<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the least positive integer greater than 1 that leaves a remainder of 2 when divided by each of 2, 3, 4, 5, and 6?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the least positive integer greater than 1 that leaves a remainder of 2 when divided by each of 2, 3, 4, 5, and 6?<|im_end|>
<|im_start|>assistant
<Z_57><Z_51><Z_58><Z_50><Z_33><Z_11><Z_37><Z_71><Z_99><Z_121><Z_54><Z_67><Z_96><Z_65><Z_93><Z_71><Z_93><Z_124><Z_90><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the least positive integer greater than 1 that leaves a remainder of 2 when divided by each of 2, 3, 4, 5, and 6?<|im_end|>
<|im_start|>assistant
<Z_40><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the least positive integer greater than 1 that leaves a remainder of 2 when divided by each of 2, 3, 4, 5, and 6?<|im_end|>
<|im_start|>assistant
<Z_109><Z_62><Z_20><Z_10><Z_9><Z_84><Z_4><Z_52><Z_88><Z_18><Z_124><Z_78><Z_34><Z_101><Z_78><Z_66><Z_5><Z_92><Z_87><ANSWER>

Question: What is the least positive integer greater than 1 that leaves a remainder of 2 when divided by each of 2, 3, 4, 5, and 6?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
From a checkered square $7 \times 7$, an equal number of $2 \x 2$ squares and $1 \times 4$ rectangles were cut along the cell boundaries. What is the maximum number of such figures that could have been cut out?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
From a checkered square $7 \times 7$, an equal number of $2 \x 2$ squares and $1 \times 4$ rectangles were cut along the cell boundaries. What is the maximum number of such figures that could have been cut out?<|im_end|>
<|im_start|>assistant
<Z_94><Z_1><Z_62><Z_87><Z_72><Z_59><Z_61><Z_117><Z_83><Z_123><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
From a checkered square $7 \times 7$, an equal number of $2 \x 2$ squares and $1 \times 4$ rectangles were cut along the cell boundaries. What is the maximum number of such figures that could have been cut out?<|im_end|>
<|im_start|>assistant
<Z_122><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
From a checkered square $7 \times 7$, an equal number of $2 \x 2$ squares and $1 \times 4$ rectangles were cut along the cell boundaries. What is the maximum number of such figures that could have been cut out?<|im_end|>
<|im_start|>assistant
<Z_77><Z_62><Z_58><Z_114><Z_89><Z_115><Z_38><Z_81><Z_79><Z_125><ANSWER>

Question: From a checkered square $7 \times 7$, an equal number of $2 \x 2$ squares and $1 \times 4$ rectangles were cut along the cell boundaries. What is the maximum number of such figures that could have been cut out?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Assume that $x_1, x_2, \ldots, x_7$ are real numbers such that
\[
\begin{aligned}
x_1 + 3x_2 + 5x_3 + 7x_4 + 9x_5 + 11x_6 + 13x_7 &= 3, \\
3x_1 + 5x_2 + 7x_3 + 9x_4 + 11x_5 + 13x_6 + 15x_7 &= 15, \\
5x_1 + 7x_2 + 9x_3 + 11x_4 + 13x_5 + 15x_6 + 17x_7 &= 85.
\end{aligned}
\]
Find the value of $7x_1 + 9x_2 + 11x_3 + 13x_4 + 15x_5 + 17x_6 + 19x_7$.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Assume that $x_1, x_2, \ldots, x_7$ are real numbers such that
\[
\begin{aligned}
x_1 + 3x_2 + 5x_3 + 7x_4 + 9x_5 + 11x_6 + 13x_7 &= 3, \\
3x_1 + 5x_2 + 7x_3 + 9x_4 + 11x_5 + 13x_6 + 15x_7 &= 15, \\
5x_1 + 7x_2 + 9x_3 + 11x_4 + 13x_5 + 15x_6 + 17x_7 &= 85.
\end{aligned}
\]
Find the value of $7x_1 + 9x_2 + 11x_3 + 13x_4 + 15x_5 + 17x_6 + 19x_7$.<|im_end|>
<|im_start|>assistant
<Z_104><Z_68><Z_89><Z_50><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Assume that $x_1, x_2, \ldots, x_7$ are real numbers such that
\[
\begin{aligned}
x_1 + 3x_2 + 5x_3 + 7x_4 + 9x_5 + 11x_6 + 13x_7 &= 3, \\
3x_1 + 5x_2 + 7x_3 + 9x_4 + 11x_5 + 13x_6 + 15x_7 &= 15, \\
5x_1 + 7x_2 + 9x_3 + 11x_4 + 13x_5 + 15x_6 + 17x_7 &= 85.
\end{aligned}
\]
Find the value of $7x_1 + 9x_2 + 11x_3 + 13x_4 + 15x_5 + 17x_6 + 19x_7$.<|im_end|>
<|im_start|>assistant
<Z_29><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Assume that $x_1, x_2, \ldots, x_7$ are real numbers such that
\[
\begin{aligned}
x_1 + 3x_2 + 5x_3 + 7x_4 + 9x_5 + 11x_6 + 13x_7 &= 3, \\
3x_1 + 5x_2 + 7x_3 + 9x_4 + 11x_5 + 13x_6 + 15x_7 &= 15, \\
5x_1 + 7x_2 + 9x_3 + 11x_4 + 13x_5 + 15x_6 + 17x_7 &= 85.
\end{aligned}
\]
Find the value of $7x_1 + 9x_2 + 11x_3 + 13x_4 + 15x_5 + 17x_6 + 19x_7$.<|im_end|>
<|im_start|>assistant
<Z_101><Z_40><Z_78><Z_58><ANSWER>

Question:
Assume that $x_1, x_2, \ldots, x_7$ are real numbers such that
\[
\begin{aligned}
x_1 + 3x_2 + 5x_3 + 7x_4 + 9x_5 + 11x_6 + 13x_7 &= 3, \\
3x_1 + 5x_2 + 7x_3 + 9x_4 + 11x_5 + 13x_6 + 15x_7 &= 15, \\
5x_1 + 7x_2 + 9x_3 + 11x_4 + 13x_5 + 15x_6 + 17x_7 &= 85.
\end{aligned}
\]
Find the value of $7x_1 + 9x_2 + 11x_3 + 13x_4 + 15x_5 + 17x_6 + 19x_7$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the smallest positive integer that has exactly ten distinct positive factors?<|im_end|>
<|im_start|>assistant
<Z_94><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 positive integer that has exactly ten distinct positive factors?<|im_end|>
<|im_start|>assistant
<Z_57><Z_82><Z_73><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 positive integer that has exactly ten distinct positive factors?<|im_end|>
<|im_start|>assistant
<Z_61><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 positive integer that has exactly ten distinct positive factors?<|im_end|>
<|im_start|>assistant
<Z_122><Z_94><Z_46><ANSWER>

Question: What is the smallest positive integer that has exactly ten distinct positive factors?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the digits of the base-3 expression for $345_{10}$?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the digits of the base-3 expression for $345_{10}$?<|im_end|>
<|im_start|>assistant
<Z_94><Z_51><Z_34><Z_93><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the digits of the base-3 expression for $345_{10}$?<|im_end|>
<|im_start|>assistant
<Z_114><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the digits of the base-3 expression for $345_{10}$?<|im_end|>
<|im_start|>assistant
<Z_28><Z_45><Z_107><Z_41><ANSWER>

Question: What is the sum of the digits of the base-3 expression for $345_{10}$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The ratio of 3 numbers is 5 : 3 : 4 and their sum is 108. What is the second number of the 3 numbers?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The ratio of 3 numbers is 5 : 3 : 4 and their sum is 108. What is the second number of the 3 numbers?<|im_end|>
<|im_start|>assistant
<Z_57><Z_70><Z_66><Z_92><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The ratio of 3 numbers is 5 : 3 : 4 and their sum is 108. What is the second number of the 3 numbers?<|im_end|>
<|im_start|>assistant
<Z_8><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The ratio of 3 numbers is 5 : 3 : 4 and their sum is 108. What is the second number of the 3 numbers?<|im_end|>
<|im_start|>assistant
<Z_54><Z_33><Z_11><Z_76><ANSWER>

Question: The ratio of 3 numbers is 5 : 3 : 4 and their sum is 108. What is the second number of the 3 numbers?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Bruce purchased 8 kg of grapes at the rate of 70 per kg and 8 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Bruce purchased 8 kg of grapes at the rate of 70 per kg and 8 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?<|im_end|>
<|im_start|>assistant
<Z_94><Z_38><Z_79><Z_31><Z_81><Z_124><Z_123><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Bruce purchased 8 kg of grapes at the rate of 70 per kg and 8 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?<|im_end|>
<|im_start|>assistant
<Z_17><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Bruce purchased 8 kg of grapes at the rate of 70 per kg and 8 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?<|im_end|>
<|im_start|>assistant
<Z_4><Z_117><Z_127><Z_111><Z_2><Z_106><Z_121><ANSWER>

