Question MW2

Question text:

You are a helpful math assistant who solves math questions logically, using step-by-step reasoning. Answer the following question: Let's define an operation ◘ such that, for any real numbers x and y, x ◘ y = 2x - 3y + 1. What is the value of 4 ◘ 3? You may begin with analysis, but you must end your answer with a new line and a concise representation of the correct answer.

Strict success criteria:

0 on its own line as the last character of the response AND any reasoning provided is coherent and correct

Success criteria:

Includes the correct answer 0 in any part of the response without offering other conflicting answers

Llm

Correct

Strict Correct

Response

Nous Hermes 2 Yi 34b

Analysis:
To find the value of 4◘3, we need to substitute x = 4 and y = 3 into the given operation formula.

Solution:
Let x = 4 and y = 3. Then, according to the formula, 4◘3 is equal to:

2(4) - 3(3) + 1 = 8 - 9 + 1 = -1.

Therefore, the value of 4◘3 is -1.<|im_end|>

Mixtral 8x7b v0.1 instruct



First, we apply the operation ◘ to the numbers 4 and 3:

4 ◘ 3 = 2(4) - 3(3) + 1

Now, we simplify step by step:

= 8 - 9 + 1

= -1 + 1

= 0

The value of 4 ◘ 3 is **0**.

Zephyr 7B

Analysis:
Let's find the value of x = 4 and y = 3 in the given expression.
x ◘ y = 2x - 3y + 1
= 2(4) - 3(3) + 1
= 8 - 9 + 1
= -1
So, the value of 4 ◘ 3 is -1.

Llama 3 8B Instruct

Let's start by analyzing the definition of the ◘ operation:

x ◘ y = 2x - 3y + 1

We are asked to find the value of 4 ◘ 3. To do this, we can substitute x = 4 and y = 3 into the definition:

4 ◘ 3 = 2(4) - 3(3) + 1
= 8 - 9 + 1
= -1 + 1
= 0

So, the value of 4 ◘ 3 is:

0

Mistral 7B Instruct v0.3

 To find the value of 4 ◘ 3, we substitute x = 4 and y = 3 in the given operation ◘, which is defined as x ◘ y = 2x - 3y + 1.

So, 4 ◘ 3 = 2(4) - 3(3) + 1

Now, perform the multiplication and addition:

4 ◘ 3 = 8 - 9 + 1

Add the numbers:

4 ◘ 3 = 6

Therefore, the value of 4 ◘ 3 is 6.

In summary, 4 ◘ 3 = 6.

TinyLlama v1.0 chat 1.1b


The value of 4 ◘ 3 is: (2 + 3)(-1) = -6

CodeLlama 13b Instruct


The problem asks for the value of 4 ◘ 3. To solve this, we must apply the definition of ◘. We can start by applying the definition to x and y:


x = 4; y = 3

Using the definition given in the problem, we have that:

2x - 3y + 1 = (2(4) - 3(3)) + 1 = 15

So, we can conclude that 4 ◘ 3 = 15.

Vicuna 33b Chat

 To find the value of 4 ◘ 3, we need to apply the given operation:

4 ◘ 3 = 2 \* 4 - 3 \* 3 + 1
4 ◘ 3 = 8 - 9 + 1
4 ◘ 3 = -1

However, this result seems incorrect based on the operation's definition. There must be a mistake in my calculations. Let me try again:

4 ◘ 3 = 2 \* 4 - 3 \* 3 + 1
4 ◘ 3 = 8 - 9 + 1
4 ◘ 3 = -1 + 1
4 ◘ 3 = 0.

So, the value of 4 ◘ 3 is 0.

Llama 3.1 8B Instruct

To find the value of 4 ◘ 3, we need to substitute x = 4 and y = 3 into the given operation.

The operation is defined as x ◘ y = 2x - 3y + 1.

Substituting x = 4 and y = 3 into the operation, we get:

4 ◘ 3 = 2(4) - 3(3) + 1

First, calculate the products:
2(4) = 8
3(3) = 9

Now, substitute these values back into the equation:
4 ◘ 3 = 8 - 9 + 1

Next, perform the subtractions and additions from left to right:
8 - 9 = -1
-1 + 1 = 0

Therefore, the value of 4 ◘ 3 is 0.



