| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | B. 46 | B |
| deepseekr1 | The problem requires John to place the symbols +, ×, and - exactly once each between the numbers 2, 4, 6, and 8 (in fixed order) to achieve the highest possible result. Evaluating all six permutations of the operators: 1. **2 + 4 × 6 − 8** = 18 2. **2 + 4 − 6 × 8** = -42 3. **2 × 4 + 6 − 8** = 6 4. **2 × 4 − 6 + 8** = 10 5. **2 − 4 + 6 × 8** = 46 6. **2 − 4 × 6 + 8** = -14 The highest result is **46** (from permutation 5). While option D (99) might seem plausible, it cannot be achieved under the given constraints. The correct answer is **B**. **Answer: B** |
B |
| gpto1 | To solve this problem, let's consider all possible ways John can insert the symbols +, ×, and - between the numbers 2, 4, 6, and 8, using each symbol exactly once. There are 6 permutations (3! = 6) of the three symbols: 1. \(2 + 4 \times 6 - 8\) - Compute 4 × 6 = 24 - Calculate 2 + 24 - 8 = 18 2. \(2 + 4 - 6 \times 8\) - Compute 6 × 8 = 48 - Calculate 2 + 4 - 48 = -42 3. \(2 \times 4 + 6 - 8\) - Compute 2 × 4 = 8 - Calculate 8 + 6 - 8 = 6 4. \(2 \times 4 - 6 + 8\) - Compute 2 × 4 = 8 - Calculate 8 - 6 + 8 = 10 5. \(2 - 4 + 6 \times 8\) - Compute 6 × 8 = 48 - Calculate 2 - 4 + 48 = 46 6. \(2 - 4 \times 6 + 8\) - Compute 4 × 6 = 24 - Calculate 2 - 24 + 8 = -14 Among all these calculations, the highest value John can obtain is **46**, which corresponds to option B. **Answer:** B |
B |
| GPT-4o | To determine the highest number John can obtain by placing the symbols +, ×, and - in the blanks, we need to evaluate different possible combinations and calculate their results. Let's consider each arrangement: 1. \(2 + 4 \times 6 - 8\) 2. \(2 + 4 - 6 \times 8\) 3. \(2 \times 4 + 6 - 8\) 4. \(2 \times 4 - 6 + 8\) 5. \(2 - 4 + 6 \times 8\) 6. \(2 - 4 \times 6 + 8\) Now, we evaluate each expression step by step, respecting the order of operations (multiplication and division before addition and subtraction): 1. \(2 + 4 \times 6 - 8\) - First, perform multiplication: \(4 \times 6 = 24\) - Then, addition and subtraction: \(2 + 24 - 8 = 26 - 8 = 18\) 2. \(2 + 4 - 6 \times 8\) - First, perform multiplication: \(6 \times 8 = 48\) - Then, addition and subtraction: \(2 + 4 - 48 = 6 - 48 = -42\) 3. \(2 \times 4 + 6 - 8\) - First, perform multiplication: \(2 \times 4 = 8\) - Then, addition and subtraction: \(8 + 6 - 8 = 14 - 8 = 6\) 4. \(2 \times 4 - 6 + 8\) - First, perform multiplication: \(2 \times 4 = 8\) - Then, addition and subtraction: \(8 - 6 + 8 = 2 + 8 = 10\) 5. \(2 - 4 + 6 \times 8\) - First, perform multiplication: \(6 \times 8 = 48\) - Then, addition and subtraction: \(2 - 4 + 48 = -2 + 48 = 46\) 6. \(2 - 4 \times 6 + 8\) - First, perform multiplication: \(4 \times 6 = 24\) - Then, addition and subtraction: \(2 - 24 + 8 = -22 + 8 = -14\) Among all the evaluated possibilities, the highest number John can obtain is 46. Thus, the correct answer is: B. 46 |
B |
| llama3.1-70B-Instruct | B The highest number that John could obtain is $2 \times 4 + 6 - 8 = 6.$ Final Answer: The final answer is B. I hope it is correct. |
B |
| llama3.1-405B-Instruct | To maximize the number, we want to maximize the digits of the number and also maximize the place value of the greatest digits. To maximize the digits, we want to use the $+$ and $\times$ signs. To maximize the place value of the greatest digits, we want to put the greatest numbers first. Thus, we want to multiply $8$ by $6$ to get a large number, and add $4$ and $2$ to get a large number in the ones place. Thus, the largest number we can get is $8\times6+4+2=48+4+2=\boxed{54}$. Since there is no choice of 54, we can try another combination such as $8+6\times4+2$ which is $8+24+2=34$. Again, there is no choice of 34. Let us try another combination such as $8\times6-4+2$ which is $48-4+2=46$. The final answer is B. |
B |
| DeepSeek-Coder-V2 | B | B |
| Qwen2-72B-Instruct | D. 99 | B |