Question: Bruce purchased 8 kg of grapes at the rate of 70 per kg and 8 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Darius drove 679 miles to visit his grandmother, while Julia drove 998 miles to visit hers. On their way back, both had to detour an extra 120 miles due to a road closure. Meanwhile, their friend Thomas traveled 1,205 miles to visit his grandparents, and stopped halfway to rest for a night. What is the total number of miles Darius, Julia, and Thomas drove during their trips, including the detours and round trips? Also, calculate the total distance in kilometers, considering that 1 mile is equivalent to 1.60934 kilometers.<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Darius drove 679 miles to visit his grandmother, while Julia drove 998 miles to visit hers. On their way back, both had to detour an extra 120 miles due to a road closure. Meanwhile, their friend Thomas traveled 1,205 miles to visit his grandparents, and stopped halfway to rest for a night. What is the total number of miles Darius, Julia, and Thomas drove during their trips, including the detours and round trips? Also, calculate the total distance in kilometers, considering that 1 mile is equivalent to 1.60934 kilometers.<|im_end|>
<|im_start|>assistant
<Z_113><Z_86><Z_125><Z_66><Z_59><Z_36><Z_119><Z_114><Z_90><Z_40><Z_72><Z_33><Z_87><Z_119><Z_37><Z_78><Z_47><Z_101><Z_117><Z_47><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Darius drove 679 miles to visit his grandmother, while Julia drove 998 miles to visit hers. On their way back, both had to detour an extra 120 miles due to a road closure. Meanwhile, their friend Thomas traveled 1,205 miles to visit his grandparents, and stopped halfway to rest for a night. What is the total number of miles Darius, Julia, and Thomas drove during their trips, including the detours and round trips? Also, calculate the total distance in kilometers, considering that 1 mile is equivalent to 1.60934 kilometers.<|im_end|>
<|im_start|>assistant
<Z_102><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Darius drove 679 miles to visit his grandmother, while Julia drove 998 miles to visit hers. On their way back, both had to detour an extra 120 miles due to a road closure. Meanwhile, their friend Thomas traveled 1,205 miles to visit his grandparents, and stopped halfway to rest for a night. What is the total number of miles Darius, Julia, and Thomas drove during their trips, including the detours and round trips? Also, calculate the total distance in kilometers, considering that 1 mile is equivalent to 1.60934 kilometers.<|im_end|>
<|im_start|>assistant
<Z_59><Z_64><Z_40><Z_7><Z_95><Z_35><Z_43><Z_67><Z_13><Z_40><Z_16><Z_57><Z_47><Z_13><Z_68><Z_62><Z_102><Z_109><Z_18><Z_34><ANSWER>

Question: Darius drove 679 miles to visit his grandmother, while Julia drove 998 miles to visit hers. On their way back, both had to detour an extra 120 miles due to a road closure. Meanwhile, their friend Thomas traveled 1,205 miles to visit his grandparents, and stopped halfway to rest for a night. What is the total number of miles Darius, Julia, and Thomas drove during their trips, including the detours and round trips? Also, calculate the total distance in kilometers, considering that 1 mile is equivalent to 1.60934 kilometers.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the median of a set of numbers $a, 2, 4, 0, 5$ is $4$, then $a$ can be (only need to write one number that meets the requirement).<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the median of a set of numbers $a, 2, 4, 0, 5$ is $4$, then $a$ can be (only need to write one number that meets the requirement).<|im_end|>
<|im_start|>assistant
<Z_57><Z_99><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the median of a set of numbers $a, 2, 4, 0, 5$ is $4$, then $a$ can be (only need to write one number that meets the requirement).<|im_end|>
<|im_start|>assistant
<Z_82><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the median of a set of numbers $a, 2, 4, 0, 5$ is $4$, then $a$ can be (only need to write one number that meets the requirement).<|im_end|>
<|im_start|>assistant
<Z_115><Z_78><ANSWER>

Question: If the median of a set of numbers $a, 2, 4, 0, 5$ is $4$, then $a$ can be (only need to write one number that meets the requirement).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For how many integers $n$ is it true that $\sqrt{3n} \le \sqrt{5n - 8} < \sqrt{3n + 7}$?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For how many integers $n$ is it true that $\sqrt{3n} \le \sqrt{5n - 8} < \sqrt{3n + 7}$?<|im_end|>
<|im_start|>assistant
<Z_94><Z_43><Z_13><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For how many integers $n$ is it true that $\sqrt{3n} \le \sqrt{5n - 8} < \sqrt{3n + 7}$?<|im_end|>
<|im_start|>assistant
<Z_29><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For how many integers $n$ is it true that $\sqrt{3n} \le \sqrt{5n - 8} < \sqrt{3n + 7}$?<|im_end|>
<|im_start|>assistant
<Z_111><Z_9><Z_50><ANSWER>

Question: For how many integers $n$ is it true that $\sqrt{3n} \le \sqrt{5n - 8} < \sqrt{3n + 7}$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A pencil has some black, white, and blue parts. If 1/8 of the pencil is black, 1/2 of the remaining is white, and the remaining part is blue with a length of 7/2, find the total length of the pencil.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A pencil has some black, white, and blue parts. If 1/8 of the pencil is black, 1/2 of the remaining is white, and the remaining part is blue with a length of 7/2, find the total length of the pencil.<|im_end|>
<|im_start|>assistant
<Z_94><Z_110><Z_82><Z_72><Z_41><Z_79><Z_88><Z_123><Z_119><Z_56><Z_126><Z_61><Z_101><Z_39><Z_37><Z_123><Z_65><Z_24><Z_70><Z_76><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A pencil has some black, white, and blue parts. If 1/8 of the pencil is black, 1/2 of the remaining is white, and the remaining part is blue with a length of 7/2, find the total length of the pencil.<|im_end|>
<|im_start|>assistant
<Z_43><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A pencil has some black, white, and blue parts. If 1/8 of the pencil is black, 1/2 of the remaining is white, and the remaining part is blue with a length of 7/2, find the total length of the pencil.<|im_end|>
<|im_start|>assistant
<Z_22><Z_10><Z_124><Z_33><Z_30><Z_111><Z_0><Z_127><Z_97><Z_91><Z_127><Z_75><Z_30><Z_103><Z_22><Z_121><Z_85><Z_49><Z_93><Z_68><ANSWER>

Question: A pencil has some black, white, and blue parts. If 1/8 of the pencil is black, 1/2 of the remaining is white, and the remaining part is blue with a length of 7/2, find the total length of the pencil.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three points  $X, Y,Z$  are on a striaght line such that  $XY = 10$  and  $XZ = 3$ . What is the product of all possible values of  $YZ$ ?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three points  $X, Y,Z$  are on a striaght line such that  $XY = 10$  and  $XZ = 3$ . What is the product of all possible values of  $YZ$ ?<|im_end|>
<|im_start|>assistant
<Z_57><Z_100><Z_87><Z_30><Z_119><Z_72><Z_45><Z_83><Z_41><Z_90><Z_16><Z_96><Z_123><Z_39><Z_76><Z_75><Z_34><Z_82><Z_48><Z_60><Z_49><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three points  $X, Y,Z$  are on a striaght line such that  $XY = 10$  and  $XZ = 3$ . What is the product of all possible values of  $YZ$ ?<|im_end|>
<|im_start|>assistant
<Z_59><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Three points  $X, Y,Z$  are on a striaght line such that  $XY = 10$  and  $XZ = 3$ . What is the product of all possible values of  $YZ$ ?<|im_end|>
<|im_start|>assistant
<Z_92><Z_45><Z_65><Z_92><Z_86><Z_32><Z_87><Z_3><Z_91><Z_104><Z_78><Z_106><Z_103><Z_61><Z_112><Z_5><Z_79><Z_66><Z_55><Z_127><Z_21><ANSWER>

Question: Three points  $X, Y,Z$  are on a striaght line such that  $XY = 10$  and  $XZ = 3$ . What is the product of all possible values of  $YZ$ ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many different routes are there from point $A$ to point $B$ in a 3x3 grid (where you can only move to the right or down along the drawn segments)?

[asy]
unitsize(0.09inch);
draw((0,0)--(15,0)--(15,15)--(0,15)--cycle);
draw((5,0)--(5,15));
draw((10,0)--(10,15));
draw((0,5)--(15,5));
draw((0,10)--(15,10));
dot((0,15));
dot((15,0));
label("$A$",(0,15),NW);
label("$B$",(15,0),SE);
[/asy]<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many different routes are there from point $A$ to point $B$ in a 3x3 grid (where you can only move to the right or down along the drawn segments)?

[asy]
unitsize(0.09inch);
draw((0,0)--(15,0)--(15,15)--(0,15)--cycle);
draw((5,0)--(5,15));
draw((10,0)--(10,15));
draw((0,5)--(15,5));
draw((0,10)--(15,10));
dot((0,15));
dot((15,0));
label("$A$",(0,15),NW);
label("$B$",(15,0),SE);
[/asy]<|im_end|>
<|im_start|>assistant
<Z_57><Z_78><Z_78><Z_121><Z_78><Z_126><Z_58><Z_91><Z_56><Z_38><Z_28><Z_107><Z_99><Z_63><Z_98><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many different routes are there from point $A$ to point $B$ in a 3x3 grid (where you can only move to the right or down along the drawn segments)?

[asy]
unitsize(0.09inch);
draw((0,0)--(15,0)--(15,15)--(0,15)--cycle);
draw((5,0)--(5,15));
draw((10,0)--(10,15));
draw((0,5)--(15,5));
draw((0,10)--(15,10));
dot((0,15));
dot((15,0));
label("$A$",(0,15),NW);
label("$B$",(15,0),SE);
[/asy]<|im_end|>
<|im_start|>assistant
<Z_25><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many different routes are there from point $A$ to point $B$ in a 3x3 grid (where you can only move to the right or down along the drawn segments)?

[asy]
unitsize(0.09inch);
draw((0,0)--(15,0)--(15,15)--(0,15)--cycle);
draw((5,0)--(5,15));
draw((10,0)--(10,15));
draw((0,5)--(15,5));
draw((0,10)--(15,10));
dot((0,15));
dot((15,0));
label("$A$",(0,15),NW);
label("$B$",(15,0),SE);
[/asy]<|im_end|>
<|im_start|>assistant
<Z_70><Z_95><Z_51><Z_81><Z_94><Z_118><Z_28><Z_68><Z_123><Z_52><Z_36><Z_55><Z_111><Z_12><Z_12><ANSWER>

Question:
How many different routes are there from point $A$ to point $B$ in a 3x3 grid (where you can only move to the right or down along the drawn segments)?