0

Kunoichi DPO v2 7B

 To find the value of 4 ◘ 3, we will substitute x = 4 and y = 3 into the given operation:

x ◘ y = 2x - 3y + 1
4 ◘ 3 = 2(4) - 3(3) + 1

Now, perform the operations inside the parentheses:

4 ◘ 3 = 8 - 9 + 1

Next, perform the addition and subtraction from left to right:

4 ◘ 3 = -1 + 1

The final result is:

4 ◘ 3 = 0

So, the value of 4 ◘ 3 is 0.</s>

Claude 3.5 Sonnet

Let's approach this step-by-step:

1. We're given the definition of the operation ◘:
   For any real numbers x and y, x ◘ y = 2x - 3y + 1

2. We need to find the value of 4 ◘ 3, so let's substitute:
   x = 4
   y = 3

3. Now, let's apply the formula:
   4 ◘ 3 = 2(4) - 3(3) + 1

4. Let's solve the operations in parentheses:
   4 ◘ 3 = 8 - 9 + 1

5. Now we can perform the arithmetic:
   8 - 9 = -1
   -1 + 1 = 0

Therefore, 4 ◘ 3 = 0

0

StableLM Zephyr 3B

To find the value of 4 ◘ 3, we substitute 4 for x and 3 for y in the expression 2x - 3y + 1.

4 ◘ 3 = 2(4) - 3(3) + 1
        = 8 - 9 + 1
        = -1 + 1
        = 0

Therefore, the value of 4 ◘ 3 is 0.

The answer is: 0<|endoftext|>

Mixtral 11bx2 MoE 19b

To find the value of 4 ◘ 3 using the given operation, we substitute x = 4 and y = 3 into the expression:

x ◘ y = 2x - 3y + 1
4 ◘ 3 = 2(4) - 3(3) + 1

Now, we simplify the expression:

= 8 - 9 + 1
= -1 + 1
= 0

So, the value of 4 ◘ 3 is 0.The answer is: 0</s>

Gemma 7b IT

**Analysis:**

The operation ◘ is defined as x ◘ y = 2x - 3y + 1. To find the value of 4 ◘ 3, we need to substitute x = 4 and y = 3 into the equation.

**Solution:**

4 ◘ 3 = 2(4) - 3(3) + 1

= 8 - 9 + 1

= 0

**Answer:**

0<eos>

Gemma 2b IT

The operation ◘ is defined as, for any real numbers x and y, x ◘ y = 2x - 3y + 1.

Therefore, 4 ◘ 3 = 2(4) - 3(3) + 1 = 8 - 9 + 1 = 4.<eos>

Hermes 2 Pro Mistral 7B

First, let's apply the operation ◘ on the given numbers:

4 ◘ 3 = 2(4) - 3(3) + 1

Now, perform the arithmetic operations:

= 8 - 9 + 1

Next, add and subtract from left to right:

= -1 + 1

Finally, we get the result:

= 0

So, the value of 4 ◘ 3 is 0.<|im_end|>

Mistral Nemo Instruct 2407

To find the value of 4 ◘ 3, we need to apply the definition of the operation ◘:

4 ◘ 3 = 2(4) - 3(3) + 1
       = 8 - 9 + 1
       = -1 + 1
       = 0

So, the value of 4 ◘ 3 is 0.

H2O Danube 1.8b Chat

To solve this problem, we first need to understand the given operation ◘ and then substitute the given values to find the result.

◘ operation: x ◘ y = 2x - 3y + 1

Let's substitute the given values:

4 ◘ 3 = 2(4) - 3(4) + 1

Now, simplify the operation:

4 ◘ 3 = 8 - 12 + 1

4 ◘ 3 = -4 + 1

4 ◘ 3 = 3

So, 4 ◘ 3 = 3.

