<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Among the following propositions: \\
(1) If $m > 0$, then the equation $x^{2}-x+m=0$ has real roots; \\
(2) The converse of the proposition "If $x > 1, y > 1$, then $x+y > 2$"; \\
(3) The negation of "For all $x$ in $\{x | -2 < x < 4\}$, $|x-2| < 3$"; \\
(4) $\Delta > 0$ is a necessary and sufficient condition for a quadratic equation $ax^{2}+bx+c=0$ to have one positive root and one negative root. \\
The true propositions are \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Among the following propositions: \\
(1) If $m > 0$, then the equation $x^{2}-x+m=0$ has real roots; \\
(2) The converse of the proposition "If $x > 1, y > 1$, then $x+y > 2$"; \\
(3) The negation of "For all $x$ in $\{x | -2 < x < 4\}$, $|x-2| < 3$"; \\
(4) $\Delta > 0$ is a necessary and sufficient condition for a quadratic equation $ax^{2}+bx+c=0$ to have one positive root and one negative root. \\
The true propositions are \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_477><Z_502><Z_111><Z_468><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Among the following propositions: \\
(1) If $m > 0$, then the equation $x^{2}-x+m=0$ has real roots; \\
(2) The converse of the proposition "If $x > 1, y > 1$, then $x+y > 2$"; \\
(3) The negation of "For all $x$ in $\{x | -2 < x < 4\}$, $|x-2| < 3$"; \\
(4) $\Delta > 0$ is a necessary and sufficient condition for a quadratic equation $ax^{2}+bx+c=0$ to have one positive root and one negative root. \\
The true propositions are \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_28><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Among the following propositions: \\
(1) If $m > 0$, then the equation $x^{2}-x+m=0$ has real roots; \\
(2) The converse of the proposition "If $x > 1, y > 1$, then $x+y > 2$"; \\
(3) The negation of "For all $x$ in $\{x | -2 < x < 4\}$, $|x-2| < 3$"; \\
(4) $\Delta > 0$ is a necessary and sufficient condition for a quadratic equation $ax^{2}+bx+c=0$ to have one positive root and one negative root. \\
The true propositions are \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.<|im_end|>
<|im_start|>assistant
<Z_198><Z_44><Z_237><Z_182><ANSWER>

Question:
Among the following propositions: \\
(1) If $m > 0$, then the equation $x^{2}-x+m=0$ has real roots; \\
(2) The converse of the proposition "If $x > 1, y > 1$, then $x+y > 2$"; \\
(3) The negation of "For all $x$ in $\{x | -2 < x < 4\}$, $|x-2| < 3$"; \\
(4) $\Delta > 0$ is a necessary and sufficient condition for a quadratic equation $ax^{2}+bx+c=0$ to have one positive root and one negative root. \\
The true propositions are \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The speed of a boat in still water is 15 km/hr and the rate of current is some km/hr. The distance travelled downstream in 24 mins is 7.2 km. What is the rate of the current?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The speed of a boat in still water is 15 km/hr and the rate of current is some km/hr. The distance travelled downstream in 24 mins is 7.2 km. What is the rate of the current?<|im_end|>
<|im_start|>assistant
<Z_477><Z_91><Z_465><Z_484><Z_443><Z_470><Z_445><Z_318><Z_447><Z_48><Z_483><Z_252><Z_325><Z_87><Z_60><Z_213><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The speed of a boat in still water is 15 km/hr and the rate of current is some km/hr. The distance travelled downstream in 24 mins is 7.2 km. What is the rate of the current?<|im_end|>
<|im_start|>assistant
<Z_50><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The speed of a boat in still water is 15 km/hr and the rate of current is some km/hr. The distance travelled downstream in 24 mins is 7.2 km. What is the rate of the current?<|im_end|>
<|im_start|>assistant
<Z_243><Z_347><Z_1><Z_382><Z_412><Z_116><Z_232><Z_8><Z_153><Z_249><Z_345><Z_277><Z_322><Z_156><Z_386><Z_363><ANSWER>

Question: The speed of a boat in still water is 15 km/hr and the rate of current is some km/hr. The distance travelled downstream in 24 mins is 7.2 km. What is the rate of the current?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On the reverse sides of 2005 cards, different numbers are written (one on each). In one query, it is allowed to point to any three cards and find out the set of numbers written on them. What is the minimum number of queries needed to determine which number is written on each card?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On the reverse sides of 2005 cards, different numbers are written (one on each). In one query, it is allowed to point to any three cards and find out the set of numbers written on them. What is the minimum number of queries needed to determine which number is written on each card?<|im_end|>
<|im_start|>assistant
<Z_24><Z_87><Z_116><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On the reverse sides of 2005 cards, different numbers are written (one on each). In one query, it is allowed to point to any three cards and find out the set of numbers written on them. What is the minimum number of queries needed to determine which number is written on each card?<|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
On the reverse sides of 2005 cards, different numbers are written (one on each). In one query, it is allowed to point to any three cards and find out the set of numbers written on them. What is the minimum number of queries needed to determine which number is written on each card?<|im_end|>
<|im_start|>assistant
<Z_263><Z_180><Z_414><ANSWER>

Question: On the reverse sides of 2005 cards, different numbers are written (one on each). In one query, it is allowed to point to any three cards and find out the set of numbers written on them. What is the minimum number of queries needed to determine which number is written on each card?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain factory produces a product with a daily cost $C$ (unit: ten thousand yuan) related to the daily output $x$ (unit: tons) by the function $C = 3 + x$. The daily sales revenue $S$ (unit: ten thousand yuan) is related to the daily output $x$ by the function $S = \begin{cases}  3x + \frac{k}{x - 8} + 5, & \text{if } 0 < x < 6 \\ 14, & \text{if } x \geq 6 \end{cases}$. It is known that the daily profit $L = S - C$, and when $x = 2$, $L = 3$.
1. Find the value of $k$;
2. Determine the daily output in tons that maximizes the daily profit and calculate this maximum value.<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain factory produces a product with a daily cost $C$ (unit: ten thousand yuan) related to the daily output $x$ (unit: tons) by the function $C = 3 + x$. The daily sales revenue $S$ (unit: ten thousand yuan) is related to the daily output $x$ by the function $S = \begin{cases}  3x + \frac{k}{x - 8} + 5, & \text{if } 0 < x < 6 \\ 14, & \text{if } x \geq 6 \end{cases}$. It is known that the daily profit $L = S - C$, and when $x = 2$, $L = 3$.
1. Find the value of $k$;
2. Determine the daily output in tons that maximizes the daily profit and calculate this maximum value.<|im_end|>
<|im_start|>assistant
<Z_24><Z_224><Z_84><Z_503><Z_201><Z_460><Z_143><Z_209><Z_89><Z_469><Z_250><Z_67><Z_400><Z_140><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain factory produces a product with a daily cost $C$ (unit: ten thousand yuan) related to the daily output $x$ (unit: tons) by the function $C = 3 + x$. The daily sales revenue $S$ (unit: ten thousand yuan) is related to the daily output $x$ by the function $S = \begin{cases}  3x + \frac{k}{x - 8} + 5, & \text{if } 0 < x < 6 \\ 14, & \text{if } x \geq 6 \end{cases}$. It is known that the daily profit $L = S - C$, and when $x = 2$, $L = 3$.
1. Find the value of $k$;
2. Determine the daily output in tons that maximizes the daily profit and calculate this maximum value.<|im_end|>
<|im_start|>assistant
<Z_80><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain factory produces a product with a daily cost $C$ (unit: ten thousand yuan) related to the daily output $x$ (unit: tons) by the function $C = 3 + x$. The daily sales revenue $S$ (unit: ten thousand yuan) is related to the daily output $x$ by the function $S = \begin{cases}  3x + \frac{k}{x - 8} + 5, & \text{if } 0 < x < 6 \\ 14, & \text{if } x \geq 6 \end{cases}$. It is known that the daily profit $L = S - C$, and when $x = 2$, $L = 3$.
1. Find the value of $k$;
2. Determine the daily output in tons that maximizes the daily profit and calculate this maximum value.<|im_end|>
<|im_start|>assistant
<Z_347><Z_207><Z_484><Z_55><Z_392><Z_490><Z_227><Z_503><Z_468><Z_74><Z_400><Z_277><Z_306><Z_511><ANSWER>

Question:
A certain factory produces a product with a daily cost $C$ (unit: ten thousand yuan) related to the daily output $x$ (unit: tons) by the function $C = 3 + x$. The daily sales revenue $S$ (unit: ten thousand yuan) is related to the daily output $x$ by the function $S = \begin{cases}  3x + \frac{k}{x - 8} + 5, & \text{if } 0 < x < 6 \\ 14, & \text{if } x \geq 6 \end{cases}$. It is known that the daily profit $L = S - C$, and when $x = 2$, $L = 3$.
1. Find the value of $k$;
2. Determine the daily output in tons that maximizes the daily profit and calculate this maximum value.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Four faucets fill a 120-gallon tub in 8 minutes. How long, in seconds, does it take eight faucets to fill a 30-gallon tub?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Four faucets fill a 120-gallon tub in 8 minutes. How long, in seconds, does it take eight faucets to fill a 30-gallon tub?<|im_end|>
<|im_start|>assistant
<Z_24><Z_425><Z_202><Z_155><Z_434><Z_227><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Four faucets fill a 120-gallon tub in 8 minutes. How long, in seconds, does it take eight faucets to fill a 30-gallon tub?<|im_end|>
<|im_start|>assistant
<Z_312><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Four faucets fill a 120-gallon tub in 8 minutes. How long, in seconds, does it take eight faucets to fill a 30-gallon tub?<|im_end|>
<|im_start|>assistant
<Z_402><Z_498><Z_231><Z_122><Z_470><Z_145><ANSWER>

