✅

B

Elena invited Sofie over to try on her spare swimsuits.

✅

"Let's create our own pawn!"

Mia retrieved a spare ball from the storage.

✅

C

✅

C

D

(A) polished

If both of the above statements are true, then A) Not all employees of Duluth Paper received a bonus this year must be true. This is because Andrés did not receive a bonus, which contradicts the first statement that all employees received a bonus. The other options do not necessarily follow from the given statements.

Paul grinned and said, "It's all about being ready for the unexpected."

The author includes the detail that Liz liked the whiteness of Jim's teeth when he smiled to show that Jim has noticed Liz Coates. This detail indicates that Jim has paid attention to his appearance and that Liz has noticed these details about him.

The author's repetitive use of "She liked it" serves to emphasize the degree to which a friendship has blossomed. The repetition shows how Liz is increasingly aware of and appreciative of the various qualities Jim possesses, which suggests that their relationship is developing. Answer: A

The correct answer is B) Short and dark with a big mustache and big hands. The passage describes Jim Gilmore as short and dark in appearance, with big mustaches and big hands. The other options do not match the description given in the passage.

The correct answer is (A) If Jane cannot bake, then she is not Lisa's sister.


The initial statement tells us that every one of Lisa's sisters has the ability to bake. This implies a conditional relationship where being able to bake is necessary to be one of Lisa's sisters. Therefore, if Jane cannot bake, we can conclude that she would not meet the criteria to be Lisa's sister, according to the given conditions.



You are a logician asked to evaluate a complex scenario with multiple constraints. Analyze the following information and deduce the correct conclusion. Provide your reasoning, then conclude with a new line and the letter corresponding to the correct answer.

    "In a family, all of the uncles can play the guitar. None of the cousins can play the piano, and every cousin who can play the guitar has won a music award."

If the statement above is true, which of the following must also be true?
(A) If Uncle Jack has won a music award, then he plays the guitar
(B) If Cousin Lucas cannot play the guitar, then he has never won a music award
(C) If Cousin Emily has won a music award, she must play the guitar
(D) If Uncle Albert can play the piano, then he is not an uncle
(E) None of these

The Grandmother cannot be in Denmark because the son is not in Denmark either, and they can't be in the same country. Therefore, the Grandmother must be in Canada, which means the person in Denmark is the Father, and he has the broken sword.

The Mother has the silver watch but isn' t in Mexico, and since the Grandmother and Father are in Canada and Denmark, and the Egyptian family member has the family tree, the Mother must be in Britain.

So, the Mother is in Britain.

Mother - Britain

✅

To solve this problem, let's use algebra.

Let the width of the garden be `w` feet.
According to the problem, the length of the garden is four times its width, so the length is `4w` feet.

The perimeter of a rectangle is given by the formula: P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

In this case, P = 60 feet.

Substitute the known values into the formula:

60 = 2(4w) + 2w

Simplify the equation:

60 = 8w + 2w

Combine the terms:

60 = 10w

Now, solve for `w`:

w = 6 feet

So, the width of the garden is 6 feet.

The correct answer: Width = 6 feet.

▲ ★ ● ◆ 

Explanation:
▲ - Asim bought a ring with something special in mind (planning the proposal).
★ - Asim proposed to Meriem during a romantic dinner (the proposal).
● - Asim and Meriem had a beautiful ceremony surrounded by friends and family (the wedding).
◆ - The newlyweds arrived at the airport to start their honeymoon (post-wedding celebration).

★
●
▲

✅

Let's start by breaking down the given information. We know that Robert's students have to write n verses and twice as many verses as the number of their class rank. Let's represent the class rank of the student as r.

According to the problem, the 7th student wrote 20 verses. So, we can set up the following equation:

n + 2r = 20

Now, we need to find the value of n. Since the student is the 7th in the class, r = 7. Let's substitute r with 7 in the equation:

n + 2(7) = 20

Now, we can simplify and solve for n:

n + 14 = 20
n = 20 - 14
n = 6

So, the value of n is 6.

The correct answer is: n = 6.

✅

To determine the value of 4 ◘ 3, we will apply the definition of the operation ◘ to the given real numbers.


According to the definition, x ◘ y = 2x - 3y + 1.


Now, we'll substitute x with 4 and y with 3:


4 ◘ 3 = 2(4) - 3(3) + 1

       = 8 - 9 + 1

       = -1 + 1

       = 0


The value of 4 ◘ 3 is therefore 0.

▲◆★


The events are ordered as follows:

▲ - Max borrows his mom's camera to take photos of his school science project.

◆ - Max accidentally deletes all the photos his mom took on their vacation last month.

★ - Max downloads a new software program to try and recover the photos.


This sequence makes logical sense because it follows a typical storytelling format where the event leading to the problem (deleting photos) is followed by an action taken to resolve the problem (downloading software to recover the photos).