The value of 4 ◘ 3 is 3.</s>

Phi 3 Mini 4k Instruct

To find the value of 4 ◘ 3 using the defined operation ◘, we'll substitute x with 4 and y with 3 in the expression 2x - 3y + 1.


Step 1: Substitute x and y with 4 and 3 respectively.

4 ◘ 3 = 2(4) - 3(3) + 1


Step 2: Perform the operations inside the parentheses.

= 8 - 9 + 1


Step 3: Complete the subtraction and addition.

= -1 + 1


Step 4: Final calculation.

= 0


The value of 4 ◘ 3 is 0.<|end|>

Neural Hermes 2.5 7B

To find the value of 4 ◘ 3, we need to substitute x = 4 and y = 3 into the given operation definition.

x ◘ y = 2x - 3y + 1

Substitute x = 4 and y = 3:

4 ◘ 3 = 2(4) - 3(3) + 1

Now, perform the operations inside the parentheses:

4 ◘ 3 = 8 - 9 + 1

Next, perform the addition and subtraction from left to right:

4 ◘ 3 = -1 + 1

Finally, perform the remaining addition:

4 ◘ 3 = 0

So, the value of 4 ◘ 3 is 0.<|im_end|>

GPT 4o mini

To find the value of \( 4 ◘ 3 \) using the operation defined as \( x ◘ y = 2x - 3y + 1 \), we can follow these steps:

1. Identify the values of \( x \) and \( y \):
   - Here, \( x = 4 \) and \( y = 3 \).

2. Substitute \( x \) and \( y \) into the operation:
   \[
   4 ◘ 3 = 2(4) - 3(3) + 1
   \]

3. Calculate each term:
   - First, calculate \( 2(4) \):
     \[
     2(4) = 8
     \]
   - Next, calculate \( 3(3) \):
     \[
     3(3) = 9
     \]

4. Now, substitute these values back into the expression:
   \[
   4 ◘ 3 = 8 - 9 + 1
   \]

5. Perform the arithmetic step-by-step:
   - First, calculate \( 8 - 9 \):
     \[
     8 - 9 = -1
     \]
   - Then, add \( 1 \):
     \[
     -1 + 1 = 0
     \]

Thus, the value of \( 4 ◘ 3 \) is:

\[
\boxed{0}
\]

Nous Hermes 2 SOLAR 10.7B

To find the value of 4 ◘ 3, we will substitute x = 4 and y = 3 into the given formula for ◘:

x ◘ y = 2x - 3y + 1

Substituting x = 4 and y = 3, we get:

4 ◘ 3 = 2(4) - 3(3) + 1

Now, we will perform the arithmetic operations step by step:

4 ◘ 3 = 8 - 9 + 1

Next, subtract:

4 ◘ 3 = -1 + 1

Finally, add:

4 ◘ 3 = 0

So, the value of 4 ◘ 3 is 0.<|im_end|>

Mixtral 34x2 MoE 60b


Using the given operation ◘, we can find the value of 4 ◘ 3 by plugging in the numbers into the equation.

So, (4) ◘ (3) = 2(4) - 3(3) + 1.

Now, let's perform the calculations:

= 8 - 9 + 1
= -1 + 1
= 0

Therefore, 4 ◘ 3 equals to 0.

H2O Danube 3 4b Chat

4 ◘ 3 = 2(4) - 3(3) + 1 = 8 - 9 + 1 = -1

Starling LM 7B Beta

 To find the value of 4 ◘ 3, we will substitute x = 4 and y = 3 into the given operation definition: x ◘ y = 2x - 3y + 1.

Step 1: Substitute the values of x and y.
4 ◘ 3 = 2(4) - 3(3) + 1

Step 2: Perform the operations inside the parentheses.
4 ◘ 3 = 8 - 9 + 1

Step 3: Perform the remaining operations.
4 ◘ 3 = -1 + 1

Step 4: Simplify the expression.
4 ◘ 3 = 0

So, the value of 4 ◘ 3 is 0.<|end_of_turn|>

Claude 3 Haiku

To solve this problem, we need to use the given definition of the operation ◘.

