GPT-4o

Score051015202527Size (bn params, log scale)0.5110101001000GPT-4o

Score:

25

92.6%

Strict score:

20

74.1%

Family:

GPT-4

Size:

1800B parameters

License:

Proprietary

Quant type:

Full Float

Question

Correct

Strict Correct

Response

RCL1

The passage provides specific details about Jim Gilmore's appearance, stating that he was "short and dark with big mustaches and big hands." It does not mention him being tall, slender, clean-shaven, blond, muscular, having a prominent beard, or having a slight build and neatly combed hair. Therefore, the description that best matches Jim Gilmore's appearance from the given options is:

B) Short and dark with a big mustache and big hands

MW4

To determine the width of the rectangular garden, let's start by defining the variables and understanding the relationships given in the problem.

Let:
- \( W \) be the width of the garden in feet.
- \( L \) be the length of the garden in feet.

According to the problem, the length \( L \) is four times the width \( W \):
\[ L = 4W \]

The formula for the perimeter \( P \) of a rectangle is:
\[ P = 2L + 2W \]

We are given that the perimeter is 60 feet:
\[ 2L + 2W = 60 \]

Substituting the expression for \( L \) from the first equation into the perimeter equation:
\[ 2(4W) + 2W = 60 \]

Simplify and solve for \( W \):
\[ 8W + 2W = 60 \]
\[ 10W = 60 \]
\[ W = \frac{60}{10} \]
\[ W = 6 \]

Thus, the width of the garden is:
\[ \boxed{6} \]

RCS5

(B)

SC1

offered to lend Sofie one of her colorful swimsuits.

SC2

He placed a pebble from his pocket where the missing pawn should be.

SC4

"We forgot to charge our phones," she said worriedly.

SC5

She suggested checking the storage building's roof.

RCS1

C) By preserving it with salt

RCS2

C) shifting responsibility for the costs of recycling

RCS3

A) It is very old

LG3

To solve this problem, let's analyze the statements logically:

1. "All employees of Duluth Paper received a bonus this year."
2. "Andrés did not receive a bonus this year."

From the first statement, we understand that every single employee of Duluth Paper received a bonus. There are no exceptions.

From the second statement, Andrés did not receive a bonus.

If both statements are true, then Andrés cannot be an employee of Duluth Paper, because if he were, he would have received a bonus, which contradicts the second statement.

Therefore, the correct conclusion must be:

C) Andrés was not an employee of Duluth Paper this year

RCL3

In the passage, the author includes the detail that Jim noticed Liz's neat hair as follows: "Jim noticed that her hair was always neat behind." This indicates that Jim has observed and appreciated this particular aspect of Liz's appearance.

A) the frequency with which he thought of her - Incorrect, the passage explicitly states that Jim never thought about her.
B) his fondness for her cooking - Incorrect, there is no mention of Jim's fondness for Liz's cooking.
C) the whiteness of her teeth - Incorrect, this detail is not mentioned in relation to Jim's observations.
D) the arrangement of her hair - Correct, Jim noticed that her hair was always neat behind.

D

RCS4

(C) convenient

LG2

Let's analyze the given statements:

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

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

Let's evaluate each of the answer choices:

(A) If Izak is in the robotics club, then he is not on the basketball team.
   - This statement is not necessarily true because the robotics club can have members who are not on the chess team, and thus could be on the basketball team.

(B) If Jerry is in the robotics club, then he is on the chess team.
   - This statement is not necessarily true because being in the robotics club does not guarantee being on the chess team.

(C) If Lisa is on the basketball team, then she is not in the robotics club.
   - This statement is not necessarily true because Lisa could be in the robotics club but not on the chess team.

(D) If Sanjit is on the chess team, then he is on the basketball team.
   - This statement is false because no members of the basketball team are on the chess team.

(E) If Seong-Jin is not in the robotics club, then he is not on the chess team.
   - This statement must be true because all members of the chess team are members of the robotics club. Therefore, if someone is not in the robotics club, they cannot be on the chess team.

Thus, the correct answer is:

E

LG4

Let's analyze the given statements step by step:

1. The person in Britain has the broken sword.
2. The son, who is not in Denmark, neither has the gold doubloon nor the silver watch.
3. The family member 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.

