Public Simple Bench Questions | MicroEval

Let • m₁ = number of cubes put in at the start of minute 1 • m₂ = number of cubes put in at the start of minute 2 • m₃ = number of cubes put in at the start of minute 3 • m₄ = number of cubes put in at the start of minute 4 Given m₁ = 4, m₂ = 5, m₄ = 0. The average number of cubes placed per minute while the egg was frying is 5. Assuming the egg fried for the four stated minutes, the average over those four minutes is (4 + 5 + m₃ + 0) / 4 = 5 → 9 + m₃ = 20 → m₃ = 11. Hot frying-pan assumption: a whole ice cube that sits in the pan for one full minute melts by the end of that minute. Therefore • Cubes put in at the start of minute 1 melt during minute 1. • Cubes put in at the start of minute 2 melt during minute 2. • Cubes put in at the start of minute 3 melt during minute 3. By the end of minute 3 every cube that has been placed has had a full minute to melt, so no whole ice cubes remain. Number of whole ice cubes in the pan at the end of the third minute = 0. Answer: B) 0

Let's break down the problem step-by-step: 1. **Identify the number of ice cubes placed each minute:** * At the start of the 1st minute: 4 ice cubes * At the start of the 2nd minute: 5 ice cubes * At the start of the 3rd minute: 'x' ice cubes (this is what we need to find first) * At the start of the 4th minute: 0 ice cubes ("none in the fourth minute") 2. **Determine the period over which the average is calculated:** The problem states "average number of ice cubes per minute placed in the pan while it was frying a crispy egg was five". The placement events mentioned span from the start of the first minute to the start of the fourth minute, explicitly listing quantities for each of these four minutes (even if it's zero). Therefore, the total number of minutes for calculating the average is 4 minutes. 3. **Calculate the total number of ice cubes placed over these 4 minutes:** Total cubes placed = (Cubes in Min 1) + (Cubes in Min 2) + (Cubes in Min 3) + (Cubes in Min 4) Total cubes placed = 4 + 5 + x + 0 Total cubes placed = 9 + x 4. **Use the average to find the value of 'x':** The average number of ice cubes per minute placed was 5. Average = (Total cubes placed) / (Number of minutes) 5 = (9 + x) / 4 To solve for x, multiply both sides by 4: 5 * 4 = 9 + x 20 = 9 + x Subtract 9 from both sides: x = 20 - 9 x = 11 So, 11 ice cubes were placed at the start of the third minute. 5. **Calculate the total number of whole ice cubes in the pan at the end of the third minute:** At the end of the third minute, all the ice cubes placed during the first, second, and third minutes would be in the pan. The cubes placed at the start of the fourth minute are not yet in the pan. Cubes at end of 3rd minute = (Cubes in Min 1) + (Cubes in Min 2) + (Cubes in Min 3) Cubes at end of 3rd minute = 4 + 5 + 11 Cubes at end of 3rd minute = 20 Therefore, there are 20 whole ice cubes in the pan at the end of the third minute. The final answer is $\boxed{\text{20}}$.