The operation ◘ is defined as:
x ◘ y = 2x - 3y + 1

Now, we need to find the value of 4 ◘ 3 using this definition.

Substituting the values, we get:
4 ◘ 3 = 2(4) - 3(3) + 1
= 8 - 9 + 1
= 0

Therefore, the value of 4 ◘ 3 is 0.

0

Claude 3 Sonnet

To solve this problem, we need to substitute the given values of x and y into the expression x ◘ y = 2x - 3y + 1.

Given:
x = 4
y = 3

Substituting these values into the expression, we get:
4 ◘ 3 = 2(4) - 3(3) + 1
       = 8 - 9 + 1
       = -1

Therefore, the value of 4 ◘ 3 is:

-1

Gemma 2 9B IT

Let's break down the operation and apply it to our numbers:

1. **Understand the operation:**  We're given x ◘ y = 2x - 3y + 1. This means we need to substitute the values of x and y with 4 and 3, respectively.

2. **Substitute:**  
   x = 4 and y = 3, so we get: 4 ◘ 3 = (2 * 4) - (3 * 3) + 1

3. **Calculate:**
   4 ◘ 3 = 8 - 9 + 1

4. **Simplify:**
   4 ◘ 3 = 0


0

Claude 3 Opus

To find the value of 4 ◘ 3, we need to substitute x with 4 and y with 3 in the given formula for the operation ◘.

Given:
x ◘ y = 2x - 3y + 1

Step 1: Substitute x with 4 and y with 3 in the formula.
4 ◘ 3 = 2(4) - 3(3) + 1

Step 2: Simplify the expression.
4 ◘ 3 = 8 - 9 + 1
4 ◘ 3 = 0

Therefore, the value of 4 ◘ 3 is 0.

Answer: 0

Gemini Pro 1.0

Given the operation ◘, we have x ◘ y = 2x - 3y + 1.

Substituting x = 4 and y = 3, we get:

4 ◘ 3 = 2(4) - 3(3) + 1
= 8 - 9 + 1
= 0

Therefore, the value of 4 ◘ 3 is 0.

Gemini 1.5 Pro

## Analyzing the Problem

We are asked to find the value of 4 ◘ 3 using the given definition of the operation ◘. This means we need to substitute 4 for x and 3 for y in the expression 2x - 3y + 1.

## Solving the Problem

1. **Substitute the values:** Replace x with 4 and y with 3 in the expression: 2(4) - 3(3) + 1

2. **Perform the multiplications:** 8 - 9 + 1

3. **Perform the subtractions and addition from left to right:** -1 + 1

4. **Find the final answer:** 0

## Solution

0 

StableLM 2 1.6B Chat

To find the value of 4 ◘ 3, we first apply the given operation to both terms:

4 ◘ 3 = 2(4) - 3(3) + 1

Simplifying, we get:

4 ◘ 3 = 8 - 9 + 1

4 ◘ 3 = -1

So, the value of 4 ◘ 3 is -1.

Mistral 7B Instruct v0.2

 To find the value of 4 ◘ 3, we need to apply the definition of the operation ◘:

x ◘ y = 2x - 3y + 1

Substitute x = 4 and y = 3 in the equation:

4 ◘ 3 = 2(4) - 3(3) + 1

Perform the multiplication inside the parentheses:

= 2(4) - 3(3) + 1

= 8 - 9 + 1

Now, do the subtraction and addition:

= 1 - 1

= 0

So, the value of 4 ◘ 3 is 0.