Additionally, we are given that the daughter has the oceanic map. We need to determine where the daughter is located.

First, let's summarize the known information:

- The person in Britain has the broken sword.
- The person in Egypt has the family tree.
- The mother has the silver watch and isn't in Mexico.
- The grandmother has the gold doubloon and is in either Denmark or Canada.
- The daughter has the oceanic map.

Using the information about the mother:
- Since the mother has the silver watch and isn't in Mexico, she can't be in Egypt (family tree), Britain (broken sword), or Denmark/Canada (gold doubloon).
- Therefore, the mother must be in Canada or Denmark, but she cannot be in Canada or Denmark because those locations are taken by the grandmother with the gold doubloon. Hence, the mother must be in Britain (broken sword).

Using the information about the grandmother:
- The grandmother has the gold doubloon and can only be in Denmark or Canada. Since the mother is in Britain, the grandmother must be in Denmark or Canada.

Using the information about the son:
- The son is not in Denmark, and he doesn't have the gold doubloon or the silver watch. Therefore, he cannot be in Britain (broken sword), Egypt (family tree), or Denmark (gold doubloon). He must be in Mexico.

Since the son is in Mexico, and the mother is in Britain, and the grandmother is in either Denmark or Canada, the daughter must be in the remaining location.

Since the person in Egypt has the family tree and isn't the daughter (oceanic map), the grandmother must be in Denmark (gold doubloon), and the father must be in Egypt (family tree).

Therefore, the remaining location for the daughter is Canada.

So, the daughter is located in Canada.

LO1

▲, ◆, ★

LO2

★, ◆, ●, ▲

LO3

▲, ★, ●, ◆

LO4

★
●
▲
◆

MW1

To solve for \( n \), let's start by setting up the equation based on the given information.

Each student is supposed to write \( n \) verses plus twice their class rank. For the 7th student, this can be expressed as:
\[ n + 2 \times 7 \]

According to the problem, the 7th student wrote 20 verses. Therefore, we can set up the following equation:
\[ n + 2 \times 7 = 20 \]

First, simplify the multiplication:
\[ n + 14 = 20 \]

Next, solve for \( n \) by isolating it on one side of the equation. Subtract 14 from both sides:
\[ n = 20 - 14 \]
\[ n = 6 \]

Thus, the value of \( n \) is:
\[ n = 6 \]

RCL4

The passage provides detailed observations about Liz Coates' feelings towards Jim Gilmore. The repetitive use of "She liked it" emphasizes the various specific details Liz notices and appreciates about Jim. Each "She liked it" reveals another layer of her attention to Jim's characteristics and actions, showcasing how closely she studies and thinks about him.

Let's analyze the options:

A) degree to which a friendship has blossomed - This option doesn't quite fit because the passage does not mention the development of a friendship. It focuses more on Liz's feelings and observations of Jim rather than a mutual friendship.

B) friendliness of a person's disposition - This option is also not entirely accurate. The passage doesn't center on the friendliness of either character's disposition. It is more about Liz's detailed observations and feelings toward Jim.

C) persistence of an outward expression of love - While Liz's feelings might suggest an affection or love for Jim, the repetition of "She liked it" is more about her noticing specific details rather than expressing persistent outward love.

D) closeness with which one person studies another - This option best captures the essence of the passage. The repetitive "She liked it" emphasizes Liz's close and detailed observations of Jim, indicating how attentively she studies him.

Therefore, the correct answer is:

D

RCL5

Paragraphs 2 and 3 primarily provide insights into the sentiments that Liz Coates and Jim Gilmore have toward each other. The text explains how Jim notices Liz's neatness and jolliness but does not think much about her beyond that. Conversely, Liz has a deep admiration and affection for Jim, noticing various details about him that she likes, and even feeling funny when she thinks about certain aspects of him. This juxtaposition of their feelings highlights the difference in how each character perceives the other.

Thus, the correct answer is:

B) Juxtapose two peoples' sentiments

LG1

Given the statement "All of Lisa's sisters can bake," we need to determine which of the following options must also be true.

Let's analyze each option:

(A) If Jane cannot bake, then she is not Lisa's sister.
- This must be true. If Jane cannot bake, she cannot be one of Lisa's sisters because all of Lisa's sisters can bake.

