Number Analogy establishes a relationship between a given pair of numbers. A candidate needs to identify this relationship and apply it to a second pair where one number is missing. The format is typically A : B :: C : ?, meaning "A is related to B in the same way that C is related to the missing number."
This topic is a cornerstone of the reasoning ability section in Indian government exams because it tests a wide range of skills, including numerical ability, pattern recognition, and logical deduction, all under time pressure.
The key is to quickly test for common mathematical relationships. For a pair n₁ : n₂, the relationship can be:
n₂ = n₁ + k, n₂ = n₁ - k, n₂ = n₁ * k, n₂ = n₁ / k.n² or n³. Examples: n₁ : n₁², n₁ : n₁²+1, n₁ : n₁²-n₁, n₁ : (n₁+1)², etc.| Pattern Name | Example | Logic |
|---|---|---|
| Square | 7 : 49 | n : n² |
| Square Plus One | 8 : 65 | n : n² + 1 |
| Cube | 4 : 64 | n : n³ |
| Cube Minus One | 5 : 124 | n : n³ - 1 |
| Sum of Digits | 63 : 9 | ab : a+b |
| Product of Digits | 42 : 8 | ab : a*b |
Question 1: 6 : 18 :: 4 : ?
A) 2
B) 6
C) 8
D) 12
Answer: D) 12
Technique: Simple Multiplication.
The relationship is that the second number is three times the first number.
6 * 3 = 18
Therefore, 4 * 3 = 12.
Question 2: 7 : 49 :: 11 : ?
A) 111
B) 121
C) 132
D) 101
Answer: B) 121
Technique: Squares.
The relationship is that the second number is the square of the first number.
7² = 49
Therefore, 11² = 121.
Question 3: 8 : 65 :: 12 : ?
A) 144
B) 145
C) 150
D) 169
Answer: B) 145
Technique: Square and Add.
The relationship is that the second number is the square of the first number plus one.
8² + 1 = 64 + 1 = 65
Therefore, 12² + 1 = 144 + 1 = 145.
Question 4: 42 : 6 :: 56 : ?
A) 7
B) 11
C) 13
D) 30
Answer: B) 11
Technique: Sum of Digits.
The relationship is that the second number is the sum of the digits of the first number.
For 42, 4 + 2 = 6.
Therefore, for 56, 5 + 6 = 11.
Question 5: 5 : 124 :: 7 : ?
A) 342
B) 343
C) 248
D) 125
Answer: A) 342
Technique: Cube and Subtract.
The relationship is that the second number is the cube of the first number minus one.
5³ - 1 = 125 - 1 = 124
Therefore, 7³ - 1 = 343 - 1 = 342.
Question 6: 25 : 625 :: 35 : ?
A) 725
B) 1225
C) 1575
D) 1275
Answer: B) 1225
The second number is the square of the first. 25² = 625. Therefore, 35² = 1225.
Question 7: 14 : 9 :: 26 : ?
A) 12
B) 13
C) 15
D) 31
Answer: C) 15
The logic is: (14 / 2) + 2 = 7 + 2 = 9. Therefore, (26 / 2) + 2 = 13 + 2 = 15.
Question 8: 8 : 28 :: 27 : ?
A) 8
B) 28
C) 64
D) 65
Answer: D) 65
The first numbers are cubes: 8 = 2³ and 27 = 3³. The relationship is: 2³ : (2+1)³ + 1 -> 8 : 3³ + 1 -> 8 : 27 + 1 = 28.
Therefore, 3³ : (3+1)³ + 1 -> 27 : 4³ + 1 -> 27 : 64 + 1 = 65.
Question 9: 212 : 436 :: 560 : ?
A) 786
B) 682
C) 784
D) 688
Answer: C) 784
The relationship is a simple addition. 212 + 224 = 436. Therefore, 560 + 224 = 784.
Question 10: 121 : 12 :: 25 : ?
A) 1
B) 2
C) 6
D) 7
Answer: C) 6
The first number is a square. 121 = 11². The second number is 11 + 1 = 12.
For 25, 25 = 5². The second number will be 5 + 1 = 6.
Question 11: 18 : 30 :: 36 : ?
A) 54
B) 62
C) 64
D) 66
Answer: D) 66
The relationship is: (18 * 2) - 6 = 36 - 6 = 30.
Therefore, (36 * 2) - 6 = 72 - 6 = 66.
Question 12: 49 : 81 :: 100 : ?
A) 64
B) 144
C) 121
D) 169
Answer: B) 144
The numbers are consecutive squares of odd/even numbers. 49 = 7² and 81 = 9² (7 and 9 are consecutive odd numbers).
100 = 10². The next consecutive even number is 12. 12² = 144.
Question 13: 72 : 18 :: 56 : ?
A) 24
B) 22
C) 20
D) 16
Answer: B) 22
For 72, the sum of digits is 7 + 2 = 9. Then 9 * 2 = 18.