| baichuan4 | To obtain the highest number possible, John should use the symbols to maximize the result. The highest result can be obtained by using the multiplication symbol between the two highest numbers (6 and 8) and the addition symbol before and after the multiplication. The minus symbol should be placed between the 2 and 4 to make the first number positive. Therefore, the expression should be: \[2 - 4 + 6 \times 8\] Calculating this expression gives: \[2 - 4 + 48 = -2 + 48 = 46\] So, the highest possible number that John could obtain is 46. Answer: B. 46 |
B |
| doubao | D One possible way to get a high number is $2\times4+6-8=8+6-8=6$; another way is $2+4\times6-8=2+24-8=18$; and another way is $2+4-6\times8=2+4-48=-42$. But the highest possible number is obtained by $2\times6+4-8=12+4-8=8$. None of the options A, B, C give 8, so the answer is D. |
B |
| minimax | To obtain the highest possible number, John should aim to maximize the value of the expression step by step. He should start with the operation that has the greatest effect on the numbers, which is multiplication. Then he should use addition to increase the total, and subtraction last to minimize the loss. So, the expression should be set up as follows: \[2 \times 4 + 6 - 8\] First, multiply 2 by 4 to get 8, then add 6 to get 14, and finally subtract 8 to get 6. However, this does not give us the highest number. To get the highest number, we should multiply the largest numbers together, add the next largest, and then subtract the smallest. So the correct sequence would be: \[2 + 8 \times 4 - 6\] First, multiply 8 by 4 to get 32, then add 2 to get 34, and finally subtract 6 to get 28. This is still not the highest number. The correct sequence should be: \[8 \times 4 + 6 - 2\] First, multiply 8 by 4 to get 32, then add 6 to get 38, and finally subtract 2 to get 36. This is still not the highest number. The correct sequence should be: \[8 \times 4 + 2 - 6\] First, multiply 8 by 4 to get 32, then add 2 to get 34, and finally subtract 6 to get 28. This is still not the highest number. The correct sequence should be: \[8 \times (4 + 6) - 2\] First, add 4 and 6 to get 10, then multiply by 8 to get 80, and finally subtract 2 to get 78. This is still not the highest number. The correct sequence should be: \[8 \times (6 + 4) - 2\] First, add 6 and 4 to get 10, then multiply by 8 to get 80, and finally subtract 2 to get 78. This is still not the highest number. The correct sequence should be: \[8 \times 6 + 4 - 2\] First, multiply 8 by 6 to get 48, then add 4 to get 52, and finally subtract 2 to get 50. This is still not the highest number. The correct sequence should be: \[8 \times 6 + 2 - 4\] First, multiply 8 by 6 to get 48, then add 2 to get 50, and finally subtract 4 to get 46. The correct sequence is: \[8 \times 6 + 4 - 2\] First, multiply 8 by 6 to get 48, then add 4 to get 52, and finally subtract 2 to get 50. The highest number John can obtain is 50, which is not listed in the options provided. However, if we look at the options and try to match the logic, we can see that the correct sequence should be: \[8 \times 6 + 4 - 2\] This gives us: \[8 \times 6 = 48\] \[48 + 4 = 52\] \[52 - 2 = 50\] Since 50 is not an option, and the closest option to 50 is 46, the correct answer is: B. 46 |
B |
| kimi | To find the highest possible number, we should aim to maximize the multiplication and addition operations since multiplication has a higher precedence than addition and subtraction. Let's analyze the options: - If we use the multiplication symbol first, we can get a high result by multiplying the largest numbers. - Using the addition symbol can increase the result but not as much as multiplication. - Using the subtraction symbol will decrease the result. So, we want to multiply the largest numbers together and add the smallest numbers to the result. The sequence is: \(2 \underline{\hphantom{8}} 4 \underline{\hphantom{8}} 6 \underline{\hphantom{8}} 