Math worksheet with logical reasoning and pattern recognition questions.

Let's solve each problem step by step:

---

Problem 1:

The sum of the number of matchsticks in Pattern 2 and Pattern 4 is ______.

#### Step-by-Step Solution:
1. Pattern 1:
- This pattern consists of a single triangle.
- A triangle requires 3 matchsticks.
- Total matchsticks in Pattern 1 = 3.

2. Pattern 2:
- This pattern consists of 3 triangles arranged in a larger triangle.
- Each small triangle uses 3 matchsticks, but they share sides.
- Counting the matchsticks carefully:
- The outer edges form a large triangle with 3 sides.
- The inner matchsticks form 3 additional matchsticks (one for each side of the smaller triangles).
- Total matchsticks in Pattern 2 = 9.

3. Pattern 3:
- This pattern consists of 6 triangles arranged in a larger triangle.
- Again, counting the matchsticks carefully:
- The outer edges form a large triangle with 3 sides.
- The inner matchsticks form additional matchsticks.
- Total matchsticks in Pattern 3 = 18.

4. Pattern 4:
- Following the pattern, Pattern 4 will have 10 triangles arranged in a larger triangle.
- Using the same logic as above:
- The outer edges form a large triangle with 3 sides.
- The inner matchsticks form additional matchsticks.
- Total matchsticks in Pattern 4 = 27.

5. Sum of Pattern 2 and Pattern 4:
- Pattern 2 has 9 matchsticks.
- Pattern 4 has 27 matchsticks.
- Sum = 9 + 27 = 36.

#### Final Answer:
\[
\boxed{A}
\]

---

Problem 2:

Identify the relation between the given pair on either side of :: and find the missing term.
E : 5 :: D : ?

#### Step-by-Step Solution:
1. Understanding the Relation:
- The letters are related to their position in the alphabet.
- E is the 5th letter of the alphabet.
- Therefore, the relation is:
\[
\text{Letter} : \text{Position in the Alphabet}
\]

2. Finding the Missing Term:
- D is the 4th letter of the alphabet.
- Therefore, D corresponds to 4.

#### Final Answer:
\[
\boxed{D}
\]

---

Problem 3:

Which of the following words can be formed from the letters of the given word?
NEWSPAPER

#### Step-by-Step Solution:
1. Letters in "NEWSPAPER":
- N, E, W, S, P, A, P, E, R

2. Checking Each Option:
- A. SQUARE:
- Letters needed: S, Q, U, A, R, E
- "Q" and "U" are not in "NEWSPAPER."
- Not possible.

- B. ERASE:
- Letters needed: E, R, A, S, E
- All these letters are in "NEWSPAPER."
- Possible.

- C. REPEAT:
- Letters needed: R, E, P, E, A, T
- "T" is not in "NEWSPAPER."
- Not possible.

- D. ROAST:
- Letters needed: R, O, A, S, T
- "O" and "T" are not in "NEWSPAPER."
- Not possible.

#### Final Answer:
\[
\boxed{B}
\]

---

Problem 4:

If 'Square' means 'Circle', 'Circle' means 'Triangle', and 'Triangle' means 'Rectangle', then what is the shape of Sun?

#### Step-by-Step Solution:
1. Understanding the Problem:
- The sun is typically round, which corresponds to a circle.
- According to the given substitutions:
- Square → Circle
- Circle → Triangle
- Triangle → Rectangle

2. Substitution Process:
- Since the sun is round, it corresponds to a circle.
- According to the substitution, "Circle" means "Triangle."

#### Final Answer:
\[
\boxed{D}
\]

---

Problem 5:

If apples B and D are removed from the given arrangement, then apple A will be ______ from the right end.

#### Step-by-Step Solution:
1. Initial Arrangement:
- Apples are arranged as: B, E, F, A, G, C, H, D.

2. Removing Apples B and D:
- After removing B and D, the arrangement becomes: E, F, A, G, C, H.

3. Position of Apple A:
- In the new arrangement: E, F, A, G, C, H.
- Counting from the right end:
- H is 1st from the right.
- C is 2nd from the right.
- G is 3rd from the right.
- A is 4th from the right.

#### Final Answer:
\[
\boxed{A}
\]

---

Problem 6:

Which of the following figures can replace the question mark (?) in Figure (X)?

#### Step-by-Step Solution:
1. Analyzing Figure (X):
- The figure shows a sequence of shapes in a 2x2 grid.
- Top-left: Square
- Top-right: Diamond
- Bottom-left: Square
- Bottom-right: ?

2. Identifying the Pattern:
- The top row alternates between a square and a diamond.
- The bottom row should follow the same pattern.
- Since the bottom-left is a square, the bottom-right should be a diamond.

3. Matching the Options:
- Option A: Diamond
- Option B: Parallelogram
- Option C: Diamond
- Option D: Square

- Both A and C are diamonds, but we need to choose the correct orientation.
- The diamond in the top-right is oriented with its points up and down.
- Therefore, the bottom-right should also have a diamond with the same orientation.

#### Final Answer:
\[
\boxed{A}
\]

---

Final Answers:

1. \(\boxed{A}\)
2. \(\boxed{D}\)
3. \(\boxed{B}\)
4. \(\boxed{D}\)
5. \(\boxed{A}\)
6. \(\boxed{A}\)