For 56, the sum of digits is 5 + 6 = 11. Then 11 * 2 = 22.
Question 14: 9 : 80 :: 100 : ?
A) 901
B) 1009
C) 9801
D) 9999
Answer: D) 9999
The relationship is 9² - 1 = 81 - 1 = 80.
Therefore, 100² - 1 = 10000 - 1 = 9999.
Question 15: 2 : 7 :: 6 : ?
A) 39
B) 40
C) 41
D) 42
Answer: A) 39
There can be multiple logics.
Logic 1: n² + 3. 2² + 3 = 4 + 3 = 7. Then 6² + 3 = 36 + 3 = 39.
Logic 2: n³ - 1. 2³ - 1 = 8 - 1 = 7. Then 6³ - 1 = 216 - 1 = 215.
Since 39 is in the options, Logic 1 is the intended answer.
Question 16: 17 : 52 :: 1 : ?
A) 3
B) 4
C) 5
D) 51
Answer: B) 4
The relationship is (17 * 3) + 1 = 51 + 1 = 52.
Therefore, (1 * 3) + 1 = 3 + 1 = 4.
Question 17: 3 : 243 :: 5 : ?
A) 405
B) 465
C) 3125
D) 546
Answer: C) 3125
The relationship is 3⁵ = 3*3*3*3*3 = 243.
Therefore, 5⁵ = 5*5*5*5*5 = 3125.
Question 18: 20 : 11 :: 102 : ?
A) 49
B) 52
C) 61
D) 98
Answer: B) 52
The relationship is (20 / 2) + 1 = 10 + 1 = 11.
Therefore, (102 / 2) + 1 = 51 + 1 = 52.
Question 19: 48 : 122 :: 168 : ?
A) 215
B) 225
C) 290
D) 292
Answer: C) 290
The first number is one less than a perfect square. 48 = 7² - 1.
The second number is 122 = 11² + 1. The relation is from 7 to 11 (a difference of 4).
Let's check the second pair. 168 = 13² - 1.
So the next number should be based on 13 + 4 = 17.
The number will be 17² + 1 = 289 + 1 = 290.
Question 20: 6 : 222 :: 7 : ?
A) 336
B) 343
C) 350
D) 400
Answer: C) 350
The relationship is 6³ + 6 = 216 + 6 = 222.
Therefore, 7³ + 7 = 343 + 7 = 350.
Question 21: 2 : 3 :: 23 : ?
A) 25
B) 28
C) 29
D) 31
Answer: C) 29
2 and 3 are consecutive prime numbers.
The next prime number after 23 is 29.
Question 22: (9, 15, 21) :: (12, 18, ?)
A) 24
B) 22
C) 30
D) 28
Answer: A) 24
In the first group, the numbers are in an arithmetic progression with a common difference of 6.
9 + 6 = 15, 15 + 6 = 21.
Applying the same logic to the second group: 12 + 6 = 18. The next number will be 18 + 6 = 24.
Question 23: 68 : 130 :: ? : 350
A) 210
B) 216
C) 222
D) 240
Answer: C) 222
The numbers are in the form n³ + n.
68 = 4³ + 4.
130 = 5³ + 5. Wait, 5³+5=130. The difference is just n to n+1.
Let's re-examine. 68 = 4³+4. 130 = 5³+5. 350 = 7³+7.
So the missing number should be 6³+6 = 216+6 = 222.
Question 24: 7 : 32 :: 35 : ?
A) 144
B) 156
C) 160
D) 172
Answer: D) 172
The relationship is (7 * 5) - 3 = 35 - 3 = 32.
Therefore, (35 * 5) - 3 = 175 - 3 = 172.
Question 25: 583 : 293 :: 488 : ?
A) 291
B) 378
C) 487
D) 581
Answer: B) 378
This is based on the sum of digits.
Sum of digits of 583 = 5 + 8 + 3 = 16.
Sum of digits of 293 = 2 + 9 + 3 = 14. The difference is -2.
Let's check the second pair. Sum of digits of 488 = 4 + 8 + 8 = 20.
The sum of digits of the missing number should be 20 - 2 = 18.
Let's check the options: A) 12, B) 18, C) 19, D) 14.
Only option B (378) has a sum of digits of 18 (3+7+8=18).
Question 26: 1 : 1 :: 25 : ?
Answer: 625
Two logics are possible. 1:1 could be `n:n` or `n:n²`. We check the options. If the logic was `n:n`, the answer would be 25. If the logic is `n:n²`, the answer is `25² = 625`. As 625 is a common option in such questions, we assume the more complex logic.
Question 27: 64 : 8 :: 289 : ?
Answer: 17
The second number is the square root of the first. √64 = 8. Therefore, √289 = 17.
Question 28: 10 : 99 :: 9 : ?
Answer: 80
10² - 1 = 99. Therefore, 9² - 1 = 80.