Question: Four faucets fill a 120-gallon tub in 8 minutes. How long, in seconds, does it take eight faucets to fill a 30-gallon tub?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rationalize the denominator of $\frac{5}{3\sqrt[3]{7}}$. The answer can be written in the form $\frac{A\sqrt[3]{B}}{C}$, where $A$, $B$, and $C$ are integers, $C$ is positive, and $B$ is not divisible by the cube of any prime. Find $A+B+C$.<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rationalize the denominator of $\frac{5}{3\sqrt[3]{7}}$. The answer can be written in the form $\frac{A\sqrt[3]{B}}{C}$, where $A$, $B$, and $C$ are integers, $C$ is positive, and $B$ is not divisible by the cube of any prime. Find $A+B+C$.<|im_end|>
<|im_start|>assistant
<Z_24><Z_276><Z_490><Z_48><Z_68><Z_56><Z_403><Z_200><Z_443><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rationalize the denominator of $\frac{5}{3\sqrt[3]{7}}$. The answer can be written in the form $\frac{A\sqrt[3]{B}}{C}$, where $A$, $B$, and $C$ are integers, $C$ is positive, and $B$ is not divisible by the cube of any prime. Find $A+B+C$.<|im_end|>
<|im_start|>assistant
<Z_484><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rationalize the denominator of $\frac{5}{3\sqrt[3]{7}}$. The answer can be written in the form $\frac{A\sqrt[3]{B}}{C}$, where $A$, $B$, and $C$ are integers, $C$ is positive, and $B$ is not divisible by the cube of any prime. Find $A+B+C$.<|im_end|>
<|im_start|>assistant
<Z_6><Z_294><Z_297><Z_35><Z_180><Z_497><Z_270><Z_57><Z_6><ANSWER>

Question: Rationalize the denominator of $\frac{5}{3\sqrt[3]{7}}$. The answer can be written in the form $\frac{A\sqrt[3]{B}}{C}$, where $A$, $B$, and $C$ are integers, $C$ is positive, and $B$ is not divisible by the cube of any prime. Find $A+B+C$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What least number must be subtracted from a certain number so that the remaining number is divisible by 12? The answer is 7. What is the original number?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What least number must be subtracted from a certain number so that the remaining number is divisible by 12? The answer is 7. What is the original number?<|im_end|>
<|im_start|>assistant
<Z_369><Z_161><Z_267><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What least number must be subtracted from a certain number so that the remaining number is divisible by 12? The answer is 7. What is the original number?<|im_end|>
<|im_start|>assistant
<Z_128><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What least number must be subtracted from a certain number so that the remaining number is divisible by 12? The answer is 7. What is the original number?<|im_end|>
<|im_start|>assistant
<Z_451><Z_124><Z_476><ANSWER>

Question: What least number must be subtracted from a certain number so that the remaining number is divisible by 12? The answer is 7. What is the original number?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The side lengths of a triangle are 9 cm, 40 cm, and 41 cm. Calculate the area of this triangle in square centimeters.<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The side lengths of a triangle are 9 cm, 40 cm, and 41 cm. Calculate the area of this triangle in square centimeters.<|im_end|>
<|im_start|>assistant
<Z_24><Z_278><Z_89><Z_293><Z_445><Z_305><Z_336><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The side lengths of a triangle are 9 cm, 40 cm, and 41 cm. Calculate the area of this triangle in square centimeters.<|im_end|>
<|im_start|>assistant
<Z_178><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The side lengths of a triangle are 9 cm, 40 cm, and 41 cm. Calculate the area of this triangle in square centimeters.<|im_end|>
<|im_start|>assistant
<Z_494><Z_236><Z_402><Z_175><Z_310><Z_166><Z_17><ANSWER>

Question: The side lengths of a triangle are 9 cm, 40 cm, and 41 cm. Calculate the area of this triangle in square centimeters.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If \( x \) is a real number, find \( (x+2)^2 + 2(x+2)(4-x) + (4-x)^2 \).<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If \( x \) is a real number, find \( (x+2)^2 + 2(x+2)(4-x) + (4-x)^2 \).<|im_end|>
<|im_start|>assistant
<Z_24><Z_87><Z_456><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If \( x \) is a real number, find \( (x+2)^2 + 2(x+2)(4-x) + (4-x)^2 \).<|im_end|>
<|im_start|>assistant
<Z_310><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If \( x \) is a real number, find \( (x+2)^2 + 2(x+2)(4-x) + (4-x)^2 \).<|im_end|>
<|im_start|>assistant
<Z_319><Z_52><Z_414><ANSWER>

Question: If \( x \) is a real number, find \( (x+2)^2 + 2(x+2)(4-x) + (4-x)^2 \).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ten boys brought 15 popsicle sticks each. Twelve girls brought 12 popsicle sticks each. How many fewer popsicle sticks did the girls bring than the boys?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ten boys brought 15 popsicle sticks each. Twelve girls brought 12 popsicle sticks each. How many fewer popsicle sticks did the girls bring than the boys?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ten boys brought 15 popsicle sticks each. Twelve girls brought 12 popsicle sticks each. How many fewer popsicle sticks did the girls bring than the boys?<|im_end|>
<|im_start|>assistant
<Z_214><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ten boys brought 15 popsicle sticks each. Twelve girls brought 12 popsicle sticks each. How many fewer popsicle sticks did the girls bring than the boys?<|im_end|>
<|im_start|>assistant
<Z_32><ANSWER>

Question: Ten boys brought 15 popsicle sticks each. Twelve girls brought 12 popsicle sticks each. How many fewer popsicle sticks did the girls bring than the boys?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Call a set of positive integers "conspiratorial" if no three of them are pairwise relatively prime. What is the largest number of elements in any "conspiratorial" subset of the integers  $1$  to  $16$ ?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Call a set of positive integers "conspiratorial" if no three of them are pairwise relatively prime. What is the largest number of elements in any "conspiratorial" subset of the integers  $1$  to  $16$ ?<|im_end|>
<|im_start|>assistant
<Z_477><Z_485><Z_494><Z_61><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Call a set of positive integers "conspiratorial" if no three of them are pairwise relatively prime. What is the largest number of elements in any "conspiratorial" subset of the integers  $1$  to  $16$ ?<|im_end|>
<|im_start|>assistant
<Z_335><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Call a set of positive integers "conspiratorial" if no three of them are pairwise relatively prime. What is the largest number of elements in any "conspiratorial" subset of the integers  $1$  to  $16$ ?<|im_end|>
<|im_start|>assistant
<Z_36><Z_199><Z_482><Z_201><ANSWER>

Question: Call a set of positive integers "conspiratorial" if no three of them are pairwise relatively prime. What is the largest number of elements in any "conspiratorial" subset of the integers  $1$  to  $16$ ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of the following expression: $3 - 8 + 11 - 16 + 19 - \cdots - 62 + 65 - 68 + 71$?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of the following expression: $3 - 8 + 11 - 16 + 19 - \cdots - 62 + 65 - 68 + 71$?<|im_end|>
<|im_start|>assistant
<Z_369><Z_169><Z_483><Z_86><Z_276><Z_329><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of the following expression: $3 - 8 + 11 - 16 + 19 - \cdots - 62 + 65 - 68 + 71$?<|im_end|>
<|im_start|>assistant
<Z_352><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of the following expression: $3 - 8 + 11 - 16 + 19 - \cdots - 62 + 65 - 68 + 71$?<|im_end|>
<|im_start|>assistant
<Z_295><Z_260><Z_79><Z_414><Z_474><Z_395><ANSWER>

Question: What is the value of the following expression: $3 - 8 + 11 - 16 + 19 - \cdots - 62 + 65 - 68 + 71$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the product of the digits of the largest integer that adheres to the following properties:
$\bullet$ The sum of the squares of its digits is $85.$
$\bullet$ Each digit is smaller than the one to its left.<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the product of the digits of the largest integer that adheres to the following properties:
$\bullet$ The sum of the squares of its digits is $85.$
$\bullet$ Each digit is smaller than the one to its left.<|im_end|>
<|im_start|>assistant
<Z_477><Z_155><Z_273><Z_351><Z_284><Z_310><Z_276><Z_425><Z_151><Z_462><Z_318><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the product of the digits of the largest integer that adheres to the following properties:
$\bullet$ The sum of the squares of its digits is $85.$
$\bullet$ Each digit is smaller than the one to its left.<|im_end|>
<|im_start|>assistant
<Z_358><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the product of the digits of the largest integer that adheres to the following properties:
$\bullet$ The sum of the squares of its digits is $85.$
$\bullet$ Each digit is smaller than the one to its left.<|im_end|>
<|im_start|>assistant
<Z_449><Z_391><Z_362><Z_95><Z_73><Z_170><Z_170><Z_337><Z_395><Z_371><Z_300><ANSWER>

