Reasoning - Number Analogy | PDF | Teaching Mathematics - Free Printable

Problem Analysis

The task involves solving a series of number analogy problems. In each problem, the first two numbers have a specific relationship, and you need to identify the same relationship between the third number and one of the given options.

General Approach

1. Identify the Relationship: Analyze the first two numbers to determine the mathematical or logical relationship between them.
2. Apply the Relationship: Use the identified relationship to find the corresponding number for the third number.
3. Select the Correct Option: Choose the option that matches the derived result.

Detailed Solutions

#### Question 1: 256 : 324 :: 484 : ______
- First Pair (256, 324):
- \( \sqrt{256} = 16 \)
- \( \sqrt{324} = 18 \)
- The relationship is: \( \sqrt{256} + 2 = \sqrt{324} \).
- Third Number (484):
- \( \sqrt{484} = 22 \)
- Applying the relationship: \( 22 + 2 = 24 \).
- Square of 24: \( 24^2 = 576 \).
- Answer: 1) 576

#### Question 2: 361 : 441 :: 625 : ______
- First Pair (361, 441):
- \( \sqrt{361} = 19 \)
- \( \sqrt{441} = 21 \)
- The relationship is: \( \sqrt{361} + 2 = \sqrt{441} \).
- Third Number (625):
- \( \sqrt{625} = 25 \)
- Applying the relationship: \( 25 + 2 = 27 \).
- Square of 27: \( 27^2 = 729 \).
- Answer: 2) 729

#### Question 3: 289 : 361 :: 961 : ______
- First Pair (289, 361):
- \( \sqrt{289} = 17 \)
- \( \sqrt{361} = 19 \)
- The relationship is: \( \sqrt{289} + 2 = \sqrt{361} \).
- Third Number (961):
- \( \sqrt{961} = 31 \)
- Applying the relationship: \( 31 + 2 = 33 \).
- Square of 33: \( 33^2 = 1089 \).
- Answer: None (5)

#### Question 4: 25 : 125 :: 36 : ______
- First Pair (25, 125):
- \( 25 \times 5 = 125 \)
- The relationship is: multiply by 5.
- Third Number (36):
- \( 36 \times 5 = 180 \).
- Answer: 3) 180

#### Question 5: 72 : 100 :: 53 : ______
- First Pair (72, 100):
- \( 72 + 28 = 100 \)
- The relationship is: add 28.
- Third Number (53):
- \( 53 + 28 = 81 \).
- Answer: 1) 81

#### Question 6: 225 : 100 :: 196 : ______
- First Pair (225, 100):
- \( \sqrt{225} = 15 \)
- \( \sqrt{100} = 10 \)
- The relationship is: \( \sqrt{225} - 5 = \sqrt{100} \).
- Third Number (196):
- \( \sqrt{196} = 14 \)
- Applying the relationship: \( 14 - 5 = 9 \).
- Square of 9: \( 9^2 = 81 \).
- Answer: 2) 85

#### Question 7: 31 : 37 :: 19 : ______
- First Pair (31, 37):
- \( 37 - 31 = 6 \)
- The relationship is: add 6.
- Third Number (19):
- \( 19 + 6 = 25 \).
- Answer: None (5)

#### Question 8: 343 : 512 :: 1331 : ______
- First Pair (343, 512):
- \( \sqrt[3]{343} = 7 \)
- \( \sqrt[3]{512} = 8 \)
- The relationship is: \( \sqrt[3]{343} + 1 = \sqrt[3]{512} \).
- Third Number (1331):
- \( \sqrt[3]{1331} = 11 \)
- Applying the relationship: \( 11 + 1 = 12 \).
- Cube of 12: \( 12^3 = 1728 \).
- Answer: 1) 1728

#### Question 9: 3 : 27 :: 5 : ______
- First Pair (3, 27):
- \( 3^3 = 27 \)
- The relationship is: cube the number.
- Third Number (5):
- \( 5^3 = 125 \).
- Answer: 1) 125

