overline{PQ}$ is perpendicular to diagonal $\overline{RS}$, $RS = 52$, and $PQ = 39$. The line through $Q$ perpendicular to side $\overline{PS}$ intersects diagonal $\overline{PQ}$ at $T$ with $PT = 25$. Find $QT$.<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In convex quadrilateral $PQRS$, side $\overline{RS}$ is perpendicular to diagonal $\overline{PQ}$, side $\overline{PQ}$ is perpendicular to diagonal $\overline{RS}$, $RS = 52$, and $PQ = 39$. The line through $Q$ perpendicular to side $\overline{PS}$ intersects diagonal $\overline{PQ}$ at $T$ with $PT = 25$. Find $QT$.<|im_end|>
<|im_start|>assistant
<Z_66><Z_51><Z_183><Z_477><Z_339><Z_258><Z_385><Z_491><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In convex quadrilateral $PQRS$, side $\overline{RS}$ is perpendicular to diagonal $\overline{PQ}$, side $\overline{PQ}$ is perpendicular to diagonal $\overline{RS}$, $RS = 52$, and $PQ = 39$. The line through $Q$ perpendicular to side $\overline{PS}$ intersects diagonal $\overline{PQ}$ at $T$ with $PT = 25$. Find $QT$.<|im_end|>
<|im_start|>assistant
<Z_385><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In convex quadrilateral $PQRS$, side $\overline{RS}$ is perpendicular to diagonal $\overline{PQ}$, side $\overline{PQ}$ is perpendicular to diagonal $\overline{RS}$, $RS = 52$, and $PQ = 39$. The line through $Q$ perpendicular to side $\overline{PS}$ intersects diagonal $\overline{PQ}$ at $T$ with $PT = 25$. Find $QT$.<|im_end|>
<|im_start|>assistant
<Z_162><Z_387><Z_447><Z_391><Z_48><Z_372><Z_35><Z_481><ANSWER>

Question: In convex quadrilateral $PQRS$, side $\overline{RS}$ is perpendicular to diagonal $\overline{PQ}$, side $\overline{PQ}$ is perpendicular to diagonal $\overline{RS}$, $RS = 52$, and $PQ = 39$. The line through $Q$ perpendicular to side $\overline{PS}$ intersects diagonal $\overline{PQ}$ at $T$ with $PT = 25$. Find $QT$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
walking at 3 / 4 of his usual place , a man reaches his office 20 minute late . find his usual time ?<|im_end|>
<|im_start|>assistant
<Z_5><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
walking at 3 / 4 of his usual place , a man reaches his office 20 minute late . find his usual time ?<|im_end|>
<|im_start|>assistant
<Z_358><Z_52><Z_42><Z_435><Z_497><Z_132><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
walking at 3 / 4 of his usual place , a man reaches his office 20 minute late . find his usual time ?<|im_end|>
<|im_start|>assistant
<Z_258><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
walking at 3 / 4 of his usual place , a man reaches his office 20 minute late . find his usual time ?<|im_end|>
<|im_start|>assistant
<Z_277><Z_451><Z_161><Z_30><Z_50><Z_483><ANSWER>

Question: walking at 3 / 4 of his usual place , a man reaches his office 20 minute late . find his usual time ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
1. Let  $f(n) = n^2+6n+11$  be a function defined on positive integers. Find the sum of the first three prime values  $f(n)$  takes on.

*Proposed by winnertakeover*<|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
1. Let  $f(n) = n^2+6n+11$  be a function defined on positive integers. Find the sum of the first three prime values  $f(n)$  takes on.

*Proposed by winnertakeover*<|im_end|>
<|im_start|>assistant
<Z_358><Z_107><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
1. Let  $f(n) = n^2+6n+11$  be a function defined on positive integers. Find the sum of the first three prime values  $f(n)$  takes on.

*Proposed by winnertakeover*<|im_end|>
<|im_start|>assistant
<Z_199><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
1. Let  $f(n) = n^2+6n+11$  be a function defined on positive integers. Find the sum of the first three prime values  $f(n)$  takes on.

*Proposed by winnertakeover*<|im_end|>
<|im_start|>assistant
<Z_172><Z_462><ANSWER>

Question:
1. Let  $f(n) = n^2+6n+11$  be a function defined on positive integers. Find the sum of the first three prime values  $f(n)$  takes on.