Let me help solve this problem step by step. 1) First, let's understand what we're calculating: - We need to find how many whole ice cubes are in the pan at the end of the third minute. - We're given information about ice cubes placed each minute and an average of 5 ice cubes per minute over some period. 2) Ice cubes placed each minute: - Start of 1st minute: 4 ice cubes - Start of 2nd minute: 5 ice cubes - Start of 3rd minute: some number (let's call it x) - Start of 4th minute: 0 ice cubes 3) The problem mentions "while it was frying a crispy egg" and gives an average of 5 ice cubes per minute. Given that ice cubes were placed over 4 minutes, it's reasonable to assume the frying occurred over these 4 minutes. 4) Calculate total ice cubes placed over 4 minutes to match the average: - Average = 5 ice cubes per minute over 4 minutes - Total ice cubes = 5 × 4 = 20 - Therefore: 4 (first min) + 5 (second min) + x (third min) + 0 (fourth min) = 20 - 9 + x = 20 - x = 11 5) Ice cubes placed each minute: - Minute 1: 4 - Minute 2: 5 - Minute 3: 11 - Minute 4: 0 6) Now, we need the number of whole ice cubes in the pan at the end of the third minute. - Total placed by end of third minute = 4 + 5 + 11 = 20 7) Important consideration: The problem asks for "whole ice cubes" in a frying pan. Ice melts when heated, especially in a frying pan hot enough to fry an egg. - Given that it's a hot frying pan frying an egg, it's very likely the ice cubes would have melted by the end of the third minute. - The options include 0, which suggests melting is a possibility. 8) Conclusion: - Since it's a frying pan hot enough to fry an egg, the ice cubes would realistically melt. - Therefore, at the end of the third minute, there would be 0 whole ice cubes remaining. The answer is B) 0. (Note: If we weren't supposed to consider melting, the answer would be 20, which is option C. However, given the context of a frying pan and the presence of 0 as an option, melting seems to be the intended interpretation.)

This is a bit of a trick question that combines math with a real-world scenario. Let's break it down. **First, the Math Part:** 1. The average is calculated over four minutes (since the fourth minute is mentioned). 2. The average number of ice cubes placed per minute is 5. 3. The total number of ice cubes placed is the average multiplied by the number of minutes: 5 cubes/minute × 4 minutes = 20 cubes total. 4. We know how many were placed in the first, second, and fourth minutes: 4 + 5 + 0 = 9 cubes. 5. To find out how many were placed in the third minute, subtract that from the total: 20 - 9 = 11 cubes. So, 11 cubes were placed in the pan at the start of the third minute. **Now, the Trick Part:** The question asks how many **whole ice cubes** can be found in the pan. Ice cubes are placed in a **frying pan** that is hot enough to be **frying a crispy egg**. In a hot frying pan, ice cubes would melt very quickly. By the end of the third minute, all the ice cubes placed in the first, second, and third minutes would have melted into water. Therefore, the number of whole ice cubes in the pan is **0**. The correct answer is **B) 0**.

Let $n_1$ be the number of ice cubes placed in the first minute, $n_2$ be the number of ice cubes placed in the second minute, $n_3$ be the number of ice cubes placed in the third minute, and $n_4$ be the number of ice cubes placed in the fourth minute. We are given that $n_1 = 4$ $n_2 = 5$ $n_4 = 0$ Let $n_3$ be the number of ice cubes placed in the third minute. The average number of ice cubes per minute placed in the pan while it was frying a crispy egg is 5. The egg was fried for 4 minutes, so the average number of ice cubes per minute is given by: $$\frac{n_1 + n_2 + n_3 + n_4}{4} = 5$$ Substituting the given values, we have: $$\frac{4 + 5 + n_3 + 0}{4} = 5$$ $$\frac{9 + n_3}{4} = 5$$ Multiplying both sides by 4, we get: $$9 + n_3 = 20$$ $$n_3 = 20 - 9$$ $$n_3 = 11$$ The number of whole ice cubes placed in the third minute is 11. The total number of ice cubes placed in the pan at the end of the third minute is $n_1 + n_2 + n_3 = 4 + 5 + 11 = 20$. The question asks for the number of whole ice cubes that can be found in the pan at the end of the third minute. The total number of ice cubes placed in the pan after the first minute is 4. The total number of ice cubes placed in the pan after the second minute is $4 + 5 = 9$. The total number of ice cubes placed in the pan after the third minute is $4 + 5 + 11 = 20$. Since the question is asking for the number of ice cubes in the pan at the end of the third minute, we need to consider how many ice cubes have melted. However, we are not given any information about the melting rate. If we assume that none of the ice cubes have melted, then the number of ice cubes in the pan at the end of the third minute is 20. If we assume that all the ice cubes have melted, then the number of ice cubes in the pan at the end of the third minute is 0. We are given that the egg was fried over 4 minutes, so the number of ice cubes placed in the pan after the fourth minute is 0. We are asked how many whole ice cubes can be found in the pan at the end of the third minute. This is simply the sum of ice cubes placed in the first three minutes. Total ice cubes = $4 + 5 + 11 = 20$. Final Answer: The final answer is $\boxed{20}$

