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★●▲◆

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To solve this problem, we need to find the value of \( n \) based on the information given for the 7th student.

Each student is supposed to write:
\[
\text{Number of verses} = n + 2 \times (\text{class rank})
\]

For the 7th student:
\[
20 = n + 2 \times 7
\]
\[
20 = n + 14
\]

Subtract 14 from both sides:
\[
n = 20 - 14
\]
\[
n = 6
\]

**Answer:** 6

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To find the value of \( 4 \, \text{◘} \, 3 \), we can use the definition of the operation ◘:

\[
x \, \text{◘} \, y = 2x - 3y + 1
\]

Substitute \( x = 4 \) and \( y = 3 \):

\[
4 \, \text{◘} \, 3 = 2(4) - 3(3) + 1
\]

Compute the products:

\[
2(4) = 8 \\
3(3) = 9
\]

Substitute back into the equation:

\[
4 \, \text{◘} \, 3 = 8 - 9 + 1
\]

Simplify:

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

**Answer:**

0

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To solve this problem, we need to find all three-digit integers greater than 99 and less than 200 (i.e., numbers from 100 to 199) that have exactly one duplicate digit. This means among the three digits, there are exactly two identical digits and one different digit.

Since all numbers in the range start with the digit **1** (hundreds place), we'll consider the tens and ones places (D₂ and D₃) and find all combinations where exactly two digits are the same.

We have three cases to consider:

**Case 1: D₁ = D₂ ≠ D₃**
- Here, the first and second digits are the same, and the third is different.
- D₁ = D₂ = 1
- D₃ can be any digit from 0 to 9 except 1.
- This gives us 9 numbers:
  - 110, 112, 113, 114, 115, 116, 117, 118, 119

**Case 2: D₁ = D₃ ≠ D₂**
- The first and third digits are the same, and the second is different.
- D₁ = D₃ = 1
- D₂ can be any digit from 0 to 9 except 1.
- This gives us another 9 numbers:
  - 101, 121, 131, 141, 151, 161, 171, 181, 191

**Case 3: D₂ = D₃ ≠ D₁**
- The second and third digits are the same, and the first is different.
- Since D₁ is fixed at 1, and it must not equal D₂ and D₃, D₂ and D₃ can be any digit from 0 to 9 except 1.
- This gives us 9 more numbers:
  - 100, 122, 133, 144, 155, 166, 177, 188, 199

Adding up the numbers from all three cases:
- Case 1: 9 numbers
- Case 2: 9 numbers
- Case 3: 9 numbers
- **Total: 9 + 9 + 9 = 27 numbers**

**Answer:**
27

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To determine how long it will take John to reach the park, we use the formula:

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

John needs to travel a distance of 60 miles at a speed of 30 miles per hour:

\[
\text{Time} = \frac{60\, \text{miles}}{30\, \text{miles/hour}} = 2\, \text{hours}
\]

**Answer:**
2 hours

A

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The passage provides a detailed description of Jim Gilmore's appearance. It explicitly states, "Jim was short and dark with big mustaches and big hands." This description directly aligns with option B.

Option A is incorrect because the passage mentions that Jim is "short," not tall, and he has "big mustaches," not a clean-shaven face. Option C is incorrect as Jim is described as "dark," not blond, and there's no mention of a prominent beard. Option D doesn't fit because Jim is not of average height (he is "short") and there's no mention of a slight build or neatly combed hair.

**Answer: B**

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Given the statements:

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

From statement 1, we understand that **every** employee of Duluth Paper received a bonus. This means if someone is an employee at Duluth Paper, they **must** have received a bonus.

Statement 2 tells us that Andrés did **not** receive a bonus. If Andrés did not receive a bonus, and all Duluth Paper employees did receive bonuses, it logically follows that Andrés is **not** an employee of Duluth Paper.

Therefore, the statement that must also be true is:

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

C

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To solve this logic puzzle, let's interpret the given statements and analyze each option:

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 be in the robotics club (Chess Team ⊆ Robotics Club).

2. **No members of the basketball team are members of the chess team.** This indicates that there's no overlap between basketball team members and chess team members (Basketball Team ∩ Chess Team = ∅).

Now, let's examine each option:

**A) If Izak is in the robotics club, then he is not on the basketball team.**
- Being in the robotics club doesn't provide information about the basketball team. There could be members who are in both the robotics club and the basketball team. This option is not necessarily true.

**B) If Jerry is in the robotics club, then he is on the chess team.**
- While all chess team members are in the robotics club, not all robotics club members are necessarily on the chess team. This option is not necessarily true.

**C) If Lisa is on the basketball team, then she is not in the robotics club.**
- The statements only tell us that basketball team members are not on the chess team. They don't mention the robotics club in relation to the basketball team. This option is not necessarily true.

**D) If Sanjit is on the chess team, then he is on the basketball team.**
- This contradicts the given statements since chess team members cannot be on the basketball team. This option is false.

**E) If Seong-Jin is not in the robotics club, then he is not on the chess team.**
- Since all chess team members are in the robotics club, anyone not in the robotics club cannot be on the chess team. This is the contrapositive of statement 1 and must be true.

**E**

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To solve this logic puzzle, let's organize the given information and deduce the locations step by step.