Question:
Determine the product of the digits of the largest integer that adheres to the following properties:
$\bullet$ The sum of the squares of its digits is $85.$
$\bullet$ Each digit is smaller than the one to its left.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jack walked up a hill at a speed of $(x^2-11x-22)$ miles per hour. Meanwhile, Jill walked a total distance of $(x^2-3x-54)$ miles in $(x+6)$ hours. If Jack and Jill walked at the same speed, what is that speed, in miles per hour?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jack walked up a hill at a speed of $(x^2-11x-22)$ miles per hour. Meanwhile, Jill walked a total distance of $(x^2-3x-54)$ miles in $(x+6)$ hours. If Jack and Jill walked at the same speed, what is that speed, in miles per hour?<|im_end|>
<|im_start|>assistant
<Z_369><Z_486><Z_209><Z_209><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jack walked up a hill at a speed of $(x^2-11x-22)$ miles per hour. Meanwhile, Jill walked a total distance of $(x^2-3x-54)$ miles in $(x+6)$ hours. If Jack and Jill walked at the same speed, what is that speed, in miles per hour?<|im_end|>
<|im_start|>assistant
<Z_178><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jack walked up a hill at a speed of $(x^2-11x-22)$ miles per hour. Meanwhile, Jill walked a total distance of $(x^2-3x-54)$ miles in $(x+6)$ hours. If Jack and Jill walked at the same speed, what is that speed, in miles per hour?<|im_end|>
<|im_start|>assistant
<Z_273><Z_89><Z_313><Z_380><ANSWER>

Question: Jack walked up a hill at a speed of $(x^2-11x-22)$ miles per hour. Meanwhile, Jill walked a total distance of $(x^2-3x-54)$ miles in $(x+6)$ hours. If Jack and Jill walked at the same speed, what is that speed, in miles per hour?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Inside a circle, 16 radii of this circle and 10 circles with the same center as the circle are drawn. Into how many regions do the radii and circles divide the circle?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Inside a circle, 16 radii of this circle and 10 circles with the same center as the circle are drawn. Into how many regions do the radii and circles divide the circle?<|im_end|>
<|im_start|>assistant
<Z_477><Z_462><Z_352><Z_83><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Inside a circle, 16 radii of this circle and 10 circles with the same center as the circle are drawn. Into how many regions do the radii and circles divide the circle?<|im_end|>
<|im_start|>assistant
<Z_123><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Inside a circle, 16 radii of this circle and 10 circles with the same center as the circle are drawn. Into how many regions do the radii and circles divide the circle?<|im_end|>
<|im_start|>assistant
<Z_92><Z_456><Z_163><Z_356><ANSWER>

Question: Inside a circle, 16 radii of this circle and 10 circles with the same center as the circle are drawn. Into how many regions do the radii and circles divide the circle?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Compute $2+5\cdot3^2-4\cdot2+7\cdot3\div3$<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Compute $2+5\cdot3^2-4\cdot2+7\cdot3\div3$<|im_end|>
<|im_start|>assistant
<Z_24><Z_348><Z_322><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Compute $2+5\cdot3^2-4\cdot2+7\cdot3\div3$<|im_end|>
<|im_start|>assistant
<Z_152><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Compute $2+5\cdot3^2-4\cdot2+7\cdot3\div3$<|im_end|>
<|im_start|>assistant
<Z_508><Z_242><Z_434><ANSWER>

Question: Compute $2+5\cdot3^2-4\cdot2+7\cdot3\div3$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On Monday at work, Emily produces \( w \) widgets per hour and works for \( t \) hours. On Tuesday, feeling more tired, Emily decides to produce 6 more widgets per hour but works 3 hours less. If \( w = 2t \), how many more widgets does Emily produce on Monday compared to Tuesday?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On Monday at work, Emily produces \( w \) widgets per hour and works for \( t \) hours. On Tuesday, feeling more tired, Emily decides to produce 6 more widgets per hour but works 3 hours less. If \( w = 2t \), how many more widgets does Emily produce on Monday compared to Tuesday?<|im_end|>
<|im_start|>assistant
<Z_369><Z_448><Z_511><Z_454><Z_335><Z_351><Z_472><Z_244><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On Monday at work, Emily produces \( w \) widgets per hour and works for \( t \) hours. On Tuesday, feeling more tired, Emily decides to produce 6 more widgets per hour but works 3 hours less. If \( w = 2t \), how many more widgets does Emily produce on Monday compared to Tuesday?<|im_end|>
<|im_start|>assistant
<Z_349><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
On Monday at work, Emily produces \( w \) widgets per hour and works for \( t \) hours. On Tuesday, feeling more tired, Emily decides to produce 6 more widgets per hour but works 3 hours less. If \( w = 2t \), how many more widgets does Emily produce on Monday compared to Tuesday?<|im_end|>
<|im_start|>assistant
<Z_426><Z_365><Z_245><Z_335><Z_506><Z_429><Z_307><Z_348><ANSWER>

Question: On Monday at work, Emily produces \( w \) widgets per hour and works for \( t \) hours. On Tuesday, feeling more tired, Emily decides to produce 6 more widgets per hour but works 3 hours less. If \( w = 2t \), how many more widgets does Emily produce on Monday compared to Tuesday?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A candidate who gets 30% of the marks fails by 60 marks. Another candidate who gets 45% marks gets a certain number of marks more than necessary for passing. The number of marks for passing is approximately 240. How many more marks does the second candidate get than necessary for passing?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A candidate who gets 30% of the marks fails by 60 marks. Another candidate who gets 45% marks gets a certain number of marks more than necessary for passing. The number of marks for passing is approximately 240. How many more marks does the second candidate get than necessary for passing?<|im_end|>
<|im_start|>assistant
<Z_369><Z_425><Z_322><Z_64><Z_124><Z_359><Z_246><Z_502><Z_100><Z_393><Z_501><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A candidate who gets 30% of the marks fails by 60 marks. Another candidate who gets 45% marks gets a certain number of marks more than necessary for passing. The number of marks for passing is approximately 240. How many more marks does the second candidate get than necessary for passing?<|im_end|>
<|im_start|>assistant
<Z_18><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A candidate who gets 30% of the marks fails by 60 marks. Another candidate who gets 45% marks gets a certain number of marks more than necessary for passing. The number of marks for passing is approximately 240. How many more marks does the second candidate get than necessary for passing?<|im_end|>
<|im_start|>assistant
<Z_487><Z_230><Z_54><Z_12><Z_504><Z_225><Z_262><Z_45><Z_76><Z_92><Z_434><ANSWER>

Question: A candidate who gets 30% of the marks fails by 60 marks. Another candidate who gets 45% marks gets a certain number of marks more than necessary for passing. The number of marks for passing is approximately 240. How many more marks does the second candidate get than necessary for passing?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average weight of a, b and c is 45 kg. If the average weight of a and b is 40 kg and that of b and c is 43 kg, what is the weight of b?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average weight of a, b and c is 45 kg. If the average weight of a and b is 40 kg and that of b and c is 43 kg, what is the weight of b?<|im_end|>
<|im_start|>assistant
<Z_477><Z_214><Z_289><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average weight of a, b and c is 45 kg. If the average weight of a and b is 40 kg and that of b and c is 43 kg, what is the weight of b?<|im_end|>
<|im_start|>assistant
<Z_309><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The average weight of a, b and c is 45 kg. If the average weight of a and b is 40 kg and that of b and c is 43 kg, what is the weight of b?<|im_end|>
<|im_start|>assistant
<Z_8><Z_182><Z_453><ANSWER>

Question: The average weight of a, b and c is 45 kg. If the average weight of a and b is 40 kg and that of b and c is 43 kg, what is the weight of b?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A triangle has three different integer side lengths and a perimeter of 30 units. What is the maximum length of any one side?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A triangle has three different integer side lengths and a perimeter of 30 units. What is the maximum length of any one side?<|im_end|>
<|im_start|>assistant
<Z_477><Z_509><Z_176><Z_32><Z_499><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A triangle has three different integer side lengths and a perimeter of 30 units. What is the maximum length of any one side?<|im_end|>
<|im_start|>assistant
<Z_217><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A triangle has three different integer side lengths and a perimeter of 30 units. What is the maximum length of any one side?<|im_end|>
<|im_start|>assistant
<Z_12><Z_302><Z_176><Z_260><Z_342><ANSWER>

Question: A triangle has three different integer side lengths and a perimeter of 30 units. What is the maximum length of any one side?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the xy-plane, a triangle has vertices (0,0), (4,0), and (4,10). If a point (a, b) is selected at random from the triangular region, the probability that a - b > 0 is a certain value. What is that probability value?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the xy-plane, a triangle has vertices (0,0), (4,0), and (4,10). If a point (a, b) is selected at random from the triangular region, the probability that a - b > 0 is a certain value. What is that probability value?<|im_end|>
<|im_start|>assistant
<Z_369><Z_418><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the xy-plane, a triangle has vertices (0,0), (4,0), and (4,10). If a point (a, b) is selected at random from the triangular region, the probability that a - b > 0 is a certain value. What is that probability value?<|im_end|>
<|im_start|>assistant
<Z_476><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the xy-plane, a triangle has vertices (0,0), (4,0), and (4,10). If a point (a, b) is selected at random from the triangular region, the probability that a - b > 0 is a certain value. What is that probability value?<|im_end|>
<|im_start|>assistant
<Z_4><Z_32><ANSWER>

