input stringclasses 571
values | output stringlengths 1.13k 182k | gts stringclasses 346
values | score float64 -1 1 | step int64 5 45 | reward float64 -1.98 1 | acc bool 2
classes | pred stringclasses 933
values |
|---|---|---|---|---|---|---|---|
user
Find the largest possible real part of \[(75+117i)z+\frac{96+144i}{z}\]where $z$ is a complex number with $|z|=4$.
Please reason step by step, and put your final answer within \boxed{}.
assistant
| Alright, I have this problem to solve:
**Find the largest possible real part of**
\[
(75 + 117i)z + \frac{96 + 144i}{z}
\]
**where \( z \) is a complex number with \( |z| = 4 \).**
Alright, let's break this down.
### Understanding the Problem
First, I need to find the maximum real part of the expression:
\[
E = (75... | 540 | 1 | 10 | 1 | true | 540 |
user
Find the largest possible real part of \[(75+117i)z+\frac{96+144i}{z}\]where $z$ is a complex number with $|z|=4$.
Please reason step by step, and put your final answer within \boxed{}.
assistant
| Alright, I have this problem:
**Find the largest possible real part of \[(75 + 117i)z + \frac{96 + 144i}{z}\] where \( z \) is a complex number with \( |z| = 4 \).**
Alright, let's break this down.
### Understanding the Problem
First, I need to find the maximum real part of the expression \((75 + 117i)z + \frac{96 ... | 540 | 1 | 10 | 1 | true | 540 |
user
Find the largest possible real part of \[(75+117i)z+\frac{96+144i}{z}\]where $z$ is a complex number with $|z|=4$.
Please reason step by step, and put your final answer within \boxed{}.
assistant
| Alright, I have this problem:
**Find the largest possible real part of**
\[
(75 + 117i)z + \frac{96 + 144i}{z}
\]
**where \( z \) is a complex number with \( |z| = 4 \).**
Alright, let's break this down.
### Understanding the Problem
First, I need to find the maximum possible real part of the expression \( (75 + 11... | 540 | 1 | 10 | 1 | true | 540 |
user
Find the largest possible real part of \[(75+117i)z+\frac{96+144i}{z}\]where $z$ is a complex number with $|z|=4$.
Please reason step by step, and put your final answer within \boxed{}.
assistant
| Alright, I have this problem to solve:
**Find the largest possible real part of**
\[
(75 + 117i)z + \frac{96 + 144i}{z}
\]
**where \( z \) is a complex number with \( |z| = 4 \).**
Alright, let's break this down.
### Understanding the Problem
First, I need to find the real part of the expression:
\[
(75 + 117i)z + ... | 540 | 1 | 10 | 1 | true | 540 |
user
Find the largest possible real part of \[(75+117i)z+\frac{96+144i}{z}\]where $z$ is a complex number with $|z|=4$.
Please reason step by step, and put your final answer within \boxed{}.
assistant
| Alright, I have this problem:
**Find the largest possible real part of**
\[
(75 + 117i)z + \frac{96 + 144i}{z}
\]
**where \( z \) is a complex number with \( |z| = 4 \).**
Alright, let's break this down.
### Understanding the Problem
First, I need to find the largest possible real part of the expression \( (75 + 11... | 540 | 1 | 10 | 1 | true | 540 |
user
Find the largest possible real part of \[(75+117i)z+\frac{96+144i}{z}\]where $z$ is a complex number with $|z|=4$.
Please reason step by step, and put your final answer within \boxed{}.
assistant
| Alright, I have this problem to solve:
**Find the largest possible real part of \[(75+117i)z + \frac{96+144i}{z}\] where \( z \) is a complex number with \( |z| = 4 \).**
Alright, let's break this down.
### Understanding the Problem
First, I need to find the maximum real part of the expression \( (75 + 117i)z + \fr... | 540 | 1 | 10 | 1 | true | 540 |
user
Find the largest possible real part of \[(75+117i)z+\frac{96+144i}{z}\]where $z$ is a complex number with $|z|=4$.
Please reason step by step, and put your final answer within \boxed{}.
assistant
| Alright, I have this problem to solve:
**Find the largest possible real part of \[(75+117i)z+\frac{96+144i}{z}\] where \( z \) is a complex number with \( |z| = 4 \).**
Alright, let's break this down.
### Understanding the Problem
First, I need to understand what's being asked. I have a complex expression involving... | 540 | 1 | 10 | 1 | true | 540 |
user
Find the largest possible real part of \[(75+117i)z+\frac{96+144i}{z}\]where $z$ is a complex number with $|z|=4$.
Please reason step by step, and put your final answer within \boxed{}.
assistant
| Alright, I have this problem:
**Find the largest possible real part of \[(75 + 117i)z + \frac{96 + 144i}{z}\] where \( z \) is a complex number with \( |z| = 4 \).**
Alright, let's break this down.
### Understanding the Problem
First, I need to find the real part of the expression \((75 + 117i)z + \frac{96 + 144i}{... | 540 | 1 | 10 | 1 | true | 540 |
user
Find the largest possible real part of \[(75+117i)z+\frac{96+144i}{z}\]where $z$ is a complex number with $|z|=4$.
Please reason step by step, and put your final answer within \boxed{}.
assistant
| Alright, I have this problem to solve:
**Find the largest possible real part of \[(75+117i)z + \frac{96+144i}{z}\] where \( z \) is a complex number with \( |z| = 4 \).**
Alright, let's break this down.