Gemma 1.1 7b IT

**Analysis:**

Given the definition of the operation ◘, we can substitute the values of x and y as follows:

```
x = 4
y = 3
```

```
4 ◘ 3 = 2(4) - 3(3) + 1
```

**Solution:**

```
4 ◘ 3 = 8 - 9 + 1
4 ◘ 3 = -2
```

**Answer:**

```
-2
```

Gemma 1.1 2B IT

**Analysis:**
To evaluate 4 ◘ 3, we substitute the given operation into the formula:

$$4 ◘ 3 = 4(2) - 3(3) + 1$$

$$= 8 - 9 + 1$$

$$= -1$$

**Conclusion:**
Therefore, the value of 4 ◘ 3 is -1.

GPT-4 Turbo 0125-preview

To find the value of \(4 ◘ 3\), we use the given operation definition \(x ◘ y = 2x - 3y + 1\). Here, \(x = 4\) and \(y = 3\). Substituting these values into the operation's formula gives:

\[4 ◘ 3 = 2(4) - 3(3) + 1.\]

Doing the arithmetic:

\[= 8 - 9 + 1.\]

\[= -1.\]

Therefore, the value of \(4 ◘ 3\) is \(-1\).

GPT-3.5 Turbo 0125

To find the value of 4 ◘ 3, we substitute x = 4 and y = 3 into the operation ◘:

4 ◘ 3 = 2(4) - 3(3) + 1
4 ◘ 3 = 8 - 9 + 1
4 ◘ 3 = 0

Therefore, the value of 4 ◘ 3 is 0.

Gemma 2 27B IT

Here's how to solve the problem:

1. **Identify the given values:** We are given x = 4 and y = 3.

2. **Substitute the values into the operation definition:**
   4 ◘ 3 = (2 * 4) - (3 * 3) + 1

3. **Perform the calculations:**
   4 ◘ 3 = 8 - 9 + 1

4. **Simplify:**
   4 ◘ 3 = 0


0

Llama 3 70B

Let's break down the operation ◘ and apply it to the given values.

The operation is defined as x ◘ y = 2x - 3y + 1. We are asked to find the value of 4 ◘ 3, so we'll substitute x = 4 and y = 3 into the equation.

4 ◘ 3 = 2(4) - 3(3) + 1

= 8 - 9 + 1

= -1 + 1

= 0

So, the value of 4 ◘ 3 is:

0

Gemini 1.5 Flash

We are given the operation ◘ defined as x ◘ y = 2x - 3y + 1.  To find the value of 4 ◘ 3, we substitute x = 4 and y = 3 into the definition.

This gives us: 4 ◘ 3 = (2 * 4) - (3 * 3) + 1.

Simplifying, we get: 4 ◘ 3 = 8 - 9 + 1.

Therefore, 4 ◘ 3 = 0. 

GPT-4 Turbo 0409

To find the value of 4 ◘ 3, we need to substitute x = 4 and y = 3 into the defined operation x ◘ y = 2x - 3y + 1. 

Performing the calculation:
4 ◘ 3 = 2(4) - 3(3) + 1
       = 8 - 9 + 1
       = 0

Therefore, 4 ◘ 3 = 0.

Command-R v01

We have an interesting operation here that shifts numbers around the number line in a unique way. Let's see how it works with 4 and 3.

4 ◘ 3 = 2(4) - 3(3) + 1
= 8 - 9 + 1
= -1.

So, the solution is **−1**.

Hermes 2 Pro Llama 3

First, we will substitute the values of x and y into the given formula:

x = 4
y = 3

Now, we will plug these values into the formula for the ◘ operation:

4 ◘ 3 = 2(4) - 3(3) + 1

Next, we will solve the expression:

= 8 - 9 + 1

Finally, we will simplify the expression:

= -1

So, the value of 4 ◘ 3 is -1.

Phi 3 Mini 4k Instruct (2024-07-01)


To determine the value of 4 ◘ 3, we will apply the definition of the operation ◘ to the given real numbers.


According to the definition, x ◘ y = 2x - 3y + 1.


Now, we'll substitute x with 4 and y with 3:


4 ◘ 3 = 2(4) - 3(3) + 1

       = 8 - 9 + 1

       = -1 + 1

       = 0


The value of 4 ◘ 3 is therefore 0.