Question: In the xy-plane, a triangle has vertices (0,0), (4,0), and (4,10). If a point (a, b) is selected at random from the triangular region, the probability that a - b > 0 is a certain value. What is that probability value?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The force needed to loosen a bolt varies inversely with the length of the handle of the wrench used. A wrench with a handle length of 12 inches requires 450 pounds of force to loosen a certain bolt. If another bolt, requiring slightly less force due to its material, uses a wrench of 18 inches, how many pounds of force are required to loosen it?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The force needed to loosen a bolt varies inversely with the length of the handle of the wrench used. A wrench with a handle length of 12 inches requires 450 pounds of force to loosen a certain bolt. If another bolt, requiring slightly less force due to its material, uses a wrench of 18 inches, how many pounds of force are required to loosen it?<|im_end|>
<|im_start|>assistant
<Z_477><Z_214><Z_118><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The force needed to loosen a bolt varies inversely with the length of the handle of the wrench used. A wrench with a handle length of 12 inches requires 450 pounds of force to loosen a certain bolt. If another bolt, requiring slightly less force due to its material, uses a wrench of 18 inches, how many pounds of force are required to loosen it?<|im_end|>
<|im_start|>assistant
<Z_169><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The force needed to loosen a bolt varies inversely with the length of the handle of the wrench used. A wrench with a handle length of 12 inches requires 450 pounds of force to loosen a certain bolt. If another bolt, requiring slightly less force due to its material, uses a wrench of 18 inches, how many pounds of force are required to loosen it?<|im_end|>
<|im_start|>assistant
<Z_481><Z_168><Z_163><ANSWER>

Question: The force needed to loosen a bolt varies inversely with the length of the handle of the wrench used. A wrench with a handle length of 12 inches requires 450 pounds of force to loosen a certain bolt. If another bolt, requiring slightly less force due to its material, uses a wrench of 18 inches, how many pounds of force are required to loosen it?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Solve the equation $\sqrt{7 + 3z} = 8$.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Solve the equation $\sqrt{7 + 3z} = 8$.<|im_end|>
<|im_start|>assistant
<Z_369><Z_348><Z_407><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Solve the equation $\sqrt{7 + 3z} = 8$.<|im_end|>
<|im_start|>assistant
<Z_156><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Solve the equation $\sqrt{7 + 3z} = 8$.<|im_end|>
<|im_start|>assistant
<Z_117><Z_174><Z_91><ANSWER>

Question: Solve the equation $\sqrt{7 + 3z} = 8$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a certain colony of bacteria, the number of bacteria doubles every day. The colony starts with 3 bacteria, and has 6 at the end of day 1, 12 at the end of day 2, and so on. What is the number of the first day which ends with the colony having more than 100 bacteria?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a certain colony of bacteria, the number of bacteria doubles every day. The colony starts with 3 bacteria, and has 6 at the end of day 1, 12 at the end of day 2, and so on. What is the number of the first day which ends with the colony having more than 100 bacteria?<|im_end|>
<|im_start|>assistant
<Z_369><Z_445><Z_52><Z_400><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a certain colony of bacteria, the number of bacteria doubles every day. The colony starts with 3 bacteria, and has 6 at the end of day 1, 12 at the end of day 2, and so on. What is the number of the first day which ends with the colony having more than 100 bacteria?<|im_end|>
<|im_start|>assistant
<Z_381><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a certain colony of bacteria, the number of bacteria doubles every day. The colony starts with 3 bacteria, and has 6 at the end of day 1, 12 at the end of day 2, and so on. What is the number of the first day which ends with the colony having more than 100 bacteria?<|im_end|>
<|im_start|>assistant
<Z_395><Z_211><Z_449><Z_357><ANSWER>

Question: In a certain colony of bacteria, the number of bacteria doubles every day. The colony starts with 3 bacteria, and has 6 at the end of day 1, 12 at the end of day 2, and so on. What is the number of the first day which ends with the colony having more than 100 bacteria?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Elsa's hockey team just made the playoffs along with two other teams. They make the playoffs by having the top three highest points for their records. Teams get 2 points for a win, 1 point for a tie, and zero points for a loss. The first-place team has 12 wins and 4 ties. The second-place team has 13 wins and 1 tie. Elsa's team has 8 wins and 10 ties. What is the average number of points for the playoff teams?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Elsa's hockey team just made the playoffs along with two other teams. They make the playoffs by having the top three highest points for their records. Teams get 2 points for a win, 1 point for a tie, and zero points for a loss. The first-place team has 12 wins and 4 ties. The second-place team has 13 wins and 1 tie. Elsa's team has 8 wins and 10 ties. What is the average number of points for the playoff teams?<|im_end|>
<|im_start|>assistant
<Z_369><Z_264><Z_129><Z_391><Z_465><Z_250><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Elsa's hockey team just made the playoffs along with two other teams. They make the playoffs by having the top three highest points for their records. Teams get 2 points for a win, 1 point for a tie, and zero points for a loss. The first-place team has 12 wins and 4 ties. The second-place team has 13 wins and 1 tie. Elsa's team has 8 wins and 10 ties. What is the average number of points for the playoff teams?<|im_end|>
<|im_start|>assistant
<Z_267><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Elsa's hockey team just made the playoffs along with two other teams. They make the playoffs by having the top three highest points for their records. Teams get 2 points for a win, 1 point for a tie, and zero points for a loss. The first-place team has 12 wins and 4 ties. The second-place team has 13 wins and 1 tie. Elsa's team has 8 wins and 10 ties. What is the average number of points for the playoff teams?<|im_end|>
<|im_start|>assistant
<Z_175><Z_315><Z_429><Z_262><Z_176><Z_442><ANSWER>

Question: Elsa's hockey team just made the playoffs along with two other teams. They make the playoffs by having the top three highest points for their records. Teams get 2 points for a win, 1 point for a tie, and zero points for a loss. The first-place team has 12 wins and 4 ties. The second-place team has 13 wins and 1 tie. Elsa's team has 8 wins and 10 ties. What is the average number of points for the playoff teams?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
As $p$ ranges over the primes greater than $7$, how many different remainders can $p^2$ leave upon division by $210$?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
As $p$ ranges over the primes greater than $7$, how many different remainders can $p^2$ leave upon division by $210$?<|im_end|>
<|im_start|>assistant
<Z_369><Z_195><Z_403><Z_329><Z_437><Z_69><Z_414><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
As $p$ ranges over the primes greater than $7$, how many different remainders can $p^2$ leave upon division by $210$?<|im_end|>
<|im_start|>assistant
<Z_41><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
As $p$ ranges over the primes greater than $7$, how many different remainders can $p^2$ leave upon division by $210$?<|im_end|>
<|im_start|>assistant
<Z_44><Z_327><Z_282><Z_148><Z_62><Z_415><Z_344><ANSWER>

Question: As $p$ ranges over the primes greater than $7$, how many different remainders can $p^2$ leave upon division by $210$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the arithmetic mean of the prime numbers in this list: 24, 25, 27, 29, 31.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the arithmetic mean of the prime numbers in this list: 24, 25, 27, 29, 31.<|im_end|>
<|im_start|>assistant
<Z_477><Z_293><Z_174><Z_102><Z_199><Z_113><Z_129><Z_53><Z_139><Z_109><Z_68><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the arithmetic mean of the prime numbers in this list: 24, 25, 27, 29, 31.<|im_end|>
<|im_start|>assistant
<Z_374><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the arithmetic mean of the prime numbers in this list: 24, 25, 27, 29, 31.<|im_end|>
<|im_start|>assistant
<Z_170><Z_501><Z_105><Z_278><Z_154><Z_372><Z_54><Z_499><Z_387><Z_349><Z_271><ANSWER>

Question: Find the arithmetic mean of the prime numbers in this list: 24, 25, 27, 29, 31.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the sequence $\left\{a_{n}\right\}$, if $a_{n}^{2}-a_{n-1}^{2}=p$ (where $n \geq 2, n \in \mathbf{N^{*}}$, and $p$ is a constant), then $\left\{a_{n}\right\}$ is called an "equal variance sequence." Below are the judgments for the "equal variance sequence":

1. The sequence $\left\{(-1)^{n}\right\}$ is an equal variance sequence;
2. If $\left\{a_{n}\right\}$ is an equal variance sequence, then $ \left\{a_{n}^{2}\right\}$ is an arithmetic sequence;
3. If $\left\{a_{n}\right\}$ is an equal variance sequence, then $\left\{a_{k n}\right\}\left(k \in \mathbf{N}^{*}, k\right.$ being a constant) is also an equal variance sequence;
4. If $\left\{a_{n}\right\} $ is both an equal variance sequence and an arithmetic sequence, then this sequence is a constant sequence.