*Proposed by winnertakeover*


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jack has six plates with a flower pattern, nine plates with a checked pattern, and three plates with a striped pattern. He buys new squared-number-of-checked-plates polka dotted plates, then smashes two flowered plates and one striped plate. How many plates does he have left?<|im_end|>
<|im_start|>assistant
<Z_5><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jack has six plates with a flower pattern, nine plates with a checked pattern, and three plates with a striped pattern. He buys new squared-number-of-checked-plates polka dotted plates, then smashes two flowered plates and one striped plate. How many plates does he have left?<|im_end|>
<|im_start|>assistant
<Z_5><Z_214><Z_420><Z_338><Z_445><Z_79><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jack has six plates with a flower pattern, nine plates with a checked pattern, and three plates with a striped pattern. He buys new squared-number-of-checked-plates polka dotted plates, then smashes two flowered plates and one striped plate. How many plates does he have left?<|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
Jack has six plates with a flower pattern, nine plates with a checked pattern, and three plates with a striped pattern. He buys new squared-number-of-checked-plates polka dotted plates, then smashes two flowered plates and one striped plate. How many plates does he have left?<|im_end|>
<|im_start|>assistant
<Z_287><Z_143><Z_500><Z_152><Z_86><Z_49><ANSWER>

Question: Jack has six plates with a flower pattern, nine plates with a checked pattern, and three plates with a striped pattern. He buys new squared-number-of-checked-plates polka dotted plates, then smashes two flowered plates and one striped plate. How many plates does he have left?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the square root of $x-1$ is $\pm 2$, the cube root of $4x+y$ is $3$, and the arithmetic square root of $y-x$ is $m$.
$(1)$ Find the value of $m$;
$(2)$ If $5+m=a+b$, where $a$ is an integer and $0 \lt b \lt 1$, find $a-({\sqrt{2}-b})^2$.<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the square root of $x-1$ is $\pm 2$, the cube root of $4x+y$ is $3$, and the arithmetic square root of $y-x$ is $m$.
$(1)$ Find the value of $m$;
$(2)$ If $5+m=a+b$, where $a$ is an integer and $0 \lt b \lt 1$, find $a-({\sqrt{2}-b})^2$.<|im_end|>
<|im_start|>assistant
<Z_358><Z_301><Z_372><Z_156><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the square root of $x-1$ is $\pm 2$, the cube root of $4x+y$ is $3$, and the arithmetic square root of $y-x$ is $m$.
$(1)$ Find the value of $m$;
$(2)$ If $5+m=a+b$, where $a$ is an integer and $0 \lt b \lt 1$, find $a-({\sqrt{2}-b})^2$.<|im_end|>
<|im_start|>assistant
<Z_173><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that the square root of $x-1$ is $\pm 2$, the cube root of $4x+y$ is $3$, and the arithmetic square root of $y-x$ is $m$.
$(1)$ Find the value of $m$;
$(2)$ If $5+m=a+b$, where $a$ is an integer and $0 \lt b \lt 1$, find $a-({\sqrt{2}-b})^2$.<|im_end|>
<|im_start|>assistant
<Z_321><Z_187><Z_285><Z_208><ANSWER>

Question:
Given that the square root of $x-1$ is $\pm 2$, the cube root of $4x+y$ is $3$, and the arithmetic square root of $y-x$ is $m$.
$(1)$ Find the value of $m$;
$(2)$ If $5+m=a+b$, where $a$ is an integer and $0 \lt b \lt 1$, find $a-({\sqrt{2}-b})^2$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rectangle $ABCD$ is the base of pyramid $PABCD$. If $AB = 10$, $BC = 6$, $\overline{PA}\perp \overline{AD}$, $\overline{PA}\perp \overline{AB}$, and $PB = 26$, what is the volume of $PABCD$?<|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
Rectangle $ABCD$ is the base of pyramid $PABCD$. If $AB = 10$, $BC = 6$, $\overline{PA}\perp \overline{AD}$, $\overline{PA}\perp \overline{AB}$, and $PB = 26$, what is the volume of $PABCD$?<|im_end|>
<|im_start|>assistant
<Z_66><Z_255><Z_442><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rectangle $ABCD$ is the base of pyramid $PABCD$. If $AB = 10$, $BC = 6$, $\overline{PA}\perp \overline{AD}$, $\overline{PA}\perp \overline{AB}$, and $PB = 26$, what is the volume of $PABCD$?<|im_end|>
<|im_start|>assistant
<Z_33><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rectangle $ABCD$ is the base of pyramid $PABCD$. If $AB = 10$, $BC = 6$, $\overline{PA}\perp \overline{AD}$, $\overline{PA}\perp \overline{AB}$, and $PB = 26$, what is the volume of $PABCD$?<|im_end|>
<|im_start|>assistant
<Z_503><Z_358><Z_140><ANSWER>