[asy]
unitsize(0.09inch);
draw((0,0)--(15,0)--(15,15)--(0,15)--cycle);
draw((5,0)--(5,15));
draw((10,0)--(10,15));
draw((0,5)--(15,5));
draw((0,10)--(15,10));
dot((0,15));
dot((15,0));
label("$A$",(0,15),NW);
label("$B$",(15,0),SE);
[/asy]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The basketball team is practicing their free-throws, making as many as they can in one minute. DeShawn made some free-throws, and Kayla made 50% more than DeShawn. Annieka made 4 fewer than Kayla. Annieka made 14 free-throws. How many free-throws did DeShawn make?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The basketball team is practicing their free-throws, making as many as they can in one minute. DeShawn made some free-throws, and Kayla made 50% more than DeShawn. Annieka made 4 fewer than Kayla. Annieka made 14 free-throws. How many free-throws did DeShawn make?<|im_end|>
<|im_start|>assistant
<Z_94><Z_119><Z_87><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The basketball team is practicing their free-throws, making as many as they can in one minute. DeShawn made some free-throws, and Kayla made 50% more than DeShawn. Annieka made 4 fewer than Kayla. Annieka made 14 free-throws. How many free-throws did DeShawn make?<|im_end|>
<|im_start|>assistant
<Z_81><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The basketball team is practicing their free-throws, making as many as they can in one minute. DeShawn made some free-throws, and Kayla made 50% more than DeShawn. Annieka made 4 fewer than Kayla. Annieka made 14 free-throws. How many free-throws did DeShawn make?<|im_end|>
<|im_start|>assistant
<Z_101><Z_99><Z_26><ANSWER>

Question: The basketball team is practicing their free-throws, making as many as they can in one minute. DeShawn made some free-throws, and Kayla made 50% more than DeShawn. Annieka made 4 fewer than Kayla. Annieka made 14 free-throws. How many free-throws did DeShawn make?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $A$ equal the number of four-digit odd numbers. Let $B$ equal the number of four-digit numbers that are multiples of 3. Find $A+B$.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $A$ equal the number of four-digit odd numbers. Let $B$ equal the number of four-digit numbers that are multiples of 3. Find $A+B$.<|im_end|>
<|im_start|>assistant
<Z_104><Z_70><Z_38><Z_88><Z_91><Z_47><Z_53><Z_83><Z_95><Z_95><Z_92><Z_98><Z_75><Z_93><Z_41><Z_117><Z_31><Z_120><Z_58><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $A$ equal the number of four-digit odd numbers. Let $B$ equal the number of four-digit numbers that are multiples of 3. Find $A+B$.<|im_end|>
<|im_start|>assistant
<Z_79><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $A$ equal the number of four-digit odd numbers. Let $B$ equal the number of four-digit numbers that are multiples of 3. Find $A+B$.<|im_end|>
<|im_start|>assistant
<Z_11><Z_97><Z_80><Z_41><Z_15><Z_39><Z_85><Z_52><Z_101><Z_37><Z_102><Z_83><Z_73><Z_70><Z_63><Z_42><Z_13><Z_112><Z_70><ANSWER>

Question: Let $A$ equal the number of four-digit odd numbers. Let $B$ equal the number of four-digit numbers that are multiples of 3. Find $A+B$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The world record for longest fingernails is 26 inches. Sandy, who just turned 12 this month, has a goal for tying the record. Her fingernails are 2 inches long. Her fingernails grow at a rate of one-tenth of an inch per month. How old will she be when she achieves the world record?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The world record for longest fingernails is 26 inches. Sandy, who just turned 12 this month, has a goal for tying the record. Her fingernails are 2 inches long. Her fingernails grow at a rate of one-tenth of an inch per month. How old will she be when she achieves the world record?<|im_end|>
<|im_start|>assistant
<Z_27><Z_62><Z_88><Z_93><Z_103><Z_103><Z_49><Z_63><Z_96><Z_45><Z_93><Z_54><Z_125><Z_66><Z_45><Z_56><Z_53><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The world record for longest fingernails is 26 inches. Sandy, who just turned 12 this month, has a goal for tying the record. Her fingernails are 2 inches long. Her fingernails grow at a rate of one-tenth of an inch per month. How old will she be when she achieves the world record?<|im_end|>
<|im_start|>assistant
<Z_70><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The world record for longest fingernails is 26 inches. Sandy, who just turned 12 this month, has a goal for tying the record. Her fingernails are 2 inches long. Her fingernails grow at a rate of one-tenth of an inch per month. How old will she be when she achieves the world record?<|im_end|>
<|im_start|>assistant
<Z_26><Z_91><Z_33><Z_31><Z_53><Z_114><Z_45><Z_117><Z_103><Z_39><Z_38><Z_26><Z_41><Z_20><Z_83><Z_35><Z_46><ANSWER>

Question: The world record for longest fingernails is 26 inches. Sandy, who just turned 12 this month, has a goal for tying the record. Her fingernails are 2 inches long. Her fingernails grow at a rate of one-tenth of an inch per month. How old will she be when she achieves the world record?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On Marika's $10^{\text{th}}$ birthday, in 2006, her father said, ''My age is now five times your age.'' In what year will Marika's father be able to say, ''My age is now twice your age,'' on Marika’s birthday?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On Marika's $10^{\text{th}}$ birthday, in 2006, her father said, ''My age is now five times your age.'' In what year will Marika's father be able to say, ''My age is now twice your age,'' on Marika’s birthday?<|im_end|>
<|im_start|>assistant
<Z_57><Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On Marika's $10^{\text{th}}$ birthday, in 2006, her father said, ''My age is now five times your age.'' In what year will Marika's father be able to say, ''My age is now twice your age,'' on Marika’s birthday?<|im_end|>
<|im_start|>assistant
<Z_119><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On Marika's $10^{\text{th}}$ birthday, in 2006, her father said, ''My age is now five times your age.'' In what year will Marika's father be able to say, ''My age is now twice your age,'' on Marika’s birthday?<|im_end|>
<|im_start|>assistant
<Z_68><Z_94><ANSWER>

Question: On Marika's $10^{\text{th}}$ birthday, in 2006, her father said, ''My age is now five times your age.'' In what year will Marika's father be able to say, ''My age is now twice your age,'' on Marika’s birthday?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain sum of money is divided among A, B, C, D, and E so that for each Rs. A receives, B gets 75 paisa, C has 60 paisa, D earns 45 paisa, and E gets 30 paisa. If E's share is Rs. 96, find the total sum of money to be divided.<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain sum of money is divided among A, B, C, D, and E so that for each Rs. A receives, B gets 75 paisa, C has 60 paisa, D earns 45 paisa, and E gets 30 paisa. If E's share is Rs. 96, find the total sum of money to be divided.<|im_end|>
<|im_start|>assistant
<Z_106><Z_1><Z_81><Z_36><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain sum of money is divided among A, B, C, D, and E so that for each Rs. A receives, B gets 75 paisa, C has 60 paisa, D earns 45 paisa, and E gets 30 paisa. If E's share is Rs. 96, find the total sum of money to be divided.<|im_end|>
<|im_start|>assistant
<Z_36><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain sum of money is divided among A, B, C, D, and E so that for each Rs. A receives, B gets 75 paisa, C has 60 paisa, D earns 45 paisa, and E gets 30 paisa. If E's share is Rs. 96, find the total sum of money to be divided.<|im_end|>
<|im_start|>assistant
<Z_12><Z_43><Z_55><Z_19><ANSWER>

Question: A certain sum of money is divided among A, B, C, D, and E so that for each Rs. A receives, B gets 75 paisa, C has 60 paisa, D earns 45 paisa, and E gets 30 paisa. If E's share is Rs. 96, find the total sum of money to be divided.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 315 cups of puddings to be distributed to some students. If each of them wants an equal number of pudding cups, at least 121 more pudding cups are needed. How many students are there?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 315 cups of puddings to be distributed to some students. If each of them wants an equal number of pudding cups, at least 121 more pudding cups are needed. How many students are there?<|im_end|>
<|im_start|>assistant
<Z_106><Z_77><Z_97><Z_31><Z_55><Z_11><Z_52><Z_81><Z_47><Z_103><Z_55><Z_52><Z_60><Z_80><Z_88><Z_70><Z_126><Z_101><Z_17><Z_124><Z_83><Z_10><Z_56><Z_31><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 315 cups of puddings to be distributed to some students. If each of them wants an equal number of pudding cups, at least 121 more pudding cups are needed. How many students are there?<|im_end|>
<|im_start|>assistant
<Z_30><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are 315 cups of puddings to be distributed to some students. If each of them wants an equal number of pudding cups, at least 121 more pudding cups are needed. How many students are there?<|im_end|>
<|im_start|>assistant
<Z_39><Z_59><Z_22><Z_20><Z_8><Z_33><Z_102><Z_116><Z_20><Z_16><Z_76><Z_4><Z_43><Z_52><Z_55><Z_4><Z_34><Z_84><Z_69><Z_77><Z_101><Z_87><Z_99><Z_121><ANSWER>

Question: There are 315 cups of puddings to be distributed to some students. If each of them wants an equal number of pudding cups, at least 121 more pudding cups are needed. How many students are there?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user

On the extension of edge \( ST \) beyond point \( T \) of a regular quadrilateral pyramid \( SPQRT \) with vertex \( S \), point \( B \) is taken such that the distance from it to the plane \( SPQ \) is \( \frac{9 \sqrt{7}}{2} \). Find the segment \( BT \) if \( QR = 12 \) and \( SR = 10 \).<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user

On the extension of edge \( ST \) beyond point \( T \) of a regular quadrilateral pyramid \( SPQRT \) with vertex \( S \), point \( B \) is taken such that the distance from it to the plane \( SPQ \) is \( \frac{9 \sqrt{7}}{2} \). Find the segment \( BT \) if \( QR = 12 \) and \( SR = 10 \).<|im_end|>
<|im_start|>assistant
<Z_57><Z_74><Z_13><Z_74><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user