Among them, the correct proposition numbers are $\qquad$ (Fill in all the correct proposition numbers on the line).<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the sequence $\left\{a_{n}\right\}$, if $a_{n}^{2}-a_{n-1}^{2}=p$ (where $n \geq 2, n \in \mathbf{N^{*}}$, and $p$ is a constant), then $\left\{a_{n}\right\}$ is called an "equal variance sequence." Below are the judgments for the "equal variance sequence":

1. The sequence $\left\{(-1)^{n}\right\}$ is an equal variance sequence;
2. If $\left\{a_{n}\right\}$ is an equal variance sequence, then $ \left\{a_{n}^{2}\right\}$ is an arithmetic sequence;
3. If $\left\{a_{n}\right\}$ is an equal variance sequence, then $\left\{a_{k n}\right\}\left(k \in \mathbf{N}^{*}, k\right.$ being a constant) is also an equal variance sequence;
4. If $\left\{a_{n}\right\} $ is both an equal variance sequence and an arithmetic sequence, then this sequence is a constant sequence.

Among them, the correct proposition numbers are $\qquad$ (Fill in all the correct proposition numbers on the line).<|im_end|>
<|im_start|>assistant
<Z_369><Z_279><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the sequence $\left\{a_{n}\right\}$, if $a_{n}^{2}-a_{n-1}^{2}=p$ (where $n \geq 2, n \in \mathbf{N^{*}}$, and $p$ is a constant), then $\left\{a_{n}\right\}$ is called an "equal variance sequence." Below are the judgments for the "equal variance sequence":

1. The sequence $\left\{(-1)^{n}\right\}$ is an equal variance sequence;
2. If $\left\{a_{n}\right\}$ is an equal variance sequence, then $ \left\{a_{n}^{2}\right\}$ is an arithmetic sequence;
3. If $\left\{a_{n}\right\}$ is an equal variance sequence, then $\left\{a_{k n}\right\}\left(k \in \mathbf{N}^{*}, k\right.$ being a constant) is also an equal variance sequence;
4. If $\left\{a_{n}\right\} $ is both an equal variance sequence and an arithmetic sequence, then this sequence is a constant sequence.

Among them, the correct proposition numbers are $\qquad$ (Fill in all the correct proposition numbers on the line).<|im_end|>
<|im_start|>assistant
<Z_433><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the sequence $\left\{a_{n}\right\}$, if $a_{n}^{2}-a_{n-1}^{2}=p$ (where $n \geq 2, n \in \mathbf{N^{*}}$, and $p$ is a constant), then $\left\{a_{n}\right\}$ is called an "equal variance sequence." Below are the judgments for the "equal variance sequence":

1. The sequence $\left\{(-1)^{n}\right\}$ is an equal variance sequence;
2. If $\left\{a_{n}\right\}$ is an equal variance sequence, then $ \left\{a_{n}^{2}\right\}$ is an arithmetic sequence;
3. If $\left\{a_{n}\right\}$ is an equal variance sequence, then $\left\{a_{k n}\right\}\left(k \in \mathbf{N}^{*}, k\right.$ being a constant) is also an equal variance sequence;
4. If $\left\{a_{n}\right\} $ is both an equal variance sequence and an arithmetic sequence, then this sequence is a constant sequence.

Among them, the correct proposition numbers are $\qquad$ (Fill in all the correct proposition numbers on the line).<|im_end|>
<|im_start|>assistant
<Z_200><Z_221><ANSWER>

Question:
In the sequence $\left\{a_{n}\right\}$, if $a_{n}^{2}-a_{n-1}^{2}=p$ (where $n \geq 2, n \in \mathbf{N^{*}}$, and $p$ is a constant), then $\left\{a_{n}\right\}$ is called an "equal variance sequence." Below are the judgments for the "equal variance sequence":

1. The sequence $\left\{(-1)^{n}\right\}$ is an equal variance sequence;
2. If $\left\{a_{n}\right\}$ is an equal variance sequence, then $ \left\{a_{n}^{2}\right\}$ is an arithmetic sequence;
3. If $\left\{a_{n}\right\}$ is an equal variance sequence, then $\left\{a_{k n}\right\}\left(k \in \mathbf{N}^{*}, k\right.$ being a constant) is also an equal variance sequence;
4. If $\left\{a_{n}\right\} $ is both an equal variance sequence and an arithmetic sequence, then this sequence is a constant sequence.

Among them, the correct proposition numbers are $\qquad$ (Fill in all the correct proposition numbers on the line).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train traveling at 72 kmph crosses a platform in 31 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train traveling at 72 kmph crosses a platform in 31 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?<|im_end|>
<|im_start|>assistant
<Z_477><Z_140><Z_118><Z_454><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train traveling at 72 kmph crosses a platform in 31 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?<|im_end|>
<|im_start|>assistant
<Z_399><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A train traveling at 72 kmph crosses a platform in 31 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?<|im_end|>
<|im_start|>assistant
<Z_247><Z_468><Z_353><Z_350><ANSWER>

Question: A train traveling at 72 kmph crosses a platform in 31 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What multiple of 15 is closest to 1987?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What multiple of 15 is closest to 1987?<|im_end|>
<|im_start|>assistant
<Z_369><Z_68><Z_345><Z_456><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What multiple of 15 is closest to 1987?<|im_end|>
<|im_start|>assistant
<Z_413><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What multiple of 15 is closest to 1987?<|im_end|>
<|im_start|>assistant
<Z_416><Z_67><Z_309><Z_326><ANSWER>

Question: What multiple of 15 is closest to 1987?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $f(x) = \dfrac{6x + 2}{x - 2}$, find the value of $f(4)$.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $f(x) = \dfrac{6x + 2}{x - 2}$, find the value of $f(4)$.<|im_end|>
<|im_start|>assistant
<Z_477><Z_386><Z_456><Z_284><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $f(x) = \dfrac{6x + 2}{x - 2}$, find the value of $f(4)$.<|im_end|>
<|im_start|>assistant
<Z_486><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $f(x) = \dfrac{6x + 2}{x - 2}$, find the value of $f(4)$.<|im_end|>
<|im_start|>assistant
<Z_143><Z_51><Z_216><Z_465><ANSWER>

Question: If $f(x) = \dfrac{6x + 2}{x - 2}$, find the value of $f(4)$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Starting at $(0,0),$ an object moves in the coordinate plane via a sequence of steps, each of length one. Each step is left, right, up, or down, all four equally likely. Let $q$ be the probability that the object reaches $(3,1)$ in six or fewer steps. Given that $q$ can be written in the form $m/n,$ where $m$ and $n$ are relatively prime positive integers, find $m+n.$<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Starting at $(0,0),$ an object moves in the coordinate plane via a sequence of steps, each of length one. Each step is left, right, up, or down, all four equally likely. Let $q$ be the probability that the object reaches $(3,1)$ in six or fewer steps. Given that $q$ can be written in the form $m/n,$ where $m$ and $n$ are relatively prime positive integers, find $m+n.$<|im_end|>
<|im_start|>assistant
<Z_477><Z_384><Z_176><Z_240><Z_232><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Starting at $(0,0),$ an object moves in the coordinate plane via a sequence of steps, each of length one. Each step is left, right, up, or down, all four equally likely. Let $q$ be the probability that the object reaches $(3,1)$ in six or fewer steps. Given that $q$ can be written in the form $m/n,$ where $m$ and $n$ are relatively prime positive integers, find $m+n.$<|im_end|>
<|im_start|>assistant
<Z_211><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Starting at $(0,0),$ an object moves in the coordinate plane via a sequence of steps, each of length one. Each step is left, right, up, or down, all four equally likely. Let $q$ be the probability that the object reaches $(3,1)$ in six or fewer steps. Given that $q$ can be written in the form $m/n,$ where $m$ and $n$ are relatively prime positive integers, find $m+n.$<|im_end|>
<|im_start|>assistant
<Z_166><Z_217><Z_235><Z_152><Z_119><ANSWER>

Question: Starting at $(0,0),$ an object moves in the coordinate plane via a sequence of steps, each of length one. Each step is left, right, up, or down, all four equally likely. Let $q$ be the probability that the object reaches $(3,1)$ in six or fewer steps. Given that $q$ can be written in the form $m/n,$ where $m$ and $n$ are relatively prime positive integers, find $m+n.$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
if both 5 ^ 2, 3 ^ 3 and 11 ^ 2 are factors of n x ( 2 ^ 5 ) x ( 6 ^ 2 ) x ( 7 ^ 3 ) x ( 13 ^ 4), what is the smallest possible positive value of n?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
if both 5 ^ 2, 3 ^ 3 and 11 ^ 2 are factors of n x ( 2 ^ 5 ) x ( 6 ^ 2 ) x ( 7 ^ 3 ) x ( 13 ^ 4), what is the smallest possible positive value of n?<|im_end|>
<|im_start|>assistant
<Z_24><Z_309><Z_348><Z_468><Z_491><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
if both 5 ^ 2, 3 ^ 3 and 11 ^ 2 are factors of n x ( 2 ^ 5 ) x ( 6 ^ 2 ) x ( 7 ^ 3 ) x ( 13 ^ 4), what is the smallest possible positive value of n?<|im_end|>
<|im_start|>assistant
<Z_184><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
if both 5 ^ 2, 3 ^ 3 and 11 ^ 2 are factors of n x ( 2 ^ 5 ) x ( 6 ^ 2 ) x ( 7 ^ 3 ) x ( 13 ^ 4), what is the smallest possible positive value of n?<|im_end|>
<|im_start|>assistant
<Z_95><Z_194><Z_479><Z_508><Z_156><ANSWER>

