ChatGPT 4o Latest

Score051015202527Size (bn params, log scale)0.5110101001000ChatGPT 4o Latest

Score:

27

100.0%

Strict score:

24

88.9%

Family:

GPT-4

Size:

1800B parameters

License:

Proprietary

Quant type:

Full Float

Question

Correct

Strict Correct

Response

RCL1

The passage directly describes Jim Gilmore as "short and dark with big mustaches and big hands." It also mentions that he doesn't look much like a blacksmith, but this does not change the physical attributes of his appearance.

The correct answer is clearly stated in the text, so the best description of Jim's appearance is:

**B**

LG3

Let's analyze the statements:

1. "All employees of Duluth Paper received a bonus this year" – This means that if someone is an employee of Duluth Paper, then they must have received a bonus.
2. "Andrés did not receive a bonus this year" – This directly states that Andrés did not receive a bonus.

Now, we need to determine which conclusion logically follows if both of these statements are true. 

Since all employees of Duluth Paper received a bonus, but Andrés did not receive a bonus, it follows that Andrés cannot be an employee of Duluth Paper. If he were, he would have received a bonus, which contradicts the second statement.

Thus, the correct conclusion is that Andrés was not an employee of Duluth Paper this year.

The correct answer is:
C

RCL5

The second and third paragraphs primarily serve to juxtapose how Liz and Jim feel about each other. While Jim notices Liz but doesn't think much about her beyond some casual observations, Liz is deeply aware of and attracted to many details about Jim, including his appearance and demeanor. This comparison of their sentiments toward each other highlights the contrast between Jim's indifference and Liz's growing fondness for him.

Therefore, the correct answer is:

B) Juxtapose two peoples' sentiments

LG1

Let's break down the given statement: "All of Lisa's sisters can bake."

This implies that **if someone is Lisa's sister, then they must be able to bake**.

Now, let's evaluate each option:

(A) **If Jane cannot bake, then she is not Lisa's sister**  
- This is consistent with the original statement. If someone is Lisa's sister, they must be able to bake. So, if Jane cannot bake, she cannot be Lisa's sister.  
- **This is a valid conclusion.**

(B) **If Sarah can bake, then she is not Lisa's sister**  
- This is not necessarily true. The original statement only tells us that all of Lisa's sisters can bake, but it does not say that only Lisa's sisters can bake. So, just because Sarah can bake doesn't automatically mean she isn't Lisa's sister.  
- **This is not a valid conclusion.**

(C) **If Mary can bake, then she is Lisa's sister**  
- Similar to option B, this is not necessarily true. Many people may be able to bake, but that doesn't mean they are all Lisa's sisters.  
- **This is not a valid conclusion.**

(D) **If Emma is not Lisa's sister, then she cannot bake**  
- The original statement says that all of Lisa's sisters can bake, but it does not say that only Lisa's sisters can bake. So, even if Emma is not Lisa's sister, she could still be able to bake.  
- **This is not a valid conclusion.**

(E) **None of these**  
- Since option (A) is valid, (E) is not correct.

The correct answer is:
A

MW2

We are given an operation ◘ defined as follows:

\[
x \ ◘ \ y = 2x - 3y + 1
\]

We are asked to find the value of \( 4 \ ◘ \ 3 \).

### Step 1: Substitute \( x = 4 \) and \( y = 3 \) into the operation formula.

According to the definition, we substitute \( x = 4 \) and \( y = 3 \) into the expression \( x \ ◘ \ y = 2x - 3y + 1 \):

\[
4 \ ◘ \ 3 = 2(4) - 3(3) + 1
\]

### Step 2: Perform the calculations.

First, calculate \( 2(4) \):

\[
2(4) = 8
\]

Next, calculate \( -3(3) \):

\[
-3(3) = -9
\]

Now substitute these values into the expression:

\[
4 \ ◘ \ 3 = 8 - 9 + 1
\]

### Step 3: Simplify the expression.

\[
8 - 9 = -1
\]
\[
-1 + 1 = 0
\]

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

\[
\boxed{0}
\]

RCS5

(B)

SC1

offered to lend Sofie one of her extra swimsuits, excited for a fun day together.

SC2

He pulled a small pebble from his pocket and placed it where the missing pawn should be.

SC4

"The battery was nearly dead, and they needed directions."

SC5

She suggested checking the storage building, thinking a ball might have been left there by mistake.

RCS1

C) By preserving it with salt

RCS2

C) shifting responsibility for the costs of recycling

RCS3

A) It is very old

MW4

### Step 1: Define Variables
Let the width of the garden be denoted by \( w \) (in feet).

Since the length of the garden is four times the width, we can express the length as \( 4w \).

