推理是问答的一个子场景，它在 AI 交互中具有独特的价值。在这个场景中，prompt 的作用尤为重要，因为它不仅要求 AI 理解问题，还要求其进行逻辑推理和计算。这一场景为 ChatGPT API 的应用提供了丰富的可能性，相比其他场景，这里的竞争可能较少。
以 GMAT 数学题为例
我们可以看到 ChatGPT 如何处理复杂的逻辑推理问题。下面是一个没有任何辅助说明的简单 prompt：
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If a real estate agent received a commission of 6 percent of the selling price of a certain house, what was the selling price of the house?
(1) The selling price minus the real estate agent’s commission was $84,600.
(2) The selling price was 250 percent of the original purchase price of $36,000.
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
If a real estate agent received a commission of 6 percent of the selling price of a certain house, what was the selling price of the house? (1) The selling price minus the real estate agent’s commission was $84,600. (2) The selling price was 250 percent of the original purchase price of $36,000. (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. (D) EACH statement ALONE is sufficient. (E) Statements (1) and (2) TOGETHER are NOT sufficient.
这道题目的中文意思是这样的：
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如果一个房地产经纪人的佣金是某个房子的售价的6％，那么这个房子的售价是多少？
（1）售价减去房地产经纪人的佣金为84,600美元。
（2）购买价是36,000美元，售价是购买价的250%。
（A）仅陈述（1）足以回答问题，但仅陈述（2）不能回答问题。
（B）仅陈述（2）足以回答问题，但仅陈述（1）不能回答问题。
（C）两个陈述合起来足以回答问题，但没有一个陈述单独足以回答问题。
（D）每个陈述单独足以回答问题。
（E）陈述（1）和（2）合起来不能回答问题。
如果一个房地产经纪人的佣金是某个房子的售价的6％，那么这个房子的售价是多少？ （1）售价减去房地产经纪人的佣金为84,600美元。 （2）购买价是36,000美元，售价是购买价的250%。 （A）仅陈述（1）足以回答问题，但仅陈述（2）不能回答问题。 （B）仅陈述（2）足以回答问题，但仅陈述（1）不能回答问题。 （C）两个陈述合起来足以回答问题，但没有一个陈述单独足以回答问题。 （D）每个陈述单独足以回答问题。 （E）陈述（1）和（2）合起来不能回答问题。
AI 的输出
AI 的输出是基于提供的信息进行详细的推理和计算：
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Let's analyze the information provided in each statement and determine if we can find the selling price of the house: Statement (1): The selling price minus the real estate agent’s commission was $84,600. This statement tells us that the selling price minus the commission equals $84,600. Let P be the selling price, and C be the commission. We can write this as an equation: P - 0.06P = $84,600 Now, we can solve for P: 0.94P = $84,600 P = $84,600 / 0.94 P ≈ $90,000 Statement (1) alone is sufficient to find the selling price, which is approximately $90,000. Statement (2): The selling price was 250 percent of the original purchase price of $36,000. This statement tells us that the selling price is 250% of the original purchase price. We can calculate the selling price using this information: Selling price = 250% of $36,000 Selling price = 2.5 * $36,000 Selling price = $90,000 Statement (2) alone is also sufficient to find the selling price, which is $90,000. Both statements individually provide the same answer for the selling price, which is $90,000. Therefore, the correct answer is (D) EACH statement ALONE is sufficient to answer the question.
Let’s analyze the information provided in each statement and determine if we can find the selling price of the house: Statement (1): The selling price minus the real estate agent’s commission was $84,600. This statement tells us that the selling price minus the commission equals $84,600. Let P be the selling price, and C be the commission. We can write this as an equation: P – 0.06P = $84,600 Now, we can solve for P: 0.94P = $84,600 P = $84,600 / 0.94 P ≈ $90,000 Statement (1) alone is sufficient to find the selling price, which is approximately $90,000. Statement (2): The selling price was 250 percent of the original purchase price of $36,000. This statement tells us that the selling price is 250% of the original purchase price. We can calculate the selling price using this information: Selling price = 250% of $36,000 Selling price = 2.5 * $36,000 Selling price = $90,000 Statement (2) alone is also sufficient to find the selling price, which is $90,000. Both statements individually provide the same answer for the selling price, which is $90,000. Therefore, the correct answer is (D) EACH statement ALONE is sufficient to answer the question.
翻译成中文是这样的：
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让我们分析每个陈述提供的信息，并确定是否能找到房屋的售价：
陈述（1）：房屋售价减去房地产经纪人的佣金为84,600美元。
这个陈述告诉我们，售价减去佣金等于84,600美元。设P为售价，C为佣金。我们可以将这个情况表示为一个方程：
P - 0.06P = 84,600美元
现在，我们可以解出P的值：
0.94P = 84,600美元
P = 84,600美元 / 0.94
P ≈ 90,000美元
陈述（1）单独足以找到售价，售价约为90,000美元。
陈述（2）：售价是36,000美元原始购买价格的250%。
这个陈述告诉我们，售价是原始购买价格的250%。我们可以使用这个信息计算售价：
售价 = 36,000美元的250%
售价 = 2.5 * 36,000美元
售价 = 90,000美元
陈述（2）单独也足以找到售价，售价为90,000美元。
两个陈述分别提供了相同的售价答案，即90,000美元。因此，正确答案是（D）每个陈述单独足以回答问题。
让我们分析每个陈述提供的信息，并确定是否能找到房屋的售价： 陈述（1）：房屋售价减去房地产经纪人的佣金为84,600美元。 这个陈述告诉我们，售价减去佣金等于84,600美元。设P为售价，C为佣金。我们可以将这个情况表示为一个方程： P – 0.06P = 84,600美元 现在，我们可以解出P的值： 0.94P = 84,600美元 P = 84,600美元 / 0.94 P ≈ 90,000美元 陈述（1）单独足以找到售价，售价约为90,000美元。 陈述（2）：售价是36,000美元原始购买价格的250%。 这个陈述告诉我们，售价是原始购买价格的250%。我们可以使用这个信息计算售价： 售价 = 36,000美元的250% 售价 = 2.5 * 36,000美元 售价 = 90,000美元 陈述（2）单独也足以找到售价，售价为90,000美元。 两个陈述分别提供了相同的售价答案，即90,000美元。因此，正确答案是（D）每个陈述单独足以回答问题。
这个场景的复杂性在于，AI 需要不仅理解问题，还要应用数学知识和逻辑推理能力来提供准确的答案。可以尝试将不同类型的逻辑或数学问题输入ChatGPT，以探索其在这一领域的应用潜力。
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