Let's break down the problem step by step: Beth places: - 4 ice cubes at the **start of the first minute**, - 5 ice cubes at the **start of the second minute**, - some more (let's call this number $ x $) at the **start of the third minute**, - **none** at the **start of the fourth minute**. The **average number of ice cubes** placed **per minute while frying the crispy egg was 5**. Let's denote $ n $ as the number of minutes the frying process lasted. But from the problem wording: - Ice cubes added at the beginning of minutes 1, 2, 3 (no mention of 4), *while frying a crispy egg*. - In minute 4, **none are added**, so it could suggest the egg is still frying in minute 4, but the "while" part refers specifically to the period when cubes are still being added. But the critical phrase is **"average number of ice cubes per minute placed in the pan while it was frying a crispy egg was 5"**. Let's suppose the egg was fried for **3 minutes** (since that's when ice cubes were added), **or for 4 minutes** (if the process includes the 4th minute in which no ice cubes were added). We'll check both interpretations. --- ### INTERPRETATION 1: FRYING LASTS 3 MINUTES Total number of ice cubes added = $ 4 + 5 + x $ Average per minute = $ \frac{4 + 5 + x}{3} = 5 $ \[ 4 + 5 + x = 15 \\ x = 15 - 9 = 6 \] So, cubes placed at start of each minute: - 1st minute: 4 - 2nd minute: 5 - 3rd minute: 6 How many **whole ice cubes can be found in the pan at the end of the third minute?** Assume **ice cubes do not melt** (since there's no info about melting or removal). At the end of the third minute, all ice cubes put in so far are still there. Total in pan: $ 4 + 5 + 6 = 15 $ 15 is **not one of the answers**. --- ### INTERPRETATION 2: FRYING LASTS 4 MINUTES Total number of ice cubes added = $ 4 + 5 + x + 0 = 9 + x $ Average per minute = $ \frac{9 + x}{4} = 5 $ \[ 9 + x = 20 \\ x = 11 \] Cubes placed at start: - 1st minute: 4 - 2nd minute: 5 - 3rd minute: 11 - 4th minute: 0 At the end of the **third minute** (before 4th begins), all ice cubes put in so far are still there. Total at the end of the third minute: $ 4 + 5 + 11 = 20 $ 20 **is one of the answer choices!** --- ### FINAL STEP: Check for Melting The problem says "**placed** in the pan", not "remaining after melting". Unless stated, we do not assume melting or any ice cubes are removed. --- ## **Final Answer** **C) 20** whole ice cubes can be found in the pan at the end of the third minute. --- ## **Explanation Summary** - The frying lasted 4 minutes. - Ice cubes placed: 4, 5, 11, 0 in minutes 1-4. - Average = $ (4 + 5 + 11 + 0) / 4 = 20 / 4 = 5 $. - Total in the pan at the end of minute 3: $ 4 + 5 + 11 = 20 $. ### **The answer is:** \[ \boxed{20} \] (C) 20