Question: if both 5 ^ 2, 3 ^ 3 and 11 ^ 2 are factors of n x ( 2 ^ 5 ) x ( 6 ^ 2 ) x ( 7 ^ 3 ) x ( 13 ^ 4), what is the smallest possible positive value of n?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the 2011 Zhejiang Province Pilot Module Examination, there were a total of 18 questions. Each examinee was required to choose 6 questions to answer. Examinee A would definitely not choose questions 1, 2, 9, 15, 16, 17, and 18, while Examinee B would definitely not choose questions 3, 9, 15, 16, 17, and 18. Moreover, the 6 questions chosen by A and B had none in common. The total number of ways to select questions that meet these conditions is ______.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the 2011 Zhejiang Province Pilot Module Examination, there were a total of 18 questions. Each examinee was required to choose 6 questions to answer. Examinee A would definitely not choose questions 1, 2, 9, 15, 16, 17, and 18, while Examinee B would definitely not choose questions 3, 9, 15, 16, 17, and 18. Moreover, the 6 questions chosen by A and B had none in common. The total number of ways to select questions that meet these conditions is ______.<|im_end|>
<|im_start|>assistant
<Z_369><Z_321><Z_232><Z_114><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the 2011 Zhejiang Province Pilot Module Examination, there were a total of 18 questions. Each examinee was required to choose 6 questions to answer. Examinee A would definitely not choose questions 1, 2, 9, 15, 16, 17, and 18, while Examinee B would definitely not choose questions 3, 9, 15, 16, 17, and 18. Moreover, the 6 questions chosen by A and B had none in common. The total number of ways to select questions that meet these conditions is ______.<|im_end|>
<|im_start|>assistant
<Z_186><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In the 2011 Zhejiang Province Pilot Module Examination, there were a total of 18 questions. Each examinee was required to choose 6 questions to answer. Examinee A would definitely not choose questions 1, 2, 9, 15, 16, 17, and 18, while Examinee B would definitely not choose questions 3, 9, 15, 16, 17, and 18. Moreover, the 6 questions chosen by A and B had none in common. The total number of ways to select questions that meet these conditions is ______.<|im_end|>
<|im_start|>assistant
<Z_288><Z_433><Z_66><Z_390><ANSWER>

Question: In the 2011 Zhejiang Province Pilot Module Examination, there were a total of 18 questions. Each examinee was required to choose 6 questions to answer. Examinee A would definitely not choose questions 1, 2, 9, 15, 16, 17, and 18, while Examinee B would definitely not choose questions 3, 9, 15, 16, 17, and 18. Moreover, the 6 questions chosen by A and B had none in common. The total number of ways to select questions that meet these conditions is ______.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
We want to cut a cube with edge length of 4 units into 64 smaller cubes with edge length of 1 unit. This can be done with 9 cuts if the resulting pieces are not moved from each other. What is the minimum number of cuts required if we can rearrange the pieces as needed after each cut?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
We want to cut a cube with edge length of 4 units into 64 smaller cubes with edge length of 1 unit. This can be done with 9 cuts if the resulting pieces are not moved from each other. What is the minimum number of cuts required if we can rearrange the pieces as needed after each cut?<|im_end|>
<|im_start|>assistant
<Z_477><Z_507><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
We want to cut a cube with edge length of 4 units into 64 smaller cubes with edge length of 1 unit. This can be done with 9 cuts if the resulting pieces are not moved from each other. What is the minimum number of cuts required if we can rearrange the pieces as needed after each cut?<|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
We want to cut a cube with edge length of 4 units into 64 smaller cubes with edge length of 1 unit. This can be done with 9 cuts if the resulting pieces are not moved from each other. What is the minimum number of cuts required if we can rearrange the pieces as needed after each cut?<|im_end|>
<|im_start|>assistant
<Z_176><Z_490><ANSWER>

Question: We want to cut a cube with edge length of 4 units into 64 smaller cubes with edge length of 1 unit. This can be done with 9 cuts if the resulting pieces are not moved from each other. What is the minimum number of cuts required if we can rearrange the pieces as needed after each cut?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the remainder when \( 2^{2001} \) is divided by \( 2^7 - 1 \)?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the remainder when \( 2^{2001} \) is divided by \( 2^7 - 1 \)?<|im_end|>
<|im_start|>assistant
<Z_24><Z_425><Z_83><Z_502><Z_441><Z_443><Z_227><Z_99><Z_273><Z_443><Z_420><Z_79><Z_174><Z_406><Z_305><Z_321><Z_391><Z_414><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the remainder when \( 2^{2001} \) is divided by \( 2^7 - 1 \)?<|im_end|>
<|im_start|>assistant
<Z_490><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the remainder when \( 2^{2001} \) is divided by \( 2^7 - 1 \)?<|im_end|>
<|im_start|>assistant
<Z_368><Z_422><Z_292><Z_172><Z_88><Z_71><Z_299><Z_74><Z_118><Z_371><Z_478><Z_294><Z_62><Z_253><Z_417><Z_450><Z_122><Z_110><ANSWER>

Question: What is the remainder when \( 2^{2001} \) is divided by \( 2^7 - 1 \)?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Patrick, Manu, and Amy participate in a race. Patrick finishes the race in some time, Manu took 12 more seconds to finish the race, and Amy is twice as fast as Manu. It took Amy 36 seconds to finish the race. How long did it take Patrick to finish the race?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Patrick, Manu, and Amy participate in a race. Patrick finishes the race in some time, Manu took 12 more seconds to finish the race, and Amy is twice as fast as Manu. It took Amy 36 seconds to finish the race. How long did it take Patrick to finish the race?<|im_end|>
<|im_start|>assistant
<Z_369><Z_201><Z_294><Z_460><Z_329><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Patrick, Manu, and Amy participate in a race. Patrick finishes the race in some time, Manu took 12 more seconds to finish the race, and Amy is twice as fast as Manu. It took Amy 36 seconds to finish the race. How long did it take Patrick to finish the race?<|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
Patrick, Manu, and Amy participate in a race. Patrick finishes the race in some time, Manu took 12 more seconds to finish the race, and Amy is twice as fast as Manu. It took Amy 36 seconds to finish the race. How long did it take Patrick to finish the race?<|im_end|>
<|im_start|>assistant
<Z_500><Z_484><Z_334><Z_157><Z_333><ANSWER>

Question: Patrick, Manu, and Amy participate in a race. Patrick finishes the race in some time, Manu took 12 more seconds to finish the race, and Amy is twice as fast as Manu. It took Amy 36 seconds to finish the race. How long did it take Patrick to finish the race?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sara has saved 11 quarters from washing cars. How many cents does Sara have?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sara has saved 11 quarters from washing cars. How many cents does Sara have?<|im_end|>
<|im_start|>assistant
<Z_444><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Sara has saved 11 quarters from washing cars. How many cents does Sara have?<|im_end|>
<|im_start|>assistant
<Z_508><ANSWER>

Question: Sara has saved 11 quarters from washing cars. How many cents does Sara have?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the area of a rectangle whose base is twice the height, and the area is numerically equal to the perimeter.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the area of a rectangle whose base is twice the height, and the area is numerically equal to the perimeter.<|im_end|>
<|im_start|>assistant
<Z_24><Z_276><Z_469><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the area of a rectangle whose base is twice the height, and the area is numerically equal to the perimeter.<|im_end|>
<|im_start|>assistant
<Z_4><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the area of a rectangle whose base is twice the height, and the area is numerically equal to the perimeter.<|im_end|>
<|im_start|>assistant
<Z_361><Z_371><Z_198><ANSWER>

Question: Find the area of a rectangle whose base is twice the height, and the area is numerically equal to the perimeter.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For a project, a builder purchased 7 boxes of bolts with each box containing 11 bolts. He purchased 3 boxes of nuts with each box containing 15 nuts. He ended up finishing the project 6 days early and with 3 bolts and some nuts left over. He used 113 bolts and nuts for the project. How many nuts were left over?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For a project, a builder purchased 7 boxes of bolts with each box containing 11 bolts. He purchased 3 boxes of nuts with each box containing 15 nuts. He ended up finishing the project 6 days early and with 3 bolts and some nuts left over. He used 113 bolts and nuts for the project. How many nuts were left over?<|im_end|>
<|im_start|>assistant
<Z_369><Z_399><Z_334><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For a project, a builder purchased 7 boxes of bolts with each box containing 11 bolts. He purchased 3 boxes of nuts with each box containing 15 nuts. He ended up finishing the project 6 days early and with 3 bolts and some nuts left over. He used 113 bolts and nuts for the project. How many nuts were left over?<|im_end|>
<|im_start|>assistant
<Z_504><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For a project, a builder purchased 7 boxes of bolts with each box containing 11 bolts. He purchased 3 boxes of nuts with each box containing 15 nuts. He ended up finishing the project 6 days early and with 3 bolts and some nuts left over. He used 113 bolts and nuts for the project. How many nuts were left over?<|im_end|>
<|im_start|>assistant
<Z_80><Z_0><Z_244><ANSWER>