### Step 2: Perimeter Formula for a Rectangle
The formula for the perimeter \( P \) of a rectangle is:

\[
P = 2(\text{length} + \text{width})
\]

Substitute the values we know into this formula. The perimeter is given as 60 feet, the length is \( 4w \), and the width is \( w \):

\[
60 = 2(4w + w)
\]

### Step 3: Simplify and Solve for \( w \)
First, simplify the expression inside the parentheses:

\[
60 = 2(5w)
\]

Now, multiply the 2 and 5w:

\[
60 = 10w
\]

Next, solve for \( w \) by dividing both sides of the equation by 10:

\[
w = \frac{60}{10} = 6
\]

### Final Answer:
The width of the garden is \( \boxed{6} \) feet.

RCL3

The author includes a specific detail to show that Jim has noticed Liz Coates: "Jim noticed that her hair was always neat behind." This indicates that Jim is paying attention to her appearance, particularly her hair.

- **A) the frequency with which he thought of her**: This is incorrect because the passage explicitly says, "he never thought about her."
- **B) his fondness for her cooking**: This detail is not mentioned in the passage.
- **C) the whiteness of her teeth**: This is what Liz notices about Jim, not the other way around.
- **D) the arrangement of her hair**: This is correct, as the text mentions that Jim noticed her hair being neat behind.

The correct answer is:
**D**

RCL4

The repetitive use of "She liked it" serves to emphasize how closely Liz Coates observes and studies Jim Gilmore. Each "She liked it" phrase focuses on a different detail about Jim—his walk, his mustache, his smile, his arms—indicating that Liz is paying careful attention to his physical characteristics and mannerisms. This repetition highlights the depth of her attention and growing attraction, even down to minute details such as the contrast between his tanned and untanned skin. 

The correct answer is:
D) closeness with which one person studies another

LG2

Let's break down the provided statements:

1. "All members of the chess team are also members of the robotics club."
   - This means that if someone is on the chess team, they must also be in the robotics club.

2. "No members of the basketball team are members of the chess team."
   - This means that if someone is on the basketball team, they cannot be on the chess team.

Now, let's analyze each option:

(A) "If Izak is in the robotics club, then he is not on the basketball team."
   - This is not necessarily true. Being in the robotics club doesn't imply anything about being on the basketball team based on the given information. The statements only connect the chess team with the robotics club and the basketball team with the chess team, not directly the robotics club with the basketball team.

(B) "If Jerry is in the robotics club, then he is on the chess team."
   - This is not necessarily true. The first statement tells us that all members of the chess team are in the robotics club, but not the reverse. Someone could be in the robotics club without being on the chess team.

(C) "If Lisa is on the basketball team, then she is not in the robotics club."
   - This is not necessarily true. The second statement only tells us that Lisa cannot be on both the basketball and chess teams. It says nothing about her membership in the robotics club if she is on the basketball team.

(D) "If Sanjit is on the chess team, then he is on the basketball team."
   - This is false. The second statement tells us that no one can be on both the chess team and the basketball team.

(E) "If Seong-Jin is not in the robotics club, then he is not on the chess team."
   - This is true. According to the first statement, all members of the chess team are in the robotics club. Therefore, if Seong-Jin is not in the robotics club, he cannot be on the chess team.

The correct answer is:

E

LG4

Let's analyze the clues step by step:

1. **The person in Britain has the broken sword.**
   - Whoever is in Britain has the broken sword.

2. **The son, who is not in Denmark, neither has the gold doubloon nor the silver watch.**
   - The son is not in Denmark.
   - The son does not have the gold doubloon or the silver watch.

3. **The family member in Egypt has the family tree.**
   - The person in Egypt has the family tree.

4. **The mother has the silver watch but isn't in Mexico.**
   - The mother has the silver watch and is not in Mexico.

5. **The grandmother has the gold doubloon and is either in Denmark or Canada.**
   - The grandmother has the gold doubloon and is in either Denmark or Canada.

6. **The daughter has the oceanic map.**
   - We need to figure out where the daughter is.

### Step-by-step deduction:

- The **grandmother** has the gold doubloon and is either in Denmark or Canada (clue 5). This means the son is not in Denmark, so the grandmother must be in Denmark, and the son is not in Denmark. Therefore, the grandmother is in Denmark with the gold doubloon.

- The person in **Britain** has the broken sword (clue 1). This person is not the mother because the mother has the silver watch (clue 4). Therefore, the person in Britain is neither the mother nor the grandmother.

- The **mother** has the silver watch and is not in Mexico (clue 4). Since the grandmother is in Denmark, the mother must be in one of the remaining places: Britain, Canada, Egypt, or Mexico. Since the person in Britain has the broken sword and the mother does not have the broken sword, the mother cannot be in Britain. Also, she is not in Mexico. Therefore, the mother must be in **Canada** with the silver watch.

- The person in **Egypt** has the family tree (clue 3). This cannot be the grandmother (who is in Denmark), the mother (who is in Canada), or the son (since the son does not have the family tree and he isn't in Egypt). Therefore, the person in Egypt must be either the son or the daughter.

- The **daughter** has the oceanic map (clue 6). Since the person in Egypt has the family tree, the daughter cannot be in Egypt. Therefore, the daughter must be in **Mexico** with the oceanic map.

Thus, the daughter is located in **Mexico**.