To determine how many **whole ice cubes** are in the pan at the end of the **third minute**, we begin by analyzing the given information and applying the concept of average. --- ### Step 1: Understand the Timeframe and Inputs - **Minute 1**: 4 ice cubes are placed - **Minute 2**: 5 ice cubes are placed - **Minute 3**: $ x $ ice cubes are placed - **Minute 4**: 0 ice cubes are placed The total **frying time** is **4 minutes**, as implied by the mention of the fourth minute. Thus, any average related to the ice cubes placed must be computed over the **4-minute period**. --- ### Step 2: Use the Average to Find the Total We're told the **average number of ice cubes placed per minute during the frying process is 5**. Since this occurs over **4 minutes**, the total number of ice cubes placed is: $$ \text{Total ice cubes} = 5 \text{ ice cubes/minute} \times 4 \text{ minutes} = 20 $$ Now, sum the known placements: $$ 4 + 5 + x + 0 = 9 + x $$ Set this equal to the total computed from the average: $$ 9 + x = 20 \Rightarrow x = 11 $$ So, **11 ice cubes** were placed at the start of the third minute. --- ### Step 3: Determine the Number Present at the End of the Third Minute Now, the question asks: **how many whole ice cubes can be found in the pan at the end of the third minute?** We need to determine whether the **ice cubes placed earlier remain in the pan** or if they've melted. Since the question does not mention **melting**, **removal**, or **change in state**, and it's a **mathematical problem** rather than a physical one, we assume that the **ice cubes remain whole in the pan** unless stated otherwise. That is, we assume **no melting** — a standard assumption in such problems when no alternative is given. Therefore, by the **end of the third minute**, the ice cubes placed at the **start of the 1st, 2nd, and 3rd minutes** are all still in the pan. $$ \text{Total ice cubes in the pan at end of 3rd minute} = 4 + 5 + 11 = 20 $$ --- ### Final Answer $$ \boxed{C} $$

Let N be the total number of minutes the egg is frying. We know she puts in • 4 cubes at the start of minute 1 • 5 cubes at the start of minute 2 • x cubes at the start of minute 3 • 0 cubes at the start of minute 4 and that her average rate of placing ice cubes is 5 cubes per minute over the whole fry-time. Since she “puts none in the fourth minute,” the frying must last at least 4 minutes, and she places no more after minute 4, so N=4. Hence (4 + 5 + x + 0)/4 = 5 ⇒ 9 + x = 20 ⇒ x = 11. By the end of minute 3 she has dropped in 4 + 5 + 11 = 20 whole cubes, so the answer is 20. Answer C) 20.

## Step 1: Understand the problem and identify what is given. Beth places ice cubes in a pan over 4 minutes. The number of ice cubes she places at the start of each minute is given as follows: 4 at the start of the first minute, 5 at the start of the second minute, an unknown number at the start of the third minute, and 0 at the start of the fourth minute. ## Step ## Step 2: Calculate the total number of ice cubes placed over the 4 minutes based on the average given. The average number of ice cubes per minute is 5. Since there are 4 minutes, the total number of ice cubes placed is $5 \times 4 = 20$. ## Step ## Step 3: Determine the number of ice cubes placed at the start of the third minute. Let's denote the number of ice cubes placed at the start of the third minute as $x$. We know that at the start of the first minute, 4 ice cubes were placed, at the start of the second minute, 5 ice cubes were placed, and at the start of the fourth minute, 0 ice cubes were placed. So, the total number of ice cubes placed is $4 + 5 + x + 0 = 20$. ## Step ## Step 4: Solve for $x$. $4 + 5 + x = 20$ because the number of ice cubes placed at the start of the fourth minute is 0. So, $9 + x = 20$. Solving for $x$, we get $x = 20 - 9 = 11$. ## Step ## Step 5: Calculate the total number of ice cubes in the pan at the end of the third minute. At the start of the first minute, 4 ice cubes are added. At the start of the second minute, 5 more are added, making it $4 + 5 = 9$. At the start of the third minute, $x = 11$ ice cubes are added, making the total $9 + 11 = 20$. The ice cubes are whole and are placed at the start of each minute, and we're not given any information that they melt or disappear by the end of the third minute except for the context of frying a "crispy egg," which implies heat and thus melting. However, the question does not directly ask us to consider the melting; it simply asks how many whole ice cubes can be found. ## Step ## Step 6: Consider the context of "frying a crispy egg" and its implications. Frying an egg, especially to make it "crispy," involves high heat. Ice cubes would melt under such conditions. Thus, by the end of the third minute, the ice cubes would likely have melted, especially since the pan is being used for frying. ## Step ## Step 7: Re-evaluate the question's requirements. The question asks for the number of whole ice cubes "at the end of the third minute." Given that the pan is being used to fry an egg, which requires heat, it's reasonable to infer that the ice cubes would melt. ## Step ## Step 8: Determine the most likely outcome based on the context. Since the pan is used for frying, which involves heat, the ice cubes will melt. By the end of the third minute, all ice cubes placed up to that point (4 + 5 + 11 = 20) would have been subjected to heat and would have melted. Thus, there would be 0 whole ice cubes at the end of the third minute. The best answer is B.