★ - ● - ◆ - ▲


Explanation:

The logical order for the events would start with the scheduling of the surgery (★), followed by the surgery itself where Lucky is put under anesthesia and Dr. Hahn starts the procedure (●). Before the surgery, Dr. Hahn washes his hands thoroughly (◆), which would naturally precede the surgery. After the surgery, the veterinary assistant calls Vidya to inform her of the successful outcome (▲).

✅

To calculate the time it will take John to reach the park, we can use the formula for time, which is the distance divided by the speed. The distance John has to travel is 60 miles, and his speed is 30 mph. 

Time = Distance / Speed

Time = 60 miles / 30 mph

Time = 2 hours

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


Answer: 2 hours

Paragraphs 2 and 3 primarily serve to juxtapose two peoples' sentiments (Option B). Paragraph 2 is about Liz Coates's feelings for Jim Gilmore, and Paragraph 3 shows how those feelings evolve as she begins to notice more of Jim's physical attributes.

Let's analyze the given statements and options:

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 on 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 the options:

(A) If Izak is in the robotics club, then he is not on the basketball team
This statement is true, according to the given information. Since all members of the chess team are also members of the robotics club (Statement 1), and no members of the basketball team are members of the chess team (Statement 2), it follows that if Izak is in the robotics club, he cannot 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. Being in the robotics club doesn't guarantee that Jerry is on the chess team. He could be in the robotics club for other reasons.

(C) If Lisa is on the basketball team, then she is not in the robotics club
This statement is true, according to the given information. Since no members of the basketball team are members of the chess team (Statement 2), and all members of the chess team are also members of the robotics club (Statement 1), it follows that if Lisa is on the basketball team, she cannot be in the robotics club.

(D) If Sanjit is on the chess team, then he is on the basketball team
This statement is not necessarily true. Being on the chess team doesn't guarantee that Sanjit is on the basketball team.

(E) If Seong-Jin is not in the robotics club, then he is not on the chess team
This statement is true, according to the given information. Since all members of the chess team are also members of the robotics club (Statement 1), it follows that if Seong-Jin is not in the robotics club, he cannot be on the chess team.

Based on our analysis, the correct answer is:

(A) If Izak is in the robotics club, then he is not on the basketball team
(C) If Lisa is on the basketball team, then she is not in the robotics club
(E) If Seong-Jin is not in the robotics club, then he is not on the chess team

To find the integers greater than 99 and less than 200 with exactly one duplicate digit, we should consider the possible digits that can be used and the place values they can occupy.

For a three-digit number, the hundreds' place can only be occupied by digits 1-9 (since we're looking for numbers less than 200). The tens' and ones' places can be occupied by digits 0-9, but we need to ensure that only one digit is repeated.

Let's analyze each case:

1. If the repeated digit is in the hundreds' place, the number takes the form of AAB, where A represents the repeated digit. A can be any digit from 1 to 9.

There are 9 possibilities for A (1-9).

2. If the repeated digit is in the tens' place, the number takes the form of ABA.

Here, A can be any digit from 1-9 (since it's not 0, because we're looking for numbers greater than 99), and B can be any digit from 0-9 except A.

For each choice of A (which has 9 possibilities), B has 9 possibilities (0-9 except A). So there are 9 * 9 = 81 possibilities for ABA.

3. If the repeated digit is in the ones' place, the number takes the form of AAB.

This case is identical to the first case (AAB), so we have another 9 possibilities.

Adding the possibilities from all three cases: 9 (AAB) + 81 (ABA) + 9 (AAB) = 99 integers.

Thus, there are 99 integers greater than 99 and less than 200 with exactly one duplicate digit.

Let's solve this step by step:


- According to statement 1, the person in Britain has the broken sword. So, the person in Britain cannot have the gold doubloon, the oceanic map, or the silver watch.

- Statement 2 tells us that the son doesn' t have the gold doubloon nor the silver watch, and he isn't in Denmark. Therefore, he must be in Britain with the broken sword.

- Statement 4 tells us that the mother has the silver watch, but she isn't in Mexico. This means she could be in Britain (since the son with the broken sword is there), Denmark, or Canada. However, since we've established that the person in Britain has the broken sword, the mother must be in either Denmark or Canada.

- Statement 3 tells us that the family member in Egypt has the family tree. Since the son is in Britain with the broken sword, and the mother can't be in Mexico, it means she must be in Denmark or Canada. Therefore, the person in Egypt with the family tree could be the daughter or grandmother.

- Statement 5 tells us that the grandmother has the gold doubloon and is either in Denmark or Canada. Since the mother can't be in Mexico, and the grandmother can't be in Britain with the son, the grandmother must be in Denmark with the gold doubloon. This means the mother must be in Canada with the silver watch.

- Since the person in Britain has the broken sword, the daughter can't be there, and she doesn't have the oceanic map, that leaves Egypt as the only option for her.


The daughter is in Egypt.


The daughter is in Egypt.