Question: For a project, a builder purchased 7 boxes of bolts with each box containing 11 bolts. He purchased 3 boxes of nuts with each box containing 15 nuts. He ended up finishing the project 6 days early and with 3 bolts and some nuts left over. He used 113 bolts and nuts for the project. How many nuts were left over?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the function $f(x) = \ln(x-f'(1)x^{2}) + 5x - 4$, then $f'\left( \frac{1}{2} \right) =$ ______.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the function $f(x) = \ln(x-f'(1)x^{2}) + 5x - 4$, then $f'\left( \frac{1}{2} \right) =$ ______.<|im_end|>
<|im_start|>assistant
<Z_24><Z_229><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the function $f(x) = \ln(x-f'(1)x^{2}) + 5x - 4$, then $f'\left( \frac{1}{2} \right) =$ ______.<|im_end|>
<|im_start|>assistant
<Z_126><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If the function $f(x) = \ln(x-f'(1)x^{2}) + 5x - 4$, then $f'\left( \frac{1}{2} \right) =$ ______.<|im_end|>
<|im_start|>assistant
<Z_111><Z_210><ANSWER>

Question: If the function $f(x) = \ln(x-f'(1)x^{2}) + 5x - 4$, then $f'\left( \frac{1}{2} \right) =$ ______.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let positive numbers \( a, b, c, x, y, z \) satisfy: \( a y + b x = c \), \( c x + a z = b \), \( b z + c y = a \). Prove that:
$$
\frac{x}{1 - y z} + \frac{y}{1 - z x} + \frac{z}{1 - x y} \leqslant 2.
$$<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let positive numbers \( a, b, c, x, y, z \) satisfy: \( a y + b x = c \), \( c x + a z = b \), \( b z + c y = a \). Prove that:
$$
\frac{x}{1 - y z} + \frac{y}{1 - z x} + \frac{z}{1 - x y} \leqslant 2.
$$<|im_end|>
<|im_start|>assistant
<Z_24><Z_328><Z_116><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let positive numbers \( a, b, c, x, y, z \) satisfy: \( a y + b x = c \), \( c x + a z = b \), \( b z + c y = a \). Prove that:
$$
\frac{x}{1 - y z} + \frac{y}{1 - z x} + \frac{z}{1 - x y} \leqslant 2.
$$<|im_end|>
<|im_start|>assistant
<Z_339><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let positive numbers \( a, b, c, x, y, z \) satisfy: \( a y + b x = c \), \( c x + a z = b \), \( b z + c y = a \). Prove that:
$$
\frac{x}{1 - y z} + \frac{y}{1 - z x} + \frac{z}{1 - x y} \leqslant 2.
$$<|im_end|>
<|im_start|>assistant
<Z_304><Z_221><Z_205><ANSWER>

Question:
Let positive numbers \( a, b, c, x, y, z \) satisfy: \( a y + b x = c \), \( c x + a z = b \), \( b z + c y = a \). Prove that:
$$
\frac{x}{1 - y z} + \frac{y}{1 - z x} + \frac{z}{1 - x y} \leqslant 2.
$$


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find a three-digit number that can be represented as the sum of two, three, four, five, and six squares of different natural numbers. Provide at least one example.<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find a three-digit number that can be represented as the sum of two, three, four, five, and six squares of different natural numbers. Provide at least one example.<|im_end|>
<|im_start|>assistant
<Z_369><Z_205><Z_418><Z_414><Z_50><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find a three-digit number that can be represented as the sum of two, three, four, five, and six squares of different natural numbers. Provide at least one example.<|im_end|>
<|im_start|>assistant
<Z_31><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find a three-digit number that can be represented as the sum of two, three, four, five, and six squares of different natural numbers. Provide at least one example.<|im_end|>
<|im_start|>assistant
<Z_418><Z_134><Z_78><Z_380><Z_158><ANSWER>

Question: Find a three-digit number that can be represented as the sum of two, three, four, five, and six squares of different natural numbers. Provide at least one example.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jenny lives 5000 feet from her school, and every day she walks home.  One day as she was walking home from school, she dropped 1 kernel of popcorn per 25 feet she walked.  Later that evening, a squirrel came and ate one-quarter of the popcorn Jenny had dropped on her way home.  If Jenny walks to school the following morning and counts the popcorn on the ground, what is the total number of popcorn kernels she will find remaining on the ground?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jenny lives 5000 feet from her school, and every day she walks home.  One day as she was walking home from school, she dropped 1 kernel of popcorn per 25 feet she walked.  Later that evening, a squirrel came and ate one-quarter of the popcorn Jenny had dropped on her way home.  If Jenny walks to school the following morning and counts the popcorn on the ground, what is the total number of popcorn kernels she will find remaining on the ground?<|im_end|>
<|im_start|>assistant
<Z_369><Z_249><Z_327><Z_310><Z_144><Z_295><Z_64><Z_80><Z_109><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jenny lives 5000 feet from her school, and every day she walks home.  One day as she was walking home from school, she dropped 1 kernel of popcorn per 25 feet she walked.  Later that evening, a squirrel came and ate one-quarter of the popcorn Jenny had dropped on her way home.  If Jenny walks to school the following morning and counts the popcorn on the ground, what is the total number of popcorn kernels she will find remaining on the ground?<|im_end|>
<|im_start|>assistant
<Z_379><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jenny lives 5000 feet from her school, and every day she walks home.  One day as she was walking home from school, she dropped 1 kernel of popcorn per 25 feet she walked.  Later that evening, a squirrel came and ate one-quarter of the popcorn Jenny had dropped on her way home.  If Jenny walks to school the following morning and counts the popcorn on the ground, what is the total number of popcorn kernels she will find remaining on the ground?<|im_end|>
<|im_start|>assistant
<Z_122><Z_230><Z_66><Z_74><Z_457><Z_206><Z_270><Z_205><Z_301><ANSWER>

Question: Jenny lives 5000 feet from her school, and every day she walks home.  One day as she was walking home from school, she dropped 1 kernel of popcorn per 25 feet she walked.  Later that evening, a squirrel came and ate one-quarter of the popcorn Jenny had dropped on her way home.  If Jenny walks to school the following morning and counts the popcorn on the ground, what is the total number of popcorn kernels she will find remaining on the ground?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many different four-digit numbers can be formed by arranging the digits in 2101?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many different four-digit numbers can be formed by arranging the digits in 2101?<|im_end|>
<|im_start|>assistant
<Z_477><Z_187><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 four-digit numbers can be formed by arranging the digits in 2101?<|im_end|>
<|im_start|>assistant
<Z_192><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
How many different four-digit numbers can be formed by arranging the digits in 2101?<|im_end|>
<|im_start|>assistant
<Z_475><Z_85><Z_407><ANSWER>

Question: How many different four-digit numbers can be formed by arranging the digits in 2101?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $S_n = \{1, 2, 3, \ldots, n\}$. If $X \subseteq S_n$, the product of all elements in $X$ is called the capacity of $X$ (if $X$ contains only one element, then the value of that element is its capacity, and the capacity of the empty set is defined as 0). If the capacity of $X$ is odd (even), then $X$ is called an odd (even) subset of $S_n$. If $n=4$, the sum of the capacities of all even subsets of $S_n$ is     .<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $S_n = \{1, 2, 3, \ldots, n\}$. If $X \subseteq S_n$, the product of all elements in $X$ is called the capacity of $X$ (if $X$ contains only one element, then the value of that element is its capacity, and the capacity of the empty set is defined as 0). If the capacity of $X$ is odd (even), then $X$ is called an odd (even) subset of $S_n$. If $n=4$, the sum of the capacities of all even subsets of $S_n$ is     .<|im_end|>
<|im_start|>assistant
<Z_24><Z_349><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $S_n = \{1, 2, 3, \ldots, n\}$. If $X \subseteq S_n$, the product of all elements in $X$ is called the capacity of $X$ (if $X$ contains only one element, then the value of that element is its capacity, and the capacity of the empty set is defined as 0). If the capacity of $X$ is odd (even), then $X$ is called an odd (even) subset of $S_n$. If $n=4$, the sum of the capacities of all even subsets of $S_n$ is     .<|im_end|>
<|im_start|>assistant
<Z_302><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $S_n = \{1, 2, 3, \ldots, n\}$. If $X \subseteq S_n$, the product of all elements in $X$ is called the capacity of $X$ (if $X$ contains only one element, then the value of that element is its capacity, and the capacity of the empty set is defined as 0). If the capacity of $X$ is odd (even), then $X$ is called an odd (even) subset of $S_n$. If $n=4$, the sum of the capacities of all even subsets of $S_n$ is     .<|im_end|>
<|im_start|>assistant
<Z_399><Z_199><ANSWER>

Question: Let $S_n = \{1, 2, 3, \ldots, n\}$. If $X \subseteq S_n$, the product of all elements in $X$ is called the capacity of $X$ (if $X$ contains only one element, then the value of that element is its capacity, and the capacity of the empty set is defined as 0). If the capacity of $X$ is odd (even), then $X$ is called an odd (even) subset of $S_n$. If $n=4$, the sum of the capacities of all even subsets of $S_n$ is     .