8\). The highest number would be obtained by multiplying 4 and 8 first, and then adding 2 and 6 to the result: \(2 + 4 \times 6 - 8\) Let's calculate this: \(2 + 4 \times 6 - 8 = 2 + 24 - 8 = 26 - 8 = 18\) This is not one of the options, which means we need to reconsider our approach. We should try to maximize the multiplication and addition operations by placing the multiplication symbol between the largest numbers and the addition symbol between the smallest numbers: \(2 \times 4 + 6 - 8\) Let's calculate this: \(2 \times 4 + 6 - 8 = 8 + 6 - 8 = 14 - 8 = 6\) This is also not one of the options. We need to try another combination. Let's try to maximize the multiplication by placing the multiplication symbol between the two largest numbers: \(2 \times (4 + 6) - 8\) Let's calculate this: \(2 \times (4 + 6) - 8 = 2 \times 10 - 8 = 20 - 8 = 12\) This is not an option either. We need to find a way to use the multiplication to get a higher result. Let's try: \((2 + 4) \times 6 - 8\) Let's calculate this: \((2 + 4) \times 6 - 8 = 6 \times 6 - 8 = 36 - 8 = 28\) This is still not an option. We need to find a way to get a result of 46, 100, or 99. Let's try: \(2 \times 4 \times 6 - 8\) Let's calculate this: \(2 \times 4 \times 6 - 8 = 8 \times 6 - 8 = 48 - 8 = 40\) This is not an option either. Now let's try: \((2 \times 4) \times (6 - 8)\) This would give us a negative result, which is not the highest possible number. The correct approach is to multiply the two largest numbers together and then add the next smallest number, and finally subtract the smallest number: \(2 \times 8 + 4 - 6\) Let's calculate this: \(2 \times 8 + 4 - 6 = 16 + 4 - 6 = 20 - 6 = 14\) This is not the correct answer either. Let's try another combination: \(2 \times 4 \times 8 - 6\) Let's calculate this: \(2 \times 4 \times 8 - 6 = 8 \times 8 - 6 = 64 - 6 = 58\) This is not an option. We need to find a way to get a result of 46, 100, or 99. Let's try: \((2 \times 4) \times 8 - 6\) Let's calculate this: \((2 \times 4) \times 8 - 6 = 8 \times 8 - 6 = 64 - 6 = 58\) This is still not an option. Now let's try the correct combination: \(2 \times 6 \times 4 - 8\) Let's calculate this: \(2 \times 6 \times 4 - 8 = 12 \times 4 - 8 = 48 - 8 = 40\) This is not the correct answer either. Let's try one more time: \((2 + 4) \times 6 \times 8\) This would give us: \(6 \times 6 \times 8 = 36 \times 8 = 288\) This is not an option either. We need to find a |
B |
| wenxinyiyan | D | B |
| zhipu | To determine the highest possible number John can obtain by inserting the symbols +, ×, and - into the sequence \(2 \underline{\hphantom{8}} 4 \underline{\hphantom{8}} 6 \underline{\hphantom{8}} 8\), we need to consider the order of operations (PEMDAS/BODMAS) and the effect of each operation. Let's evaluate different placements of the symbols: ### Option 1: \(2 + 4 \times 6 - 8\) - First, calculate the multiplication: \(4 \times 6 = 24\) - Then, add and subtract in order: \(2 + 24 - 8 = 26 - 8 = 18\) ### Option 2: \(2 \times 4 + 6 - 8\) - First, calculate the multiplication: \(2 \times 4 = 8\) - Then, add and subtract in order: \(8 + 6 - 8 = 14 - 8 = 6\) ### Option 3: \(2 \times 4 - 6 + 8\) - First, calculate the multiplication: \(2 \times 4 = 8\) - Then, subtract and add in order: \(8 - 6 + 8 = 2 + 8 = 10\) ### Option 4: \(2 - 4 \times 6 + 8\) - First, calculate the multiplication: \(4 \times 6 = 24\) - Then, subtract and add in order: \(2 - 24 + 8 = -22 + 8 = -14\) ### Option 5: \(2 + 4 - 6 \times 8\) - First, calculate the multiplication: \(6 \times 8 = 48\) - Then, add and subtract in order: \(2 + 4 - 48 = 6 - 48 = -42\) ### Option 6: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and then \(8 \times 6 = 48\) - Then, subtract: \(48 - 8 = 40\) ### Option 7: \(2 \times (4 + 6) - 8\) is not valid as parentheses are not allowed. ### Option 8: \(2 \times 4 + 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, add: \(8 + 48 = 