On the extension of edge \( ST \) beyond point \( T \) of a regular quadrilateral pyramid \( SPQRT \) with vertex \( S \), point \( B \) is taken such that the distance from it to the plane \( SPQ \) is \( \frac{9 \sqrt{7}}{2} \). Find the segment \( BT \) if \( QR = 12 \) and \( SR = 10 \).<|im_end|>
<|im_start|>assistant
<Z_111><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user

On the extension of edge \( ST \) beyond point \( T \) of a regular quadrilateral pyramid \( SPQRT \) with vertex \( S \), point \( B \) is taken such that the distance from it to the plane \( SPQ \) is \( \frac{9 \sqrt{7}}{2} \). Find the segment \( BT \) if \( QR = 12 \) and \( SR = 10 \).<|im_end|>
<|im_start|>assistant
<Z_14><Z_116><Z_5><Z_22><ANSWER>

Question: On the extension of edge \( ST \) beyond point \( T \) of a regular quadrilateral pyramid \( SPQRT \) with vertex \( S \), point \( B \) is taken such that the distance from it to the plane \( SPQ \) is \( \frac{9 \sqrt{7}}{2} \). Find the segment \( BT \) if \( QR = 12 \) and \( SR = 10 \).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A, B, C, and D enter into a partnership. A subscribes 1/3 of the capital, B 1/4, C 1/5, and D the rest. A gets a share of Rs. 805 in a profit. What is the total profit amount?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A, B, C, and D enter into a partnership. A subscribes 1/3 of the capital, B 1/4, C 1/5, and D the rest. A gets a share of Rs. 805 in a profit. What is the total profit amount?<|im_end|>
<|im_start|>assistant
<Z_113><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A, B, C, and D enter into a partnership. A subscribes 1/3 of the capital, B 1/4, C 1/5, and D the rest. A gets a share of Rs. 805 in a profit. What is the total profit amount?<|im_end|>
<|im_start|>assistant
<Z_14><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A, B, C, and D enter into a partnership. A subscribes 1/3 of the capital, B 1/4, C 1/5, and D the rest. A gets a share of Rs. 805 in a profit. What is the total profit amount?<|im_end|>
<|im_start|>assistant
<Z_65><ANSWER>

Question: A, B, C, and D enter into a partnership. A subscribes 1/3 of the capital, B 1/4, C 1/5, and D the rest. A gets a share of Rs. 805 in a profit. What is the total profit amount?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 40 and the turban . find the price of the turban .<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 40 and the turban . find the price of the turban .<|im_end|>
<|im_start|>assistant
<Z_57><Z_37><Z_125><Z_68><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 40 and the turban . find the price of the turban .<|im_end|>
<|im_start|>assistant
<Z_127><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 40 and the turban . find the price of the turban .<|im_end|>
<|im_start|>assistant
<Z_92><Z_35><Z_95><Z_7><ANSWER>

Question: gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 40 and the turban . find the price of the turban .


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. 20% of the votes polled were invalid. B got 1859 valid votes. How many total votes were polled in the election?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. 20% of the votes polled were invalid. B got 1859 valid votes. How many total votes were polled in the election?<|im_end|>
<|im_start|>assistant
<Z_57><Z_51><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. 20% of the votes polled were invalid. B got 1859 valid votes. How many total votes were polled in the election?<|im_end|>
<|im_start|>assistant
<Z_74><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. 20% of the votes polled were invalid. B got 1859 valid votes. How many total votes were polled in the election?<|im_end|>
<|im_start|>assistant
<Z_100><Z_119><ANSWER>

Question: In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. 20% of the votes polled were invalid. B got 1859 valid votes. How many total votes were polled in the election?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the given triangle, what is the positive difference between the greatest and least possible integral values of $x$?

[asy]
defaultpen(linewidth(0.7));
pair a,b,c;
b = (2,3); c = (4,0);
draw(a--b--c--a);
label("$x$",a--b,dir(135)); label("10",b--c,dir(45)); label("8",c--a,S);
[/asy]<|im_end|>
<|im_start|>assistant
<Z_104><Z_68><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the given triangle, what is the positive difference between the greatest and least possible integral values of $x$?

[asy]
defaultpen(linewidth(0.7));
pair a,b,c;
b = (2,3); c = (4,0);
draw(a--b--c--a);
label("$x$",a--b,dir(135)); label("10",b--c,dir(45)); label("8",c--a,S);
[/asy]<|im_end|>
<|im_start|>assistant
<Z_94><Z_36><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the given triangle, what is the positive difference between the greatest and least possible integral values of $x$?

[asy]
defaultpen(linewidth(0.7));
pair a,b,c;
b = (2,3); c = (4,0);
draw(a--b--c--a);
label("$x$",a--b,dir(135)); label("10",b--c,dir(45)); label("8",c--a,S);
[/asy]<|im_end|>
<|im_start|>assistant
<Z_78><Z_116><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the given triangle, what is the positive difference between the greatest and least possible integral values of $x$?

[asy]
defaultpen(linewidth(0.7));
pair a,b,c;
b = (2,3); c = (4,0);
draw(a--b--c--a);
label("$x$",a--b,dir(135)); label("10",b--c,dir(45)); label("8",c--a,S);
[/asy]<|im_end|>
<|im_start|>assistant
<Z_86><Z_91><ANSWER>

Question:
In the given triangle, what is the positive difference between the greatest and least possible integral values of $x$?

[asy]
defaultpen(linewidth(0.7));
pair a,b,c;
b = (2,3); c = (4,0);
draw(a--b--c--a);
label("$x$",a--b,dir(135)); label("10",b--c,dir(45)); label("8",c--a,S);
[/asy]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A total of 23 teams participate in a single-elimination tournament. How many total games must be played before a winner is declared, given that there are no ties?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A total of 23 teams participate in a single-elimination tournament. How many total games must be played before a winner is declared, given that there are no ties?<|im_end|>
<|im_start|>assistant
<Z_94><Z_108><Z_73><Z_1><Z_59><Z_59><Z_66><Z_39><Z_93><Z_12><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A total of 23 teams participate in a single-elimination tournament. How many total games must be played before a winner is declared, given that there are no ties?<|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
A total of 23 teams participate in a single-elimination tournament. How many total games must be played before a winner is declared, given that there are no ties?<|im_end|>
<|im_start|>assistant
<Z_38><Z_67><Z_117><Z_60><Z_109><Z_15><Z_2><Z_126><Z_68><Z_64><ANSWER>

Question: A total of 23 teams participate in a single-elimination tournament. How many total games must be played before a winner is declared, given that there are no ties?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
(This question is worth 8 points)
Use the Euclidean algorithm to find the greatest common divisor of 5280 and 12155.<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
(This question is worth 8 points)
Use the Euclidean algorithm to find the greatest common divisor of 5280 and 12155.<|im_end|>
<|im_start|>assistant
<Z_113><Z_12><Z_81><Z_49><Z_120><Z_87><Z_36><Z_52><Z_38><Z_47><Z_59><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
(This question is worth 8 points)
Use the Euclidean algorithm to find the greatest common divisor of 5280 and 12155.<|im_end|>
<|im_start|>assistant
<Z_8><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
(This question is worth 8 points)
Use the Euclidean algorithm to find the greatest common divisor of 5280 and 12155.<|im_end|>
<|im_start|>assistant
<Z_49><Z_19><Z_110><Z_50><Z_44><Z_6><Z_55><Z_119><Z_114><Z_67><Z_86><ANSWER>

Question:
(This question is worth 8 points)
Use the Euclidean algorithm to find the greatest common divisor of 5280 and 12155.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Consider a string of $n$ $7$'s, $7777\cdots77,$ into which $+$ signs are inserted to create an arithmetic expression. For example, $7+777+7=791$ could be derived from four $7$'s. For how many values of $n$ is it possible to insert $+$ signs so that the resulting expression sums to $3100$?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Consider a string of $n$ $7$'s, $7777\cdots77,$ into which $+$ signs are inserted to create an arithmetic expression. For example, $7+777+7=791$ could be derived from four $7$'s. For how many values of $n$ is it possible to insert $+$ signs so that the resulting expression sums to $3100$?<|im_end|>
<|im_start|>assistant
<Z_57><Z_63><Z_12><Z_81><Z_61><Z_65><Z_121><Z_48><Z_54><Z_119><Z_12><Z_126><Z_126><Z_48><Z_45><Z_24><Z_117><Z_24><Z_45><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Consider a string of $n$ $7$'s, $7777\cdots77,$ into which $+$ signs are inserted to create an arithmetic expression. For example, $7+777+7=791$ could be derived from four $7$'s. For how many values of $n$ is it possible to insert $+$ signs so that the resulting expression sums to $3100$?<|im_end|>
<|im_start|>assistant
<Z_127><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Consider a string of $n$ $7$'s, $7777\cdots77,$ into which $+$ signs are inserted to create an arithmetic expression. For example, $7+777+7=791$ could be derived from four $7$'s. For how many values of $n$ is it possible to insert $+$ signs so that the resulting expression sums to $3100$?<|im_end|>
<|im_start|>assistant
<Z_35><Z_90><Z_111><Z_76><Z_97><Z_97><Z_33><Z_61><Z_4><Z_113><Z_79><Z_100><Z_12><Z_51><Z_7><Z_17><Z_66><Z_126><Z_82><ANSWER>