GPT-4o

To solve for the value of \( 4 \ ◘ \ 3 \) using the given operation \( \◘ \), we need to follow the definition of the operation. The operation \( x \ ◘ \ y \) is defined as:

\[ x \ ◘ \ y = 2x - 3y + 1 \]

We are given \( x = 4 \) and \( y = 3 \). Substituting these values into the operation definition, we get:

\[ 4 \ ◘ \ 3 = 2(4) - 3(3) + 1 \]

Now, perform the calculations step-by-step:

1. Calculate \( 2(4) \):
   \[ 2 \times 4 = 8 \]

2. Calculate \( 3(3) \):
   \[ 3 \times 3 = 9 \]

3. Substitute these results back into the expression:
   \[ 4 \ ◘ \ 3 = 8 - 9 + 1 \]

4. Simplify the expression:
   \[ 8 - 9 = -1 \]
   \[ -1 + 1 = 0 \]

Thus, the value of \( 4 \ ◘ \ 3 \) is:

\[ 0 \]

Hermes 2 Theta Llama 3 8B

To find the value of 4 ◘ 3, we can plug in x = 4 and y = 3 into the definition of ◘:

4 ◘ 3 = 2(4) - 3(3) + 1

Now, we can simplify:

= 8 - 9 + 1

= -1 + 1

= 0

So, 4 ◘ 3 = 0. 

Answer:
0

SFR Iterated DPO Llama 3 8B R

Step 1:  First, we understand the operation ◘ is defined as x ◘ y = 2x - 3y + 1 for any real numbers x and y.
Step 2:  To find the value of 4 ◘ 3, we substitute x = 4 and y = 3 into the given operation.
Step 3:  We calculate 4 ◘ 3 as (2 * 4) - (3 * 3) + 1.
Step 4:  This simplifies to 8 - 9 + 1.
Step 5:  Upon further computation, we get 8 - 9 + 1 = 0.
Step 6:  Therefore, 4 ◘ 3 = 0.
Step 7:  Thus, the value of 4 ◘ 3 is 0.

Answer:
0

Yi 1.5 6B Chat

To find the value of 4 ◘ 3, we will substitute x with 4 and y with 3 in the given operation definition:

4 ◘ 3 = 2(4) - 3(3) + 1

Now, we will perform the operations step-by-step:

= 8 - 9 + 1

= -1 + 1

= 0

So, the value of 4 ◘ 3 is 0.<|im_end|>

Yi 1.5 9B Chat

To find the value of 4 ◘ 3, we need to apply the given operation ◘ to the real numbers 4 and 3 according to the definition provided: x ◘ y = 2x - 3y + 1.

Step 1: Identify the values of x and y.
In this case, x = 4 and y = 3.

Step 2: Apply the operation ◘ using the values of x and y.
Using the definition x ◘ y = 2x - 3y + 1, we substitute x = 4 and y = 3 into the equation:

4 ◘ 3 = 2(4) - 3(3) + 1

Step 3: Perform the operations within the equation.
2(4) = 8 (multiplication)
3(3) = 9 (multiplication)

Now the equation looks like this:

4 ◘ 3 = 8 - 9 + 1

Step 4: Complete the operations to find the final value.
8 - 9 = -1 (subtraction)
-1 + 1 = 0 (addition)

Therefore, the value of 4 ◘ 3 is 0.

The answer is: 0<|im_end|>

Yi 1.5 34B Chat

To find the value of 4 ◘ 3 using the defined operation x ◘ y = 2x - 3y + 1, we will substitute x with 4 and y with 3 and then calculate the result step by step.

Step 1: Substitute x with 4 and y with 3 in the expression 2x - 3y + 1.
2(4) - 3(3) + 1

Step 2: Perform the multiplication.
8 - 9 + 1

Step 3: Perform the addition and subtraction.
8 - 9 + 1 = -1 + 1 = 0

Therefore, the value of 4 ◘ 3 is 0.<|im_end|>

Llama 3 Refueled

To find the value of 4 ◘ 3, we substitute x = 4 and y = 3 into the expression x ◘ y = 2x - 3y + 1.

So, 4 ◘ 3 = 2(4) - 3(3) + 1.

Calculating, we get 4 ◘ 3 = 8 - 9 + 1.

Simplifying, we find 4 ◘ 3 = -1.

Thus, the value of 4 ◘ 3 is -1.