Question: Rectangle $ABCD$ is the base of pyramid $PABCD$. If $AB = 10$, $BC = 6$, $\overline{PA}\perp \overline{AD}$, $\overline{PA}\perp \overline{AB}$, and $PB = 26$, what is the volume of $PABCD$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two boxes contain black and white marbles, with a total of $24$ marbles combined. One marble is taken from each box randomly. The probability that both marbles are black is $28/45$. Find the probability that both marbles are white, expressed as $m/n$ where $m$ and $n$ are coprime integers. What is $m + n$?<|im_end|>
<|im_start|>assistant
<Z_176><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two boxes contain black and white marbles, with a total of $24$ marbles combined. One marble is taken from each box randomly. The probability that both marbles are black is $28/45$. Find the probability that both marbles are white, expressed as $m/n$ where $m$ and $n$ are coprime integers. What is $m + n$?<|im_end|>
<|im_start|>assistant
<Z_358><Z_389><Z_461><Z_85><Z_218><Z_447><Z_98><Z_278><Z_199><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two boxes contain black and white marbles, with a total of $24$ marbles combined. One marble is taken from each box randomly. The probability that both marbles are black is $28/45$. Find the probability that both marbles are white, expressed as $m/n$ where $m$ and $n$ are coprime integers. What is $m + n$?<|im_end|>
<|im_start|>assistant
<Z_363><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Two boxes contain black and white marbles, with a total of $24$ marbles combined. One marble is taken from each box randomly. The probability that both marbles are black is $28/45$. Find the probability that both marbles are white, expressed as $m/n$ where $m$ and $n$ are coprime integers. What is $m + n$?<|im_end|>
<|im_start|>assistant
<Z_358><Z_52><Z_333><Z_30><Z_286><Z_84><Z_123><Z_10><Z_142><ANSWER>

Question: Two boxes contain black and white marbles, with a total of $24$ marbles combined. One marble is taken from each box randomly. The probability that both marbles are black is $28/45$. Find the probability that both marbles are white, expressed as $m/n$ where $m$ and $n$ are coprime integers. What is $m + n$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kennedy grew tomatoes from three plants she had in her backyard.  The first tomato plant produced two dozen tomatoes.  The second plant produced 5 more than half as many tomatoes as the first plant.  And the third plant produced two more tomatoes than the second plant.  How many tomatoes did the three plants produce?<|im_end|>
<|im_start|>assistant
<Z_5><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kennedy grew tomatoes from three plants she had in her backyard.  The first tomato plant produced two dozen tomatoes.  The second plant produced 5 more than half as many tomatoes as the first plant.  And the third plant produced two more tomatoes than the second plant.  How many tomatoes did the three plants produce?<|im_end|>
<|im_start|>assistant
<Z_195><Z_98><Z_403><Z_233><Z_358><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Kennedy grew tomatoes from three plants she had in her backyard.  The first tomato plant produced two dozen tomatoes.  The second plant produced 5 more than half as many tomatoes as the first plant.  And the third plant produced two more tomatoes than the second plant.  How many tomatoes did the three plants produce?<|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
Kennedy grew tomatoes from three plants she had in her backyard.  The first tomato plant produced two dozen tomatoes.  The second plant produced 5 more than half as many tomatoes as the first plant.  And the third plant produced two more tomatoes than the second plant.  How many tomatoes did the three plants produce?<|im_end|>
<|im_start|>assistant
<Z_255><Z_466><Z_189><Z_268><Z_103><ANSWER>

Question: Kennedy grew tomatoes from three plants she had in her backyard.  The first tomato plant produced two dozen tomatoes.  The second plant produced 5 more than half as many tomatoes as the first plant.  And the third plant produced two more tomatoes than the second plant.  How many tomatoes did the three plants produce?