Question: Consider a string of $n$ $7$'s, $7777\cdots77,$ into which $+$ signs are inserted to create an arithmetic expression. For example, $7+777+7=791$ could be derived from four $7$'s. For how many values of $n$ is it possible to insert $+$ signs so that the resulting expression sums to $3100$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jim reads at a rate of 40 pages an hour.  He reads a total of 600 pages per week.  He increases his reading speed to 150% of its former speed but reads 4 hours less per week.  How many pages does he read a week now?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jim reads at a rate of 40 pages an hour.  He reads a total of 600 pages per week.  He increases his reading speed to 150% of its former speed but reads 4 hours less per week.  How many pages does he read a week now?<|im_end|>
<|im_start|>assistant
<Z_57><Z_62><Z_51><Z_100><Z_51><Z_50><Z_91><Z_79><Z_41><Z_82><Z_107><Z_82><Z_88><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jim reads at a rate of 40 pages an hour.  He reads a total of 600 pages per week.  He increases his reading speed to 150% of its former speed but reads 4 hours less per week.  How many pages does he read a week now?<|im_end|>
<|im_start|>assistant
<Z_78><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jim reads at a rate of 40 pages an hour.  He reads a total of 600 pages per week.  He increases his reading speed to 150% of its former speed but reads 4 hours less per week.  How many pages does he read a week now?<|im_end|>
<|im_start|>assistant
<Z_43><Z_68><Z_35><Z_33><Z_9><Z_25><Z_70><Z_113><Z_63><Z_86><Z_104><Z_43><Z_49><ANSWER>

Question: Jim reads at a rate of 40 pages an hour.  He reads a total of 600 pages per week.  He increases his reading speed to 150% of its former speed but reads 4 hours less per week.  How many pages does he read a week now?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $a_n$ be the integer obtained by writing all the integers from $1$ to $n$ from left to right. For example, $a_3 = 123$ and $a_{11} = 1234567891011$. Compute the remainder when $a_{44}$ is divided by $45$.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $a_n$ be the integer obtained by writing all the integers from $1$ to $n$ from left to right. For example, $a_3 = 123$ and $a_{11} = 1234567891011$. Compute the remainder when $a_{44}$ is divided by $45$.<|im_end|>
<|im_start|>assistant
<Z_29><Z_114><Z_125><Z_65><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $a_n$ be the integer obtained by writing all the integers from $1$ to $n$ from left to right. For example, $a_3 = 123$ and $a_{11} = 1234567891011$. Compute the remainder when $a_{44}$ is divided by $45$.<|im_end|>
<|im_start|>assistant
<Z_103><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $a_n$ be the integer obtained by writing all the integers from $1$ to $n$ from left to right. For example, $a_3 = 123$ and $a_{11} = 1234567891011$. Compute the remainder when $a_{44}$ is divided by $45$.<|im_end|>
<|im_start|>assistant
<Z_103><Z_12><Z_57><Z_77><ANSWER>

Question: Let $a_n$ be the integer obtained by writing all the integers from $1$ to $n$ from left to right. For example, $a_3 = 123$ and $a_{11} = 1234567891011$. Compute the remainder when $a_{44}$ is divided by $45$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Suppose the graph of the function $y=f(x)$ includes the points $(2, 6)$, $(3, 4)$, and $(4, 2)$. Assuming the graph of $y=g(x)$ includes the points $(2,4)$, $(3,2)$, and $(5,6)$, determine the two points that must be on the graph of $y=g(f(x))$. If we let these points be $(a,b)$ and $(c,d)$, what is $ab+cd$?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Suppose the graph of the function $y=f(x)$ includes the points $(2, 6)$, $(3, 4)$, and $(4, 2)$. Assuming the graph of $y=g(x)$ includes the points $(2,4)$, $(3,2)$, and $(5,6)$, determine the two points that must be on the graph of $y=g(f(x))$. If we let these points be $(a,b)$ and $(c,d)$, what is $ab+cd$?<|im_end|>
<|im_start|>assistant
<Z_106><Z_91><Z_50><Z_36><Z_108><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Suppose the graph of the function $y=f(x)$ includes the points $(2, 6)$, $(3, 4)$, and $(4, 2)$. Assuming the graph of $y=g(x)$ includes the points $(2,4)$, $(3,2)$, and $(5,6)$, determine the two points that must be on the graph of $y=g(f(x))$. If we let these points be $(a,b)$ and $(c,d)$, what is $ab+cd$?<|im_end|>
<|im_start|>assistant
<Z_124><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Suppose the graph of the function $y=f(x)$ includes the points $(2, 6)$, $(3, 4)$, and $(4, 2)$. Assuming the graph of $y=g(x)$ includes the points $(2,4)$, $(3,2)$, and $(5,6)$, determine the two points that must be on the graph of $y=g(f(x))$. If we let these points be $(a,b)$ and $(c,d)$, what is $ab+cd$?<|im_end|>
<|im_start|>assistant
<Z_9><Z_8><Z_5><Z_118><Z_88><ANSWER>

Question: Suppose the graph of the function $y=f(x)$ includes the points $(2, 6)$, $(3, 4)$, and $(4, 2)$. Assuming the graph of $y=g(x)$ includes the points $(2,4)$, $(3,2)$, and $(5,6)$, determine the two points that must be on the graph of $y=g(f(x))$. If we let these points be $(a,b)$ and $(c,d)$, what is $ab+cd$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A man sitting in a train which is travelling at 50 kmph observes that a goods train travelling in the opposite direction, takes 6 seconds to pass him. If the goods train is 400 m long, find its speed.<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A man sitting in a train which is travelling at 50 kmph observes that a goods train travelling in the opposite direction, takes 6 seconds to pass him. If the goods train is 400 m long, find its speed.<|im_end|>
<|im_start|>assistant
<Z_94><Z_100><Z_77><Z_103><Z_41><Z_78><Z_87><Z_103><Z_72><Z_76><Z_93><Z_34><Z_78><Z_16><Z_16><Z_119><Z_37><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A man sitting in a train which is travelling at 50 kmph observes that a goods train travelling in the opposite direction, takes 6 seconds to pass him. If the goods train is 400 m long, find its speed.<|im_end|>
<|im_start|>assistant
<Z_25><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A man sitting in a train which is travelling at 50 kmph observes that a goods train travelling in the opposite direction, takes 6 seconds to pass him. If the goods train is 400 m long, find its speed.<|im_end|>
<|im_start|>assistant
<Z_6><Z_2><Z_21><Z_3><Z_106><Z_73><Z_15><Z_29><Z_27><Z_122><Z_98><Z_50><Z_17><Z_83><Z_10><Z_10><Z_102><ANSWER>

Question: A man sitting in a train which is travelling at 50 kmph observes that a goods train travelling in the opposite direction, takes 6 seconds to pass him. If the goods train is 400 m long, find its speed.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $\mathbf{B} = \begin{pmatrix} p & q \\ r & s \end{pmatrix}$, then its transpose is given by
\[\mathbf{B}^T = \begin{pmatrix} p & r \\ q & s \end{pmatrix}.\]
Given that $\mathbf{B}^T = 2\mathbf{B}^{-1}$, find $p^2 + q^2 + r^2 + s^2.$<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $\mathbf{B} = \begin{pmatrix} p & q \\ r & s \end{pmatrix}$, then its transpose is given by
\[\mathbf{B}^T = \begin{pmatrix} p & r \\ q & s \end{pmatrix}.\]
Given that $\mathbf{B}^T = 2\mathbf{B}^{-1}$, find $p^2 + q^2 + r^2 + s^2.$<|im_end|>
<|im_start|>assistant
<Z_113><Z_62><Z_78><Z_58><Z_43><Z_83><Z_82><Z_61><Z_39><Z_56><Z_119><Z_95><Z_93><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $\mathbf{B} = \begin{pmatrix} p & q \\ r & s \end{pmatrix}$, then its transpose is given by
\[\mathbf{B}^T = \begin{pmatrix} p & r \\ q & s \end{pmatrix}.\]
Given that $\mathbf{B}^T = 2\mathbf{B}^{-1}$, find $p^2 + q^2 + r^2 + s^2.$<|im_end|>
<|im_start|>assistant
<Z_59><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $\mathbf{B} = \begin{pmatrix} p & q \\ r & s \end{pmatrix}$, then its transpose is given by
\[\mathbf{B}^T = \begin{pmatrix} p & r \\ q & s \end{pmatrix}.\]
Given that $\mathbf{B}^T = 2\mathbf{B}^{-1}$, find $p^2 + q^2 + r^2 + s^2.$<|im_end|>
<|im_start|>assistant
<Z_102><Z_10><Z_51><Z_127><Z_92><Z_7><Z_92><Z_51><Z_53><Z_87><Z_94><Z_111><Z_48><ANSWER>

Question:
If $\mathbf{B} = \begin{pmatrix} p & q \\ r & s \end{pmatrix}$, then its transpose is given by
\[\mathbf{B}^T = \begin{pmatrix} p & r \\ q & s \end{pmatrix}.\]
Given that $\mathbf{B}^T = 2\mathbf{B}^{-1}$, find $p^2 + q^2 + r^2 + s^2.$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a cistern is normally filled in 6 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a cistern is normally filled in 6 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?<|im_end|>
<|im_start|>assistant
<Z_94><Z_81><Z_59><Z_107><Z_117><Z_66><Z_59><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a cistern is normally filled in 6 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?<|im_end|>
<|im_start|>assistant
<Z_87><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a cistern is normally filled in 6 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?<|im_end|>
<|im_start|>assistant
<Z_47><Z_9><Z_69><Z_94><Z_36><Z_109><Z_13><ANSWER>