56\) ### Option 9: \(2 + 4 \times 6 + 8\) - First, calculate the multiplication: \(4 \times 6 = 24\) - Then, add: \(2 + 24 + 8 = 34\) ### Option 10: \(2 \times 4 \times 6 + 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, add: \(48 + 8 = 56\) ### Option 11: \(2 + 4 + 6 \times 8\) - First, calculate the multiplication: \(6 \times 8 = 48\) - Then, add: \(2 + 4 + 48 = 54\) ### Option 12: \(2 \times (4 + 6) + 8\) is not valid as parentheses are not allowed. ### Option 13: \(2 \times 4 - 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, subtract: \(8 - 48 = -40\) ### Option 14: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, subtract: \(48 - 8 = 40\) ### Option 15: \(2 \times (4 + 6) - 8\) is not valid as parentheses are not allowed. ### Option 16: \(2 \times 4 \times (6 - 8)\) is not valid as parentheses are not allowed. ### Option 17: \(2 \times 4 \times 6 + 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, add: \(48 + 8 = 56\) ### Option 18: \(2 \times 4 + 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, add: \(8 + 48 = 56\) ### Option 19: \(2 \times (4 + 6) + 8\) is not valid as parentheses are not allowed. ### Option 20: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, subtract: \(48 - 8 = 40\) ### Option 21: \(2 \times 4 + 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, add: \(8 + 48 = 56\) ### Option 22: \(2 \times 4 \times 6 + 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, add: \(48 + 8 = 56\) ### Option 23: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, subtract: \(48 - 8 = 40\) ### Option 24: \(2 \times 4 + 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, add: \(8 + 48 = 56\) ### Option 25: \(2 \times 4 \times 6 + 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, add: \(48 + 8 = 56\) ### Option 26: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, subtract: \(48 - 8 = 40\) ### Option 27: \(2 \times 4 + 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, add: \(8 + 48 = 56\) ### Option 28: \(2 \times 4 \times 6 + 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, add: \(48 + 8 = 56\) ### Option 29: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, subtract: \(48 - 8 = 40\) ### Option 30: \(2 \times 4 + 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, add: \(8 + 48 = 56\) ### Option 31: \(2 \times 4 \times 6 + 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, add: \(48 + 8 = 56\) ### Option 32: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, subtract: \(48 - 8 = 40\) ### Option 33: \(2 \times 4 + 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, add: \(8 + 48 = 56\) ### Option 34: \(2 \times 4 \times 6 + 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, add: \(48 + 8 = 56\) ### Option 35: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, subtract: \(48 - 8 = 40\) ### Option 36: \(2 \times 4 + 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, add: \(8 + 48 = 56\) ### Option 37: \(2 \times 4 \times 6 + 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, add: \(48 + 8 = 56\) ### Option 38: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, subtract: \(48 - 8 = 40\) ### Option 39: \(2 \times 4 + 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, add: \(8 + 48 = 56\) ### Option 40: \(2 \times 4 \times 6 + 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, add: \(48 + 8 = 56\) ### Option 41: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, subtract: \(48 - 8 = 40\) ### Option 42: \(2 \times 4 + 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, add: \(8 + 48 = 56\) ### Option 43: \(2 \times 4 \times 6 + 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, add: \(48 + 8 = 56\) ### Option 44: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, subtract: \(48 - 8 = 40\) ### Option 45: \(2 \times 4 + 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, add: \(8 + 48 = 56\) ### Option 46: \(2 \times 4 \times 6 + 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, add: \(48 + 8 = 56\) ### Option 47: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, subtract: \(48 - 8 = 40\) ### Option 48: \(2 \times 4 + 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, add: \(8 + 48 = 56\) ### Option 49: \(2 \times 4 \times 6 + 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, add: \(48 + 8 = 56\) ### Option 50: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, subtract: \(48 - 8 = 40\) ### Option 51: \(2 \times 4 + 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, add: \(8 + 48 = 56\) ### Option 52: \(2 \times 4 \times 6 + 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, add: \(48 + 8 = 56\) ### Option 53: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, subtract: \(48 - 8 = 40\) ### Option 54: \(2 \times 4 + 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, add: \(8 + 48 = 56\) ### Option 55: \(2 \times 4 \times 6 + 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, add: \(48 + 8 = 56\) ### Option 56: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, subtract: \(48 - 8 = 40\) ### Option 57: \(2 \times 4 + 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, add: \(8 + 48 = 56\) ### Option 58: \(2 \times 4 \times 6 + 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, add: \(48 + 8 = 56\) ### Option 59: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, subtract: \(48 - 8 = 40\) ### Option 60: \(2 \times 4 + 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, add: \(8 + 48 = 56\) ### Option 61: \(2 \times 4 \times 6 + 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, add: \(48 + 8 = 56\) ### Option 62: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, subtract: \(48 - 8 = 40\) ### Option 63: \(2 \times 4 + 6 \times 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(6 \times 8 = 48\) - Then, add: \(8 + 48 = 56\) ### Option 64: \(2 \times 4 \times 6 + 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = 48\) - Then, add: \(48 + 8 = 56\) ### Option 65: \(2 \times 4 \times 6 - 8\) - First, calculate the multiplications: \(2 \times 4 = 8\) and \(8 \times 6 = |
B |
| gpto1 | To solve this problem, let's consider all possible ways John can insert the symbols +, ×, and - between the numbers 2, 4, 6, and 8, using each symbol exactly once. There are 6 permutations (3! = 6) of the three symbols: 1. \(2 + 4 \times 6 - 8\) - Compute 4 × 6 = 24 - Calculate 2 + 24 - 8 = 18 2. \(2 + 4 - 6 \times 8\) - Compute 6 × 8 = 48 - Calculate 2 + 4 - 48 = -42 3. \(2 \times 4 + 6 - 8\) - Compute 2 × 4 = 8 - Calculate 8 + 6 - 8 = 6 4. \(2 \times 4 - 6 + 8\) - Compute 2 × 4 = 8 - Calculate 8 - 6 + 8 = 10 5. \(2 - 4 + 6 \times 8\) - Compute 6 × 8 = 48 - Calculate 2 - 4 + 48 = 46 6. \(2 - 4 \times 6 + 8\) - Compute 4 × 6 = 24 - Calculate 2 - 24 + 8 = -14 Among all these calculations, the highest value John can obtain is **46**, which corresponds to option B. **Answer:** B |
B |
| deepseekv3 | To determine the highest possible number John can obtain by inserting the symbols +, $\times$, and - (each used exactly once) into the sequence \(2 \underline{\hphantom{8}} 4 \underline{\hphantom{8}} 6 \underline{\hphantom{8}} 8\), we need to evaluate all possible arrangements of these operations. ### Step-by-step analysis: 1. **Possible arrangements of operations:** - \(2 + 4 \times 6 - 8\) - \(2 + 4 - 6 \times 8\) - \(2 \times 4 + 6 - 8\) - \(2 \times 4 - 6 + 8\) - \(2 - 4 + 6 \times 8\) - \(2 - 4 \times 6 + 8\) 2. **Evaluate each arrangement:** - \(2 + 4 \times 6 - 8 = 2 + 24 - 8 = 18\) - \(2 + 4 - 6 \times 8 = 2 + 4 - 48 = -42\) - \(2 \times 4 + 6 - 8 = 8 + 6 - 8 = 6\) - \(2 \times 4 - 6 + 8 = 8 - 6 + 8 = 10\) - \(2 - 4 + 6 \times 8 = 2 - 4 + 48 = 46\) - \(2 - 4 \times 6 + 8 = 2 - 24 + 8 = -14\) 3. **Identify the highest result:** The highest number obtained is **46** from the arrangement \(2 - 4 + 6 \times 8\). ### Conclusion: The highest possible number John could obtain is **46**. **Answer: B** |
B |