### Understanding the Problem
First, I need to understand what's being asked. We have a complex expression involv... | 540 | 1 | 10 | 1 | true | 540 |
user
Find the largest possible real part of \[(75+117i)z+\frac{96+144i}{z}\]where $z$ is a complex number with $|z|=4$.
Please reason step by step, and put your final answer within \boxed{}.
assistant
| Alright, I have this problem to solve:
**Find the largest possible real part of \[(75 + 117i)z + \frac{96 + 144i}{z}\] where \( z \) is a complex number with \( |z| = 4 \).**
Alright, let's break this down.
### Understanding the Problem
First, I need to find the maximum real part of the expression \((75 + 117i)z + ... | 540 | -1 | 10 | -1 | false | 12\sqrt{1930} |
user
Find the largest possible real part of \[(75+117i)z+\frac{96+144i}{z}\]where $z$ is a complex number with $|z|=4$.
Please reason step by step, and put your final answer within \boxed{}.
assistant
| Alright, I have this problem to solve:
**Find the largest possible real part of**
\[
(75 + 117i)z + \frac{96 + 144i}{z}
\]
**where \( z \) is a complex number with \( |z| = 4 \).**
Alright, let's break this down.
### Understanding the Problem
First, I need to find the maximum possible real part of the expression:
\... | 540 | 1 | 10 | 1 | true | 540 |
user
Find the largest possible real part of \[(75+117i)z+\frac{96+144i}{z}\]where $z$ is a complex number with $|z|=4$.
Please reason step by step, and put your final answer within \boxed{}.
assistant
| Alright, I have this problem to solve:
**Find the largest possible real part of**
\[
(75 + 117i)z + \frac{96 + 144i}{z}
\]
**where \( z \) is a complex number with \( |z| = 4 \).**
Alright, let's break this down.
### Understanding the Problem
First, I need to find the largest possible real part of the expression:
\... | 540 | 1 | 10 | 1 | true | 540 |
user
Find the largest possible real part of \[(75+117i)z+\frac{96+144i}{z}\]where $z$ is a complex number with $|z|=4$.
Please reason step by step, and put your final answer within \boxed{}.
assistant
| Alright, I have this problem:
**Find the largest possible real part of \[(75+117i)z + \frac{96+144i}{z}\] where \( z \) is a complex number with \( |z| = 4 \).**
Alright, let's break this down.
### Understanding the Problem
First, I need to understand what's being asked. We have an expression involving a complex nu... | 540 | 1 | 10 | 1 | true | 540 |
user
Find the largest possible real part of \[(75+117i)z+\frac{96+144i}{z}\]where $z$ is a complex number with $|z|=4$.
Please reason step by step, and put your final answer within \boxed{}.
assistant
| Alright, I have this problem to solve:
**Find the largest possible real part of**
\[
(75 + 117i)z + \frac{96 + 144i}{z}
\]
**where \( z \) is a complex number with \( |z| = 4 \).**
Alright, let's break this down.
### Understanding the Problem
First, I need to find the real part of the expression:
\[
(75 + 117i)z + ... | 540 | 1 | 10 | 1 | true | 540 |
user
Find the largest possible real part of \[(75+117i)z+\frac{96+144i}{z}\]where $z$ is a complex number with $|z|=4$.
Please reason step by step, and put your final answer within \boxed{}.
assistant
| Alright, I have this problem:
**Find the largest possible real part of \[(75+117i)z + \frac{96+144i}{z}\] where \( z \) is a complex number with \( |z| = 4 \).**
Alright, let's break this down.
### Understanding the Problem
First, I need to find the maximum possible real part of the expression \((75 + 117i)z + \fra... | 540 | 1 | 10 | 1 | true | 540 |
user
Find the largest possible real part of \[(75+117i)z+\frac{96+144i}{z}\]where $z$ is a complex number with $|z|=4$.
Please reason step by step, and put your final answer within \boxed{}.
assistant
| Alright, I have this problem to solve:
**Find the largest possible real part of \[(75 + 117i)z + \frac{96 + 144i}{z}\] where \( z \) is a complex number with \( |z| = 4 \).**
Alright, let's break this down.
### Understanding the Problem
First, I need to find the maximum possible real part of the expression \((75 + ... | 540 | 1 | 10 | 1 | true | 540 |
user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes,... | Alright, I have this problem about Aya's morning walk. Let's try to understand what's going on and figure out how to solve it step by step.
**Understanding the Problem:**
Aya walks 9 kilometers every morning and stops at a coffee shop afterward. The total time she spends on her walk includes the time she's actually w... | 204 | 1 | 10 | 1 | true | 204 |
user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes,... | Alright, I have this problem about Aya's morning walk. Let's try to understand what's going on and solve it step by step.
### Understanding the Problem
First, let's summarize the information given:
1. **Distance of the walk:** 9 kilometers.
2. **First scenario:**
- Walking speed: \( s \) km/h.
- Total time tak... | 204 | 1 | 10 | 1 | true | 204 |
user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes,... | Alright, I have this problem about Aya's morning walk. Let's try to understand what's going on and figure out how to solve it step by step.
### Understanding the Problem
First, let's summarize the information given:
1. **First Scenario:**
- Aya walks **9 kilometers**.
- Her walking speed is **\( s \) kilometer... | 204 | 1 | 10 | 1 | true | 204 |
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