Question: a cistern is normally filled in 6 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A box contains a mixture of green socks and yellow socks, with at most 2023 socks in total. The probability of randomly pulling out two socks of the same color is exactly $\frac{1}{3}$. What is the largest possible number of green socks in the box?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A box contains a mixture of green socks and yellow socks, with at most 2023 socks in total. The probability of randomly pulling out two socks of the same color is exactly $\frac{1}{3}$. What is the largest possible number of green socks in the box?<|im_end|>
<|im_start|>assistant
<Z_113><Z_82><Z_89><Z_12><Z_49><Z_11><Z_56><Z_91><Z_114><Z_49><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A box contains a mixture of green socks and yellow socks, with at most 2023 socks in total. The probability of randomly pulling out two socks of the same color is exactly $\frac{1}{3}$. What is the largest possible number of green socks in the box?<|im_end|>
<|im_start|>assistant
<Z_122><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A box contains a mixture of green socks and yellow socks, with at most 2023 socks in total. The probability of randomly pulling out two socks of the same color is exactly $\frac{1}{3}$. What is the largest possible number of green socks in the box?<|im_end|>
<|im_start|>assistant
<Z_90><Z_88><Z_51><Z_30><Z_32><Z_59><Z_46><Z_69><Z_1><Z_102><ANSWER>

Question: A box contains a mixture of green socks and yellow socks, with at most 2023 socks in total. The probability of randomly pulling out two socks of the same color is exactly $\frac{1}{3}$. What is the largest possible number of green socks in the box?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sequence 12, 15, 18, 21, 51, 81, $\ldots$ consists of all positive multiples of 3 where the sum of the digits is exactly 10. What is the $30^{\mathrm{th}}$ term of the sequence?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sequence 12, 15, 18, 21, 51, 81, $\ldots$ consists of all positive multiples of 3 where the sum of the digits is exactly 10. What is the $30^{\mathrm{th}}$ term of the sequence?<|im_end|>
<|im_start|>assistant
<Z_94><Z_43><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sequence 12, 15, 18, 21, 51, 81, $\ldots$ consists of all positive multiples of 3 where the sum of the digits is exactly 10. What is the $30^{\mathrm{th}}$ term of the sequence?<|im_end|>
<|im_start|>assistant
<Z_55><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The sequence 12, 15, 18, 21, 51, 81, $\ldots$ consists of all positive multiples of 3 where the sum of the digits is exactly 10. What is the $30^{\mathrm{th}}$ term of the sequence?<|im_end|>
<|im_start|>assistant
<Z_96><Z_55><ANSWER>

Question: The sequence 12, 15, 18, 21, 51, 81, $\ldots$ consists of all positive multiples of 3 where the sum of the digits is exactly 10. What is the $30^{\mathrm{th}}$ term of the sequence?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It was Trevor's job to collect fresh eggs from the family's 4 chickens every morning. He got 4 eggs from Gertrude, 3 eggs from Blanche, some eggs from Nancy, and 2 eggs from Martha. On the way, he dropped 2 eggs. Trevor had 9 eggs left. How many eggs did he get from Nancy?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It was Trevor's job to collect fresh eggs from the family's 4 chickens every morning. He got 4 eggs from Gertrude, 3 eggs from Blanche, some eggs from Nancy, and 2 eggs from Martha. On the way, he dropped 2 eggs. Trevor had 9 eggs left. How many eggs did he get from Nancy?<|im_end|>
<|im_start|>assistant
<Z_94><Z_38><Z_49><Z_80><Z_20><Z_87><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It was Trevor's job to collect fresh eggs from the family's 4 chickens every morning. He got 4 eggs from Gertrude, 3 eggs from Blanche, some eggs from Nancy, and 2 eggs from Martha. On the way, he dropped 2 eggs. Trevor had 9 eggs left. How many eggs did he get from Nancy?<|im_end|>
<|im_start|>assistant
<Z_49><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It was Trevor's job to collect fresh eggs from the family's 4 chickens every morning. He got 4 eggs from Gertrude, 3 eggs from Blanche, some eggs from Nancy, and 2 eggs from Martha. On the way, he dropped 2 eggs. Trevor had 9 eggs left. How many eggs did he get from Nancy?<|im_end|>
<|im_start|>assistant
<Z_60><Z_127><Z_124><Z_18><Z_34><Z_124><ANSWER>

Question: It was Trevor's job to collect fresh eggs from the family's 4 chickens every morning. He got 4 eggs from Gertrude, 3 eggs from Blanche, some eggs from Nancy, and 2 eggs from Martha. On the way, he dropped 2 eggs. Trevor had 9 eggs left. How many eggs did he get from Nancy?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In trapezoid $EFGH$, where $EF$ and $GH$ are the parallel sides, we have $EG=EH=15$, $EF=14$, and $GH=28$. The trapezoid is divided by line $IJ$ connecting midpoints of $EG$ and $EH$. Let $K$ be a point on $EF$ such that $GK$ is perpendicular to $EF$. Determine the ratio of the areas of trapezoid $EFIJ$ to trapezoid $IJGH$ in simplified form, then find the sum of these two numbers in the ratio.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In trapezoid $EFGH$, where $EF$ and $GH$ are the parallel sides, we have $EG=EH=15$, $EF=14$, and $GH=28$. The trapezoid is divided by line $IJ$ connecting midpoints of $EG$ and $EH$. Let $K$ be a point on $EF$ such that $GK$ is perpendicular to $EF$. Determine the ratio of the areas of trapezoid $EFIJ$ to trapezoid $IJGH$ in simplified form, then find the sum of these two numbers in the ratio.<|im_end|>
<|im_start|>assistant
<Z_106><Z_125><Z_77><Z_78><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In trapezoid $EFGH$, where $EF$ and $GH$ are the parallel sides, we have $EG=EH=15$, $EF=14$, and $GH=28$. The trapezoid is divided by line $IJ$ connecting midpoints of $EG$ and $EH$. Let $K$ be a point on $EF$ such that $GK$ is perpendicular to $EF$. Determine the ratio of the areas of trapezoid $EFIJ$ to trapezoid $IJGH$ in simplified form, then find the sum of these two numbers in the ratio.<|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
In trapezoid $EFGH$, where $EF$ and $GH$ are the parallel sides, we have $EG=EH=15$, $EF=14$, and $GH=28$. The trapezoid is divided by line $IJ$ connecting midpoints of $EG$ and $EH$. Let $K$ be a point on $EF$ such that $GK$ is perpendicular to $EF$. Determine the ratio of the areas of trapezoid $EFIJ$ to trapezoid $IJGH$ in simplified form, then find the sum of these two numbers in the ratio.<|im_end|>
<|im_start|>assistant
<Z_84><Z_56><Z_56><Z_86><ANSWER>

Question: In trapezoid $EFGH$, where $EF$ and $GH$ are the parallel sides, we have $EG=EH=15$, $EF=14$, and $GH=28$. The trapezoid is divided by line $IJ$ connecting midpoints of $EG$ and $EH$. Let $K$ be a point on $EF$ such that $GK$ is perpendicular to $EF$. Determine the ratio of the areas of trapezoid $EFIJ$ to trapezoid $IJGH$ in simplified form, then find the sum of these two numbers in the ratio.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A magician guesses the area of a convex 2008-gon \( A_{1} A_{2} \ldots A_{2008} \) located behind a screen. He announces two points on the perimeter of the polygon; the audience marks these points, draws a line through them, and tells the magician the smaller area of the two parts into which the 2008-gon is divided by this line. The magician can name a point either as a vertex or a point dividing a specified side in a specified numerical ratio. Prove that with 2006 questions, the magician can guess the area of the polygon.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A magician guesses the area of a convex 2008-gon \( A_{1} A_{2} \ldots A_{2008} \) located behind a screen. He announces two points on the perimeter of the polygon; the audience marks these points, draws a line through them, and tells the magician the smaller area of the two parts into which the 2008-gon is divided by this line. The magician can name a point either as a vertex or a point dividing a specified side in a specified numerical ratio. Prove that with 2006 questions, the magician can guess the area of the polygon.<|im_end|>
<|im_start|>assistant
<Z_57><Z_114><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A magician guesses the area of a convex 2008-gon \( A_{1} A_{2} \ldots A_{2008} \) located behind a screen. He announces two points on the perimeter of the polygon; the audience marks these points, draws a line through them, and tells the magician the smaller area of the two parts into which the 2008-gon is divided by this line. The magician can name a point either as a vertex or a point dividing a specified side in a specified numerical ratio. Prove that with 2006 questions, the magician can guess the area of the polygon.<|im_end|>
<|im_start|>assistant
<Z_14><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A magician guesses the area of a convex 2008-gon \( A_{1} A_{2} \ldots A_{2008} \) located behind a screen. He announces two points on the perimeter of the polygon; the audience marks these points, draws a line through them, and tells the magician the smaller area of the two parts into which the 2008-gon is divided by this line. The magician can name a point either as a vertex or a point dividing a specified side in a specified numerical ratio. Prove that with 2006 questions, the magician can guess the area of the polygon.<|im_end|>
<|im_start|>assistant
<Z_122><Z_37><ANSWER>

Question: A magician guesses the area of a convex 2008-gon \( A_{1} A_{2} \ldots A_{2008} \) located behind a screen. He announces two points on the perimeter of the polygon; the audience marks these points, draws a line through them, and tells the magician the smaller area of the two parts into which the 2008-gon is divided by this line. The magician can name a point either as a vertex or a point dividing a specified side in a specified numerical ratio. Prove that with 2006 questions, the magician can guess the area of the polygon.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A teacher had 34 worksheets to grade. She graded 7, but then some more worksheets were turned in. Now, she has to grade 63 worksheets. How many worksheets were turned in after she graded the first 7?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A teacher had 34 worksheets to grade. She graded 7, but then some more worksheets were turned in. Now, she has to grade 63 worksheets. How many worksheets were turned in after she graded the first 7?<|im_end|>
<|im_start|>assistant
<Z_94><Z_34><Z_64><Z_36><Z_124><Z_79><Z_125><Z_76><Z_49><Z_115><Z_5><Z_52><Z_5><Z_11><Z_45><Z_56><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A teacher had 34 worksheets to grade. She graded 7, but then some more worksheets were turned in. Now, she has to grade 63 worksheets. How many worksheets were turned in after she graded the first 7?<|im_end|>
<|im_start|>assistant
<Z_115><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A teacher had 34 worksheets to grade. She graded 7, but then some more worksheets were turned in. Now, she has to grade 63 worksheets. How many worksheets were turned in after she graded the first 7?<|im_end|>
<|im_start|>assistant
<Z_127><Z_2><Z_28><Z_68><Z_7><Z_76><Z_117><Z_124><Z_32><Z_88><Z_3><Z_56><Z_16><Z_18><Z_56><Z_111><ANSWER>