(B) If Sarah can bake, then she is not Lisa's sister.
- This is not necessarily true. Sarah could be a sister who can bake, but it doesn't state that she cannot be Lisa's sister.

(C) If Mary can bake, then she is Lisa's sister.
- This is not necessarily true. Mary could be someone who can bake but is not necessarily one of Lisa's sisters.

(D) If Emma is not Lisa's sister, then she cannot bake.
- This is not necessarily true. Emma could be someone who is not Lisa's sister but can still bake.

(E) None of these.
- This is incorrect because option (A) is true.

So, the correct answer is:

A

MW2

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:

\[ 0 \]

MW3

To determine how long it will take John to travel to the park, we need to use the basic formula for time, which is derived from the relationship between distance, speed, and time. The formula is:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Here, the distance John needs to travel is 60 miles, and his planned speed is 30 miles per hour.

Substitute the given values into the formula:

\[ \text{Time} = \frac{60 \text{ miles}}{30 \text{ mph}} \]

Calculate the division:

\[ \text{Time} = 2 \text{ hours} \]

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

LG5

Let's analyze the given statements step-by-step:

1. The person in Britain has the broken sword.
2. The son, who is not in Denmark, neither has the gold doubloon nor the silver watch.
3. The family member 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.

We need to determine the location of the Mother if the Grandmother is in Denmark.

If the Grandmother is in Denmark:
- The Grandmother has the gold doubloon.
- The Son is not in Denmark (as per statement 2).

From statement 3:
- The family member in Egypt has the family tree, so the Grandmother is not in Egypt.

From statement 4:
- The Mother has the silver watch but isn't in Mexico.

So far, the locations with known heirlooms are:
- Denmark: Gold doubloon (Grandmother)
- Britain: Broken sword
- Egypt: Family tree

Since the Son isn't in Denmark, and the Grandmother is in Denmark, the Son could be in either Mexico, Britain, Canada, or Egypt.

The Mother has the silver watch and is not in Mexico (per statement 4). Therefore, the Mother could be in either Britain, Canada, Denmark, or Egypt. However, since the Grandmother is in Denmark and the family member in Egypt has the family tree, the Mother cannot be in Denmark or Egypt.

This leaves Britain and Canada as possible locations for the Mother.

Given that the person in Britain has the broken sword (per statement 1), and it isn't specified that the Mother has the broken sword, the Mother must be in Canada.

Therefore, if the Grandmother is in Denmark, the Mother is in Canada.

Answer:
Canada

MW5

To determine how many integers greater than 99 and less than 200 have exactly one duplicate digit, we will analyze the possible numbers step by step.

### Step 1: Define the Range
The integers we are considering are from 100 to 199, inclusive.

### Step 2: Identify the Form of the Numbers
The numbers in this range are of the form \(1AB\), where \(A\) and \(B\) are digits from 0 to 9.

### Step 3: Conditions for Exactly One Duplicate Digit
For \(1AB\) to have exactly one duplicate digit:
- Either \(A\) must be equal to \(B\), and both must not be 1 (since the hundreds digit is fixed as 1).
- \(A\) must not equal 1 (as that would mean the digit 1 is repeated twice), and \(B\) must not equal 1 (same reason).

### Step 4: List Valid Possibilities
1. If \(A = B\), \(A\) and \(B\) can be any digit from 0 to 9, excluding 1.

Thus, the possible values for \(A\) (and hence \(B\)) are: 0, 2, 3, 4, 5, 6, 7, 8, 9. This gives us 9 valid choices.

### Step 5: Form the Numbers
For each valid digit (other than 1), the corresponding numbers will be:
- If \(A = 0\), the number is 100.
- If \(A = 2\), the number is 122.
- If \(A = 3\), the number is 133.
- If \(A = 4\), the number is 144.
- If \(A = 5\), the number is 155.
- If \(A = 6\), the number is 166.
- If \(A = 7\), the number is 177.
- If \(A = 8\), the number is 188.
- If \(A = 9\), the number is 199.

### Step 6: Count the Numbers
We have listed exactly 9 numbers that satisfy the condition of having exactly one duplicate digit.

Therefore, the total number of integers greater than 99 and less than 200 that have exactly one duplicate digit is:
\[ \boxed{9} \]