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as some eggs. The cost of each pound of rice is $0.33. How many eggs cost the same as a half-liter of kerosene, and how many cents does a liter of kerosene cost?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as some eggs. The cost of each pound of rice is $0.33. How many eggs cost the same as a half-liter of kerosene, and how many cents does a liter of kerosene cost?<|im_end|>
<|im_start|>assistant
<Z_477><Z_250><Z_351><Z_135><Z_334><Z_357><Z_245><Z_246><Z_215><Z_294><Z_165><Z_201><Z_50><Z_361><Z_421><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as some eggs. The cost of each pound of rice is $0.33. How many eggs cost the same as a half-liter of kerosene, and how many cents does a liter of kerosene cost?<|im_end|>
<|im_start|>assistant
<Z_244><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as some eggs. The cost of each pound of rice is $0.33. How many eggs cost the same as a half-liter of kerosene, and how many cents does a liter of kerosene cost?<|im_end|>
<|im_start|>assistant
<Z_121><Z_388><Z_70><Z_246><Z_397><Z_465><Z_151><Z_129><Z_79><Z_34><Z_481><Z_486><Z_210><Z_465><Z_64><ANSWER>

Question: In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as some eggs. The cost of each pound of rice is $0.33. How many eggs cost the same as a half-liter of kerosene, and how many cents does a liter of kerosene cost?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the sum of all possible positive values of $a$ for which the zeros of the function $f(x) = x^2 - ax + a^2 - a - 2$ are integers.<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the sum of all possible positive values of $a$ for which the zeros of the function $f(x) = x^2 - ax + a^2 - a - 2$ are integers.<|im_end|>
<|im_start|>assistant
<Z_24><Z_493><Z_107><Z_210><Z_352><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the sum of all possible positive values of $a$ for which the zeros of the function $f(x) = x^2 - ax + a^2 - a - 2$ are integers.<|im_end|>
<|im_start|>assistant
<Z_105><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Determine the sum of all possible positive values of $a$ for which the zeros of the function $f(x) = x^2 - ax + a^2 - a - 2$ are integers.<|im_end|>
<|im_start|>assistant
<Z_167><Z_66><Z_332><Z_124><Z_184><ANSWER>

Question: Determine the sum of all possible positive values of $a$ for which the zeros of the function $f(x) = x^2 - ax + a^2 - a - 2$ are integers.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Create a sequence that consists of all positive multiples of 4 that contain at least one digit that is a 4. What is the $50^{\mathrm{th}}$ term of this sequence?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Create a sequence that consists of all positive multiples of 4 that contain at least one digit that is a 4. What is the $50^{\mathrm{th}}$ term of this sequence?<|im_end|>
<|im_start|>assistant
<Z_477><Z_178><Z_229><Z_276><Z_67><Z_445><Z_374><Z_175><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Create a sequence that consists of all positive multiples of 4 that contain at least one digit that is a 4. What is the $50^{\mathrm{th}}$ term of this sequence?<|im_end|>
<|im_start|>assistant
<Z_294><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Create a sequence that consists of all positive multiples of 4 that contain at least one digit that is a 4. What is the $50^{\mathrm{th}}$ term of this sequence?<|im_end|>
<|im_start|>assistant
<Z_220><Z_3><Z_179><Z_494><Z_414><Z_335><Z_130><Z_438><ANSWER>

Question: Create a sequence that consists of all positive multiples of 4 that contain at least one digit that is a 4. What is the $50^{\mathrm{th}}$ term of this sequence?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For testing a certain product, there are 6 different genuine items and 4 different defective items. The test is conducted one by one until all the defective items are identified. If all defective items are exactly identified by the fifth test, then there are     possible methods for such testing (answer in digits).<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For testing a certain product, there are 6 different genuine items and 4 different defective items. The test is conducted one by one until all the defective items are identified. If all defective items are exactly identified by the fifth test, then there are     possible methods for such testing (answer in digits).<|im_end|>
<|im_start|>assistant
<Z_369><Z_403><Z_319><Z_143><Z_159><Z_231><Z_264><Z_334><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For testing a certain product, there are 6 different genuine items and 4 different defective items. The test is conducted one by one until all the defective items are identified. If all defective items are exactly identified by the fifth test, then there are     possible methods for such testing (answer in digits).<|im_end|>
<|im_start|>assistant
<Z_167><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
For testing a certain product, there are 6 different genuine items and 4 different defective items. The test is conducted one by one until all the defective items are identified. If all defective items are exactly identified by the fifth test, then there are     possible methods for such testing (answer in digits).<|im_end|>
<|im_start|>assistant
<Z_48><Z_232><Z_379><Z_193><Z_153><Z_507><Z_214><Z_244><ANSWER>

Question: For testing a certain product, there are 6 different genuine items and 4 different defective items. The test is conducted one by one until all the defective items are identified. If all defective items are exactly identified by the fifth test, then there are     possible methods for such testing (answer in digits).


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 14 adults have their meal , find the total number of children that can be catered with the remaining food .<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 14 adults have their meal , find the total number of children that can be catered with the remaining food .<|im_end|>
<|im_start|>assistant
<Z_477><Z_247><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 14 adults have their meal , find the total number of children that can be catered with the remaining food .<|im_end|>
<|im_start|>assistant
<Z_402><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 14 adults have their meal , find the total number of children that can be catered with the remaining food .<|im_end|>
<|im_start|>assistant
<Z_187><Z_253><ANSWER>

Question: a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 14 adults have their meal , find the total number of children that can be catered with the remaining food .


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
While writing an exam, Sanyi glanced at his watch and determined that the time elapsed for the exam was five times the remaining time. After $M$ minutes, this ratio changed to 8. What will be the ratio after another $M$ minutes?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
While writing an exam, Sanyi glanced at his watch and determined that the time elapsed for the exam was five times the remaining time. After $M$ minutes, this ratio changed to 8. What will be the ratio after another $M$ minutes?<|im_end|>
<|im_start|>assistant
<Z_24><Z_95><Z_473><Z_315><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
While writing an exam, Sanyi glanced at his watch and determined that the time elapsed for the exam was five times the remaining time. After $M$ minutes, this ratio changed to 8. What will be the ratio after another $M$ minutes?<|im_end|>
<|im_start|>assistant
<Z_289><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
While writing an exam, Sanyi glanced at his watch and determined that the time elapsed for the exam was five times the remaining time. After $M$ minutes, this ratio changed to 8. What will be the ratio after another $M$ minutes?<|im_end|>
<|im_start|>assistant
<Z_391><Z_69><Z_8><Z_166><ANSWER>

Question: While writing an exam, Sanyi glanced at his watch and determined that the time elapsed for the exam was five times the remaining time. After $M$ minutes, this ratio changed to 8. What will be the ratio after another $M$ minutes?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Some men make 1400 toys in 5 days. 1 day after work, 14 more workers join. The work can finish in 2 days. How many men were initially working on making the toys?<|im_end|>
<|im_start|>assistant
<Z_477><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Some men make 1400 toys in 5 days. 1 day after work, 14 more workers join. The work can finish in 2 days. How many men were initially working on making the toys?<|im_end|>
<|im_start|>assistant
<Z_477><Z_55><Z_322><Z_205><Z_344><Z_225><Z_310><Z_286><Z_99><Z_465><Z_497><Z_68><Z_181><Z_483><Z_378><Z_37><Z_464><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Some men make 1400 toys in 5 days. 1 day after work, 14 more workers join. The work can finish in 2 days. How many men were initially working on making the toys?<|im_end|>
<|im_start|>assistant
<Z_359><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Some men make 1400 toys in 5 days. 1 day after work, 14 more workers join. The work can finish in 2 days. How many men were initially working on making the toys?<|im_end|>
<|im_start|>assistant
<Z_483><Z_311><Z_335><Z_416><Z_187><Z_131><Z_212><Z_122><Z_198><Z_292><Z_322><Z_118><Z_417><Z_480><Z_271><Z_247><Z_125><ANSWER>

Question: Some men make 1400 toys in 5 days. 1 day after work, 14 more workers join. The work can finish in 2 days. How many men were initially working on making the toys?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In Jacob's toy bin, there are 18 red blocks, some more yellow blocks than red blocks, and 14 more blue blocks than red blocks. There are 75 blocks in all. How many more yellow blocks are there than red blocks?<|im_end|>
<|im_start|>assistant
<Z_369><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In Jacob's toy bin, there are 18 red blocks, some more yellow blocks than red blocks, and 14 more blue blocks than red blocks. There are 75 blocks in all. How many more yellow blocks are there than red blocks?<|im_end|>
<|im_start|>assistant
<Z_369><Z_188><Z_128><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In Jacob's toy bin, there are 18 red blocks, some more yellow blocks than red blocks, and 14 more blue blocks than red blocks. There are 75 blocks in all. How many more yellow blocks are there than red blocks?<|im_end|>
<|im_start|>assistant
<Z_316><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In Jacob's toy bin, there are 18 red blocks, some more yellow blocks than red blocks, and 14 more blue blocks than red blocks. There are 75 blocks in all. How many more yellow blocks are there than red blocks?<|im_end|>
<|im_start|>assistant
<Z_127><Z_370><Z_182><ANSWER>

Question: In Jacob's toy bin, there are 18 red blocks, some more yellow blocks than red blocks, and 14 more blue blocks than red blocks. There are 75 blocks in all. How many more yellow blocks are there than red blocks?