Question: A teacher had 34 worksheets to grade. She graded 7, but then some more worksheets were turned in. Now, she has to grade 63 worksheets. How many worksheets were turned in after she graded the first 7?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a cage, there are a total of 28 heads. The total number of rabbit legs is 12 more than 3 times the total number of chicken legs. How many rabbits are in the cage?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a cage, there are a total of 28 heads. The total number of rabbit legs is 12 more than 3 times the total number of chicken legs. How many rabbits are in the cage?<|im_end|>
<|im_start|>assistant
<Z_94><Z_115><Z_40><Z_37><Z_75><Z_38><Z_48><Z_96><Z_48><Z_53><Z_58><Z_117><Z_88><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a cage, there are a total of 28 heads. The total number of rabbit legs is 12 more than 3 times the total number of chicken legs. How many rabbits are in the cage?<|im_end|>
<|im_start|>assistant
<Z_73><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a cage, there are a total of 28 heads. The total number of rabbit legs is 12 more than 3 times the total number of chicken legs. How many rabbits are in the cage?<|im_end|>
<|im_start|>assistant
<Z_120><Z_70><Z_112><Z_118><Z_125><Z_98><Z_18><Z_43><Z_19><Z_89><Z_59><Z_23><Z_112><ANSWER>

Question: In a cage, there are a total of 28 heads. The total number of rabbit legs is 12 more than 3 times the total number of chicken legs. How many rabbits are in the cage?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is a very large room that has 4 tables, 1 sofa and 2 chairs that have 4 legs each.  There are also 3 tables with 3 legs each, 1 table with 1 leg, and 1 rocking chair with 2 legs.  How many legs are there in the room?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is a very large room that has 4 tables, 1 sofa and 2 chairs that have 4 legs each.  There are also 3 tables with 3 legs each, 1 table with 1 leg, and 1 rocking chair with 2 legs.  How many legs are there in the room?<|im_end|>
<|im_start|>assistant
<Z_94><Z_77><Z_91><Z_33><Z_9><Z_124><Z_87><Z_82><Z_98><Z_96><Z_39><Z_82><Z_52><Z_37><Z_5><Z_52><Z_10><Z_10><Z_91><Z_119><Z_12><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is a very large room that has 4 tables, 1 sofa and 2 chairs that have 4 legs each.  There are also 3 tables with 3 legs each, 1 table with 1 leg, and 1 rocking chair with 2 legs.  How many legs are there in the room?<|im_end|>
<|im_start|>assistant
<Z_47><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is a very large room that has 4 tables, 1 sofa and 2 chairs that have 4 legs each.  There are also 3 tables with 3 legs each, 1 table with 1 leg, and 1 rocking chair with 2 legs.  How many legs are there in the room?<|im_end|>
<|im_start|>assistant
<Z_108><Z_121><Z_85><Z_77><Z_25><Z_1><Z_76><Z_99><Z_80><Z_90><Z_4><Z_125><Z_104><Z_49><Z_81><Z_43><Z_21><Z_9><Z_32><Z_42><Z_69><ANSWER>

Question: There is a very large room that has 4 tables, 1 sofa and 2 chairs that have 4 legs each.  There are also 3 tables with 3 legs each, 1 table with 1 leg, and 1 rocking chair with 2 legs.  How many legs are there in the room?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A company donates some pencils to a school. The pencils are divided evenly among 9 classrooms, and the rest of the pencils, 8 of them, are given to the library. How many pencils were donated in total?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A company donates some pencils to a school. The pencils are divided evenly among 9 classrooms, and the rest of the pencils, 8 of them, are given to the library. How many pencils were donated in total?<|im_end|>
<|im_start|>assistant
<Z_94><Z_100><Z_51><Z_119><Z_82><Z_51><Z_91><Z_22><Z_125><Z_117><Z_72><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A company donates some pencils to a school. The pencils are divided evenly among 9 classrooms, and the rest of the pencils, 8 of them, are given to the library. How many pencils were donated in total?<|im_end|>
<|im_start|>assistant
<Z_54><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A company donates some pencils to a school. The pencils are divided evenly among 9 classrooms, and the rest of the pencils, 8 of them, are given to the library. How many pencils were donated in total?<|im_end|>
<|im_start|>assistant
<Z_92><Z_63><Z_67><Z_118><Z_108><Z_80><Z_7><Z_123><Z_43><Z_87><Z_33><ANSWER>

Question: A company donates some pencils to a school. The pencils are divided evenly among 9 classrooms, and the rest of the pencils, 8 of them, are given to the library. How many pencils were donated in total?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( S = \{1, 2, \cdots, 10\} \). \( A_{1}, A_{2}, \cdots, A_{k} \) are subsets of \( S \) satisfying the following conditions:
1. \( \left|A_{i}\right| = 5 \) for \( i = 1, 2, \cdots, k \).
2. \( \left|A_{i} \cap A_{j}\right| \leqslant 2 \) for \( 1 \leqslant i < j \leqslant k \).

Find the maximum value of \( k \).<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( S = \{1, 2, \cdots, 10\} \). \( A_{1}, A_{2}, \cdots, A_{k} \) are subsets of \( S \) satisfying the following conditions:
1. \( \left|A_{i}\right| = 5 \) for \( i = 1, 2, \cdots, k \).
2. \( \left|A_{i} \cap A_{j}\right| \leqslant 2 \) for \( 1 \leqslant i < j \leqslant k \).

Find the maximum value of \( k \).<|im_end|>
<|im_start|>assistant
<Z_94><Z_100><Z_124><Z_103><Z_43><Z_115><Z_88><Z_120><Z_117><Z_78><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( S = \{1, 2, \cdots, 10\} \). \( A_{1}, A_{2}, \cdots, A_{k} \) are subsets of \( S \) satisfying the following conditions:
1. \( \left|A_{i}\right| = 5 \) for \( i = 1, 2, \cdots, k \).
2. \( \left|A_{i} \cap A_{j}\right| \leqslant 2 \) for \( 1 \leqslant i < j \leqslant k \).

Find the maximum value of \( k \).<|im_end|>
<|im_start|>assistant
<Z_74><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let \( S = \{1, 2, \cdots, 10\} \). \( A_{1}, A_{2}, \cdots, A_{k} \) are subsets of \( S \) satisfying the following conditions:
1. \( \left|A_{i}\right| = 5 \) for \( i = 1, 2, \cdots, k \).
2. \( \left|A_{i} \cap A_{j}\right| \leqslant 2 \) for \( 1 \leqslant i < j \leqslant k \).

Find the maximum value of \( k \).<|im_end|>
<|im_start|>assistant
<Z_15><Z_111><Z_95><Z_117><Z_120><Z_21><Z_116><Z_96><Z_112><Z_85><ANSWER>

Question:
Let \( S = \{1, 2, \cdots, 10\} \). \( A_{1}, A_{2}, \cdots, A_{k} \) are subsets of \( S \) satisfying the following conditions:
1. \( \left|A_{i}\right| = 5 \) for \( i = 1, 2, \cdots, k \).
2. \( \left|A_{i} \cap A_{j}\right| \leqslant 2 \) for \( 1 \leqslant i < j \leqslant k \).

Find the maximum value of \( k \).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alex is at the candy store buying jellybeans. He wants to buy at least 120 jellybeans. He wants to buy the least amount such that he would have exactly $14$ leftover after dividing the jellybeans evenly among $15$ people. How many jellybeans should Alex buy?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alex is at the candy store buying jellybeans. He wants to buy at least 120 jellybeans. He wants to buy the least amount such that he would have exactly $14$ leftover after dividing the jellybeans evenly among $15$ people. How many jellybeans should Alex buy?<|im_end|>
<|im_start|>assistant
<Z_57><Z_114><Z_97><Z_81><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alex is at the candy store buying jellybeans. He wants to buy at least 120 jellybeans. He wants to buy the least amount such that he would have exactly $14$ leftover after dividing the jellybeans evenly among $15$ people. How many jellybeans should Alex buy?<|im_end|>
<|im_start|>assistant
<Z_16><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Alex is at the candy store buying jellybeans. He wants to buy at least 120 jellybeans. He wants to buy the least amount such that he would have exactly $14$ leftover after dividing the jellybeans evenly among $15$ people. How many jellybeans should Alex buy?<|im_end|>
<|im_start|>assistant
<Z_45><Z_5><Z_45><Z_0><ANSWER>

Question: Alex is at the candy store buying jellybeans. He wants to buy at least 120 jellybeans. He wants to buy the least amount such that he would have exactly $14$ leftover after dividing the jellybeans evenly among $15$ people. How many jellybeans should Alex buy?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
4 hours 35 minutes =     minutes
4 tons 35 kilograms =     kilograms
678 seconds =     minutes     seconds
120000 square meters =     hectares.<|im_end|>
<|im_start|>assistant
<Z_94><Z_27><Z_100><Z_100><Z_99><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
4 hours 35 minutes =     minutes
4 tons 35 kilograms =     kilograms
678 seconds =     minutes     seconds
120000 square meters =     hectares.<|im_end|>
<|im_start|>assistant
<Z_104><Z_97><Z_124><Z_68><Z_73><Z_22><Z_91><Z_16><Z_39><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
4 hours 35 minutes =     minutes
4 tons 35 kilograms =     kilograms
678 seconds =     minutes     seconds
120000 square meters =     hectares.<|im_end|>
<|im_start|>assistant
<Z_118><Z_115><Z_50><Z_9><Z_14><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
4 hours 35 minutes =     minutes
4 tons 35 kilograms =     kilograms
678 seconds =     minutes     seconds
120000 square meters =     hectares.<|im_end|>
<|im_start|>assistant
<Z_56><Z_45><Z_35><Z_120><Z_108><Z_60><Z_15><Z_126><Z_123><ANSWER>