Answer: **Mexico**

LG5

Let's break down the clues systematically:

1. The person in Britain has the broken sword.
2. The son is not in Denmark and neither has the gold doubloon nor the silver watch.
3. The person in Egypt has the family tree.
4. The mother has the silver watch but isn't in Mexico.
5. The grandmother has the gold doubloon and is either in Denmark or Canada.

Now, let's analyze the clues:

- **Clue 5:** The grandmother has the gold doubloon and is either in Denmark or Canada. If the grandmother is in Denmark, she has the gold doubloon.
- **Clue 2:** The son is not in Denmark, so he must be in another country. He also does not have the gold doubloon (which the grandmother has) or the silver watch (which the mother has).
- **Clue 4:** The mother has the silver watch but is not in Mexico. So, she must be in one of the remaining countries: Britain, Canada, or Egypt.
- **Clue 1:** The person in Britain has the broken sword. This means the mother isn't in Britain because she has the silver watch.
- **Clue 3:** The person in Egypt has the family tree, so the mother isn't in Egypt either.

By process of elimination, the mother must be in **Canada**.

Answer:
Canada

LO1

▲ → ◆ → ★

LO2

★ → ◆ → ● → ▲

LO3

▲ ★ ● ◆

LO4

★ ● ▲ ◆

RCS4

(C) convenient

MW1

Let's begin by analyzing the problem step-by-step.

We are told that each student is supposed to write a number of verses that consists of two parts:
1. \( n \) verses (a fixed number for all students),
2. Plus twice as many verses as the number of their class rank.

For the 7th student, their class rank is 7. The number of verses they write can be expressed as:
\[
n + 2 \times (\text{class rank})
\]
For the 7th student, this becomes:
\[
n + 2 \times 7 = n + 14
\]
We are also told that the 7th student wrote 20 verses, so we can set up the following equation:
\[
n + 14 = 20
\]
Now, solve for \( n \):
\[
n = 20 - 14
\]
\[
n = 6
\]

Thus, the value of \( n \) is:
\[
\boxed{6}
\]

MW3

We are given that John is traveling from his home to a park 60 miles away, and he plans to drive at a steady speed of 30 miles per hour (mph). We need to determine how long this trip will take in hours.

### Step-by-step solution:

1. **Distance formula**: 
   The relationship between distance, speed, and time is given by the formula:
   \[
   \text{Distance} = \text{Speed} \times \text{Time}
   \]
   We can rearrange this formula to solve for time:
   \[
   \text{Time} = \frac{\text{Distance}}{\text{Speed}}
   \]

2. **Substitute the given values**:
   We know the distance is 60 miles, and the speed is 30 miles per hour.
   \[
   \text{Time} = \frac{60 \text{ miles}}{30 \text{ miles per hour}} = 2 \text{ hours}
   \]

Thus, it will take John 2 hours to reach the park.

**Answer:**
\[
\boxed{2 \text{ hours}}
\]

MW5

We are tasked with finding how many integers between 100 and 199 have exactly one duplicate digit. Let’s break this down step by step.

### Step 1: Define the structure of the number
We are looking for three-digit numbers of the form \( \overline{abc} \), where:
- \( a \) is the hundreds digit, which must be 1 (since the number is between 100 and 199).
- \( b \) and \( c \) are the tens and ones digits, respectively.
- There must be exactly one duplicate digit, meaning either \( b = c \) or one of them equals \( a \), but not all three digits can be the same.

### Step 2: Consider the cases
We now examine the possible cases that satisfy the condition of having exactly one duplicate digit.

#### Case 1: \( b = c \) and \( b \neq a \)
- In this case, \( a = 1 \), but \( b \) and \( c \) must be the same (since they are the duplicate digits), and \( b \neq 1 \) (to ensure it's not a full repetition of all three digits).
- The possible choices for \( b \) are 0, 2, 3, 4, 5, 6, 7, 8, 9.
- This gives 9 possibilities for this case.

#### Case 2: \( b = a \) and \( c \neq a \)
- Here, \( a = 1 \), and \( b = 1 \), but \( c \) must be different from both \( a \) and \( b \).
- The possible choices for \( c \) are 0, 2, 3, 4, 5, 6, 7, 8, 9.
- This gives 9 possibilities for this case.

#### Case 3: \( c = a \) and \( b \neq a \)
- In this case, \( a = 1 \), and \( c = 1 \), but \( b \) must be different from both \( a \) and \( c \).
- The possible choices for \( b \) are 0, 2, 3, 4, 5, 6, 7, 8, 9.
- This gives 9 possibilities for this case.

### Step 3: Exclude overcounted cases
The three cases we've considered are mutually exclusive, meaning there is no overlap between them (because each case corresponds to a different pair of digits being equal). Therefore, we can simply sum the possibilities from each case.

### Step 4: Calculate the total
- Case 1 gives 9 possibilities.
- Case 2 gives 9 possibilities.
- Case 3 gives 9 possibilities.

Thus, the total number of integers between 100 and 199 that have exactly one duplicate digit is:
\[
9 + 9 + 9 = 27.
\]

### Final Answer:
27