**Family Members**: Grandmother, Father, Mother, Son, Daughter  
**Locations**: Mexico, Britain, Canada, Denmark, Egypt  
**Heirlooms**: Gold Doubloon, Broken Sword, Oceanic Map, Family Tree, Silver Watch

**Given Information**:

1. **Britain** → **Broken Sword**
2. **Son**: Not in Denmark, doesn't have Gold Doubloon or Silver Watch
3. **Egypt** → **Family Tree**
4. **Mother**: Has Silver Watch, not in Mexico
5. **Grandmother**: Has Gold Doubloon, in Denmark or Canada
6. **Daughter**: Has Oceanic Map (from the question)

**Step-by-Step Deduction**:

- **Grandmother** must be in **Denmark** or **Canada** with the **Gold Doubloon**.
- **Son** cannot be in **Denmark**; possible locations are **Britain**, **Mexico**, **Canada**, or **Egypt**.
- Since the **Broken Sword** is in **Britain**, and the **Son** doesn't have the **Gold Doubloon** or **Silver Watch**, he must be in **Britain** with the **Broken Sword**.
- **Mother** cannot be in **Mexico**; possible locations are **Canada**, **Denmark**, **Egypt**, or **Britain**. Since **Britain** is taken by the **Son** and **Denmark** is possibly taken by the **Grandmother**, **Mother** must be in **Canada** or **Egypt**.
- However, **Egypt** has the **Family Tree**, and the **Mother** has the **Silver Watch**, so **Mother** must be in **Canada**.
- This means the **Grandmother** is in **Denmark** with the **Gold Doubloon**.
- **Father** must be the one in **Egypt** with the **Family Tree**.
- The remaining location is **Mexico**, which must be where the **Daughter** is with the **Oceanic Map**.

**Conclusion**:

The **Daughter** is in **Mexico**.

---

**Answer:** Mexico

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B

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offered to lend Sofie one of her swimsuits.

He placed his hat on the board to replace the missing pawn.

✅

"I forgot our chargers at home."

✅

"Mia pointed to the roof. 'Maybe there are balls up there,' she suggested."

✅

C

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C

✅

A

✅

D

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The author's repetitive use of "She liked it..." emphasizes the detailed and intimate observations Liz makes of Jim, highlighting how closely she studies him. Each "She liked it..." introduces a new specific trait or behavior of Jim that Liz notices, from his physical features to his interactions with others. This repetition serves to illustrate the depth of her attention and interest in him, emphasizing the closeness with which she observes and appreciates him.

D

✅

B

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To solve this logic problem, let's first restate the given:

- **All of Lisa's sisters can bake.**

This means that if someone is Lisa's sister, then they can bake. In logical terms:

- **If someone is Lisa's sister, then they can bake.**

The **contrapositive** of this statement is logically equivalent and states:

- **If someone cannot bake, then they are not Lisa's sister.**

Now, let's evaluate each option:

**Option A:** *If Jane cannot bake, then she is not Lisa's sister.*

- This directly aligns with the contrapositive of the original statement. If Jane cannot bake, she cannot be Lisa's sister.

**Option B:** *If Sarah can bake, then she is not Lisa's sister.*

- This is incorrect because many people can bake without being Lisa's sister. The ability to bake does not imply one is not her sister.

**Option C:** *If Mary can bake, then she is Lisa's sister.*

- This is also incorrect. While all of Lisa's sisters can bake, not all people who can bake are her sisters.

**Option D:** *If Emma is not Lisa's sister, then she cannot bake.*

- This is false because people who are not Lisa's sisters may still be able to bake. The statement does not provide information about non-sisters.

**Option E:** *None of these.*

- Since Option A is true, this option is incorrect.

**Answer:** **A**

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To solve this problem, let's let the width of the garden be \( w \) feet. Since the length is four times the width, the length is \( L = 4w \) feet.

The perimeter \( P \) of a rectangle is given by:
\[ P = 2(\text{length} + \text{width}) \]

Substitute the given perimeter and the expressions for length and width:
\[ 60 = 2(4w + w) \]
Simplify:
\[ 60 = 2(5w) \]
\[ 60 = 10w \]
Solve for \( w \):
\[ w = \frac{60}{10} \]
\[ w = 6 \]

**Answer:** 6

✅

To solve the problem, we'll deduce the positions of each family member based on the given clues.

**Given Clues:**

1. **Britain**: The person here has the **broken sword**.
2. **Son**: Not in Denmark; does **not** have the **gold doubloon** or **silver watch**.
3. **Egypt**: The person here has the **family tree**.
4. **Mother**: Has the **silver watch**; **not** in **Mexico**.
5. **Grandmother**: Has the **gold doubloon**; is in **Denmark** or **Canada**.
6. **Scenario**: Grandmother is in **Denmark**.

**Deduction Steps:**

- **Grandmother**:
  - Is in **Denmark** (given).
  - Has the **gold doubloon**.

- **Mother**:
  - Has the **silver watch** (Clue 4).
  - Not in **Mexico** (Clue 4).
  - Cannot be in **Britain** (since the person there has the **broken sword**, and she has the **silver watch**).
  - Cannot be in **Egypt** (since the person there has the **family tree**).
  - Cannot be in **Denmark** (Grandmother is there).
  - **Therefore, Mother must be in **Canada**.**

- **Son**:
  - Not in **Denmark** (Clue 2).
  - Does not have the **gold doubloon** (Grandmother has it) or **silver watch** (Mother has it).
  - Remaining objects: **broken sword**, **family tree**, **oceanic map**.
  - The **broken sword** is in **Britain**, and the **family tree** is in **Egypt**.
  - **Therefore, the Son has the **oceanic map**.**

- **Remaining Family Members**:
  - **Father** and **Daughter** are left to be placed in **Mexico**, **Britain**, and **Egypt**.
  - Using the remaining clues and process of elimination, they can be assigned accordingly, but the question doesn't require their exact positions.

**Answer:**

Canada

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