Question:
4 hours 35 minutes =     minutes
4 tons 35 kilograms =     kilograms
678 seconds =     minutes     seconds
120000 square meters =     hectares.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In writing the integers from 100 through 999 inclusive, how many times is the digit 6 written?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In writing the integers from 100 through 999 inclusive, how many times is the digit 6 written?<|im_end|>
<|im_start|>assistant
<Z_104><Z_59><Z_62><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In writing the integers from 100 through 999 inclusive, how many times is the digit 6 written?<|im_end|>
<|im_start|>assistant
<Z_101><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In writing the integers from 100 through 999 inclusive, how many times is the digit 6 written?<|im_end|>
<|im_start|>assistant
<Z_32><Z_62><Z_108><ANSWER>

Question: In writing the integers from 100 through 999 inclusive, how many times is the digit 6 written?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train that is 360 meters long is running at a speed of 50 km/hour. It passes a bridge of certain length in 36 seconds. What is the length of the bridge?<|im_end|>
<|im_start|>assistant
<Z_57><Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train that is 360 meters long is running at a speed of 50 km/hour. It passes a bridge of certain length in 36 seconds. What is the length of the bridge?<|im_end|>
<|im_start|>assistant
<Z_104><Z_64><Z_41><Z_125><Z_78><Z_52><Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train that is 360 meters long is running at a speed of 50 km/hour. It passes a bridge of certain length in 36 seconds. What is the length of the bridge?<|im_end|>
<|im_start|>assistant
<Z_46><Z_123><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train that is 360 meters long is running at a speed of 50 km/hour. It passes a bridge of certain length in 36 seconds. What is the length of the bridge?<|im_end|>
<|im_start|>assistant
<Z_123><Z_106><Z_19><Z_90><Z_91><Z_4><Z_105><ANSWER>

Question: A train that is 360 meters long is running at a speed of 50 km/hour. It passes a bridge of certain length in 36 seconds. What is the length of the bridge?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are ninety-eight cats in the little town. If ninety-two of them are a asleep, how many cats are still awake?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are ninety-eight cats in the little town. If ninety-two of them are a asleep, how many cats are still awake?<|im_end|>
<|im_start|>assistant
<Z_57><Z_97><Z_64><Z_107><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are ninety-eight cats in the little town. If ninety-two of them are a asleep, how many cats are still awake?<|im_end|>
<|im_start|>assistant
<Z_74><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There are ninety-eight cats in the little town. If ninety-two of them are a asleep, how many cats are still awake?<|im_end|>
<|im_start|>assistant
<Z_22><Z_40><Z_1><Z_119><ANSWER>

Question: There are ninety-eight cats in the little town. If ninety-two of them are a asleep, how many cats are still awake?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Define an odd function $f(x)$ on $\mathbb{R}$ such that for any $x$, $f(x-1) = f(4-x)$ and $f(x)=x$ for $x \in (0, \frac{3}{2})$. Calculate $f(2012) - f(2010)$.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Define an odd function $f(x)$ on $\mathbb{R}$ such that for any $x$, $f(x-1) = f(4-x)$ and $f(x)=x$ for $x \in (0, \frac{3}{2})$. Calculate $f(2012) - f(2010)$.<|im_end|>
<|im_start|>assistant
<Z_94><Z_77><Z_81><Z_52><Z_115><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Define an odd function $f(x)$ on $\mathbb{R}$ such that for any $x$, $f(x-1) = f(4-x)$ and $f(x)=x$ for $x \in (0, \frac{3}{2})$. Calculate $f(2012) - f(2010)$.<|im_end|>
<|im_start|>assistant
<Z_113><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Define an odd function $f(x)$ on $\mathbb{R}$ such that for any $x$, $f(x-1) = f(4-x)$ and $f(x)=x$ for $x \in (0, \frac{3}{2})$. Calculate $f(2012) - f(2010)$.<|im_end|>
<|im_start|>assistant
<Z_118><Z_43><Z_119><Z_0><Z_35><ANSWER>

Question: Define an odd function $f(x)$ on $\mathbb{R}$ such that for any $x$, $f(x-1) = f(4-x)$ and $f(x)=x$ for $x \in (0, \frac{3}{2})$. Calculate $f(2012) - f(2010)$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The product of the midline of a trapezoid and the segment connecting the midpoints of its diagonals equals 25. Find the area of the trapezoid if its height is three times the difference of its bases.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The product of the midline of a trapezoid and the segment connecting the midpoints of its diagonals equals 25. Find the area of the trapezoid if its height is three times the difference of its bases.<|im_end|>
<|im_start|>assistant
<Z_104><Z_86><Z_91><Z_125><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The product of the midline of a trapezoid and the segment connecting the midpoints of its diagonals equals 25. Find the area of the trapezoid if its height is three times the difference of its bases.<|im_end|>
<|im_start|>assistant
<Z_37><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The product of the midline of a trapezoid and the segment connecting the midpoints of its diagonals equals 25. Find the area of the trapezoid if its height is three times the difference of its bases.<|im_end|>
<|im_start|>assistant
<Z_100><Z_67><Z_50><Z_77><ANSWER>

Question: The product of the midline of a trapezoid and the segment connecting the midpoints of its diagonals equals 25. Find the area of the trapezoid if its height is three times the difference of its bases.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
what is the square root of 625 , divided by 5 ?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
what is the square root of 625 , divided by 5 ?<|im_end|>
<|im_start|>assistant
<Z_94><Z_82><Z_40><Z_96><Z_96><Z_114><Z_114><Z_93><Z_33><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
what is the square root of 625 , divided by 5 ?<|im_end|>
<|im_start|>assistant
<Z_110><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
what is the square root of 625 , divided by 5 ?<|im_end|>
<|im_start|>assistant
<Z_25><Z_30><Z_25><Z_93><Z_3><Z_102><Z_45><Z_59><Z_19><ANSWER>

Question: what is the square root of 625 , divided by 5 ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If 15% of 40 is greater than 25% of a number by a certain value, and the number is 16, what is the value?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If 15% of 40 is greater than 25% of a number by a certain value, and the number is 16, what is the value?<|im_end|>
<|im_start|>assistant
<Z_57><Z_82><Z_97><Z_124><Z_63><Z_56><Z_75><Z_22><Z_118><Z_66><Z_53><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If 15% of 40 is greater than 25% of a number by a certain value, and the number is 16, what is the value?<|im_end|>
<|im_start|>assistant
<Z_76><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If 15% of 40 is greater than 25% of a number by a certain value, and the number is 16, what is the value?<|im_end|>
<|im_start|>assistant
<Z_33><Z_91><Z_71><Z_12><Z_21><Z_84><Z_94><Z_35><Z_101><Z_2><Z_40><ANSWER>

Question: If 15% of 40 is greater than 25% of a number by a certain value, and the number is 16, what is the value?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a division sum, the remainder is 0. A student mistook the divisor by 12 instead of 21 and obtained some quotient. The correct quotient is 36. What quotient did the student obtain by mistake?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a division sum, the remainder is 0. A student mistook the divisor by 12 instead of 21 and obtained some quotient. The correct quotient is 36. What quotient did the student obtain by mistake?<|im_end|>
<|im_start|>assistant
<Z_94><Z_110><Z_43><Z_64><Z_58><Z_99><Z_114><Z_80><Z_52><Z_88><Z_22><Z_119><Z_53><Z_93><Z_90><Z_91><Z_6><Z_118><Z_72><Z_54><Z_75><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a division sum, the remainder is 0. A student mistook the divisor by 12 instead of 21 and obtained some quotient. The correct quotient is 36. What quotient did the student obtain by mistake?<|im_end|>
<|im_start|>assistant
<Z_113><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a division sum, the remainder is 0. A student mistook the divisor by 12 instead of 21 and obtained some quotient. The correct quotient is 36. What quotient did the student obtain by mistake?<|im_end|>
<|im_start|>assistant
<Z_49><Z_123><Z_109><Z_111><Z_50><Z_20><Z_19><Z_6><Z_71><Z_21><Z_105><Z_69><Z_76><Z_66><Z_0><Z_47><Z_75><Z_111><Z_10><Z_66><Z_50><ANSWER>

Question: In a division sum, the remainder is 0. A student mistook the divisor by 12 instead of 21 and obtained some quotient. The correct quotient is 36. What quotient did the student obtain by mistake?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tickets cost 4 dollars for students, and 6 dollars for general admission. A certain number of tickets were sold and 2876 dollars were collected. If 388 general admission tickets were sold, how many total tickets were sold?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tickets cost 4 dollars for students, and 6 dollars for general admission. A certain number of tickets were sold and 2876 dollars were collected. If 388 general admission tickets were sold, how many total tickets were sold?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tickets cost 4 dollars for students, and 6 dollars for general admission. A certain number of tickets were sold and 2876 dollars were collected. If 388 general admission tickets were sold, how many total tickets were sold?<|im_end|>
<|im_start|>assistant
<Z_59><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tickets cost 4 dollars for students, and 6 dollars for general admission. A certain number of tickets were sold and 2876 dollars were collected. If 388 general admission tickets were sold, how many total tickets were sold?<|im_end|>
<|im_start|>assistant
<Z_55><ANSWER>

Question: Tickets cost 4 dollars for students, and 6 dollars for general admission. A certain number of tickets were sold and 2876 dollars were collected. If 388 general admission tickets were sold, how many total tickets were sold?