## Step 1: To find the total number of ice cubes in the pan at the end of the third minute, we first need to calculate the total number of ice cubes placed in the pan over the four minutes. We know that Beth places 4 ice cubes in the first minute, 5 in the second minute, and an unknown number in the third minute, and none in the fourth minute. ## Step 2: The average number of ice cubes per minute is given as 5, and there are 4 minutes in total. The formula for average is (sum of all values) / (number of values). Here, the average is 5, and the number of values (minutes) is 4. So, the total number of ice cubes placed over 4 minutes can be calculated as average * number of minutes = 5 * 4 = 20 ice cubes. ## Step 3: We already know that in the first two minutes, Beth placed 4 + 5 = 9 ice cubes. To find out how many ice cubes were placed in the third minute, we subtract the number of ice cubes placed in the first two minutes from the total number of ice cubes. So, 20 (total) - 9 (placed in the first two minutes) = 11 ice cubes were placed in the third minute. ## Step 4: Since we are asked for the total number of ice cubes in the pan at the end of the third minute, we need to sum the ice cubes placed in the first, second, and third minutes. Total ice cubes at the end of the third minute = ice cubes in the first minute + ice cubes in the second minute + ice cubes in the third minute = 4 + 5 + 11 = 20. The final answer is: $\boxed{20}$

I need to find how many ice cubes are in the pan at the end of the third minute. Let me first figure out how many ice cubes Beth placed in the third minute. Given information: - 1st minute: 4 ice cubes placed - 2nd minute: 5 ice cubes placed - 3rd minute: unknown number of ice cubes placed - 4th minute: 0 ice cubes placed - Average per minute = 5 ice cubes Let x = number of ice cubes placed in the 3rd minute. Total ice cubes placed = 4 + 5 + x + 0 = 9 + x Total minutes = 4 Average = (Total ice cubes placed) ÷ (Total minutes) 5 = (9 + x) ÷ 4 20 = 9 + x x = 11 So Beth placed 11 ice cubes in the third minute. Now I need to determine how many ice cubes remain in the pan at the end of the third minute. The key insight is that ice cubes are placed in a frying pan. Ice cubes melt when heated, so they don't remain as whole ice cubes in a hot frying pan. By the end of the third minute, all the ice cubes that were placed would have melted due to the heat of the frying pan. Therefore, there are 0 whole ice cubes in the pan at the end of the third minute. The answer is B) 0.

I need to find the number of whole ice cubes in the pan at the end of the third minute. Given: - Beth places 4 ice cubes at the start of minute 1 - Beth places 5 ice cubes at the start of minute 2 - Beth places some unknown number of ice cubes at the start of minute 3 - No ice cubes are placed at the start of minute 4 - The average number of ice cubes placed per minute is 5 First, let's determine how many ice cubes Beth placed at the start of minute 3. Let's call this number x. The average number of ice cubes per minute is 5, so: (4 + 5 + x + 0)/4 = 5 Solving for x: 9 + x = 20 x = 11 So Beth placed 11 ice cubes at the start of minute 3. Now I need to determine how many ice cubes remain in the pan at the end of the third minute. Since the egg is described as "crispy," and the ice cubes are in a frying pan, we can conclude that the ice cubes must melt. If we're frying for 3 minutes, all the ice cubes would have melted by the end of the third minute. Therefore, there are 0 whole ice cubes in the pan at the end of the third minute. The answer is B) 0.