Question 29: 37 : 6 :: 82 : ?
Answer: 9
The first number is a square plus one. 37 = 6² + 1. Therefore, 82 = 9² + 1. The missing number is 9.
Question 30: 5 : 30 :: 8 : ?
Answer: 72
5 * (5+1) = 5 * 6 = 30. Therefore, 8 * (8+1) = 8 * 9 = 72.
Question 31: 12 : 140 :: 156 : ?
Answer: 1820
This is complex. 12 -> 140. 12² - 4 = 140.
Let's try 156² - 4 = 24336 - 4 = 24332. Not an option.
Let's try another logic. 12 * 11 = 132. No.
How about 12 * 12 - 4 = 140.
Let's try 156 * 12 - 4 = 1872 - 4 = 1868.
Let's try this: 12 = 3 * 4. 140.
Let's try a simpler one. 12 : 140. 12^2 - 4 = 140. No, 144-4.
Let's try 11 * 12 + 8 = 140.
Let's try 12 * 10 + 20 = 140.
This is likely a flawed question. Let's create a better one.
Revised Question 31: 11 : 132 :: 12 : ?
Answer: 156
The logic is n : n * (n+1). 11 * 12 = 132. Therefore, 12 * 13 = 156.
Question 32: 24 : 60 :: 120 : ?
Answer: 300
24 * 2.5 = 60. Therefore, 120 * 2.5 = 300.
Question 33: 4 : 17 :: 7 : ?
Answer: 50
4² + 1 = 17. Therefore, 7² + 1 = 50.
Question 34: 16 : 56 :: 32 : ?
Answer: 112
16 * 3.5 = 56. Therefore, 32 * 3.5 = 112.
Question 35: 100 : 121 :: 144 : ?
Answer: 169
100=10², 121=11². Then 144=12², so the next number is 13² = 169.
Question 36: 3265 : 4376 :: 4673 : ?
Answer: 5784
Each digit is increased by 1. 3+1=4, 2+1=3, 6+1=7, 5+1=6.
Therefore, 4+1=5, 6+1=7, 7+1=8, 3+1=4. Result: 5784.
Question 37: 5 : 21 :: 7 : ?
Answer: 45
5² - 4 = 21. Therefore, 7² - 4 = 49 - 4 = 45.
Question 38: 123 : 36 :: 221 : ?
Answer: 25
1+2+3=6, and 6² = 36.
Therefore, 2+2+1=5, and 5² = 25.
Question 39: 27 : 9 :: 64 : ?
Answer: 16
27 = 3³ and 9 = 3².
64 = 4³. The missing number is 4² = 16.
Question 40: 7 : 56 :: 9 : ?
Answer: 90
7 * (7+1) = 7 * 8 = 56.
Therefore, 9 * (9+1) = 9 * 10 = 90.
Question 41: 8 : 81 :: 64 : ?
Answer: 625
The pattern is x³ : (x+1)⁴.
8 = 2³. The second number is (2+1)⁴ = 3⁴ = 81.
64 = 4³. The missing number is (4+1)⁴ = 5⁴ = 625.
Question 42: 4 : 20 :: 6 : ?
Answer: 42
4² + 4 = 16 + 4 = 20.
Therefore, 6² + 6 = 36 + 6 = 42.
Question 43: 63 : 9 :: 68 : ?
Answer: 14
Sum of digits: 6+3=9. Therefore, 6+8=14.
Question 44: 21 : 3 :: 574 : ?
Answer: 82
21 / 7 = 3. Therefore, 574 / 7 = 82.
Question 45: 24 : 12 :: 36 : ?
Answer: 18
24 / 2 = 12. Therefore, 36 / 2 = 18.
Question 46: 11 : 110 :: 15 : ?
Answer: 210
11² - 11 = 121 - 11 = 110.
Therefore, 15² - 15 = 225 - 15 = 210.
Question 47: 456 : 15 :: 789 : ?
Answer: 24
Sum of digits: 4+5+6 = 15.
Therefore, 7+8+9 = 24.
Question 48: 5 : 35 :: 13 : ?
Answer: 195
5 * 7 = 35. 5 and 7 are consecutive primes.
13. The next prime is 17. 13 * 17 = 221. Not an option.
Let's try another logic. 5 * (5+2) = 35.
Then 13 * (13+2) = 13 * 15 = 195. This works.
Question 49: 7528 : 5306 :: 4673 : ?
Answer: 2451
Each digit is reduced by 2. 7-2=5, 5-2=3, 2-2=0, 8-2=6.
Therefore, 4-2=2, 6-2=4, 7-2=5, 3-2=1. Result: 2451.
Question 50: 9 : 28 :: 56 : ?
Answer: 169
(9 * 3) + 1 = 27 + 1 = 28.
Therefore, (56 * 3) + 1 = 168 + 1 = 169.