#### Question 10: 90 : 390 :: 890 : ______
- First Pair (90, 390):
- \( 390 - 90 = 300 \)
- The relationship is: add 300.
- Third Number (890):
- \( 890 + 300 = 1190 \).
- Answer: None (5)

#### Question 11: 890 : 89 :: 23 : ______
- First Pair (890, 89):
- \( 890 \div 10 = 89 \)
- The relationship is: divide by 10.
- Third Number (23):
- \( 23 \div 10 = 2.3 \).
- Answer: 3) 2.3

#### Question 12: 961 : 31 :: 55 : ______
- First Pair (961, 31):
- \( \sqrt{961} = 31 \)
- The relationship is: square root.
- Third Number (55):
- \( 55^2 = 3025 \).
- Answer: 1) 3025

#### Question 13: 4 : 26 :: 7 : ______
- First Pair (4, 26):
- \( 4 \times 6 + 2 = 26 \)
- The relationship is: multiply by 6 and add 2.
- Third Number (7):
- \( 7 \times 6 + 2 = 44 \).
- Answer: None (5)

#### Question 14: 2 : 3 :: 5 : ______
- First Pair (2, 3):
- \( 2 + 1 = 3 \)
- The relationship is: add 1.
- Third Number (5):
- \( 5 + 1 = 6 \).
- Answer: None (5)

#### Question 15: 17 : 26 :: 37 : ______
- First Pair (17, 26):
- \( 26 - 17 = 9 \)
- The relationship is: add 9.
- Third Number (37):
- \( 37 + 9 = 46 \).
- Answer: None (5)

#### Question 16: 65 : 4 :: 513 : ______
- First Pair (65, 4):
- \( 65 \div 16.25 = 4 \)
- The relationship is: divide by 16.25.
- Third Number (513):
- \( 513 \div 16.25 = 31.56 \).
- Answer: None (5)

#### Question 17: 169 : 2197 :: 225 : ______
- First Pair (169, 2197):
- \( \sqrt{169} = 13 \)
- \( 13^3 = 2197 \)
- The relationship is: cube the square root.
- Third Number (225):
- \( \sqrt{225} = 15 \)
- \( 15^3 = 3375 \).
- Answer: 3) 3375

#### Question 18: 2 : 14 :: 4 : ______
- First Pair (2, 14):
- \( 2 \times 7 = 14 \)
- The relationship is: multiply by 7.
- Third Number (4):
- \( 4 \times 7 = 28 \).
- Answer: None (5)

#### Question 19: 21 : 440 :: 18 : ______
- First Pair (21, 440):
- \( 21 \times 20 + 20 = 440 \)
- The relationship is: multiply by 20 and add 20.
- Third Number (18):
- \( 18 \times 20 + 20 = 380 \).
- Answer: None (5)

#### Question 20: 9 : 72 :: 16 : ______
- First Pair (9, 72):
- \( 9 \times 8 = 72 \)
- The relationship is: multiply by 8.
- Third Number (16):
- \( 16 \times 8 = 128 \).
- Answer: None (5)

#### Question 21: 48 : 120 :: 35 : ______
- First Pair (48, 120):
- \( 120 - 48 = 72 \)
- The relationship is: add 72.
- Third Number (35):
- \( 35 + 72 = 107 \).
- Answer: None (5)

#### Question 22: 27 : 51 :: 83 : ______
- First Pair (27, 51):
- \( 51 - 27 = 24 \)
- The relationship is: add 24.
- Third Number (83):
- \( 83 + 24 = 107 \).
- Answer: None (5)

Final Answers

\[
\boxed{
1) 576, 2) 729, 5) None, 3) 180, 1) 81, 2) 85, 5) None, 1) 1728, 1) 125, 5) None, 3) 2.3, 1) 3025, 5) None, 5) None, 5) None, 5) None, 3) 3375, 5) None, 5) None, 5) None, 5) None, 5) None
}
\]