Select the option that is related to the third number in the same way as the second number is related to the first number.
150
Understanding Number Analogies and Finding Patterns
Number analogy questions test your ability to find a relationship between two numbers and apply that same relationship to a third number to find a missing fourth number. The given analogy is:
\(6 : 252 \;\;::\;\; 5 : ?\)
This means we need to discover the pattern or rule that connects 6 to 252, and then use that same rule to find the number that relates to 5.
Analyzing the Relationship between 6 and 252
Let's examine how 6 might be related to 252. We can consider basic mathematical operations like multiplication, squaring, cubing, addition, or subtraction, or a combination of these.
- If we multiply 6 by some number to get 252: \(252 \div 6 = 42\). The relationship could be multiplying by 42. If we apply this to 5: \(5 \times 42 = 210\). However, 210 is not one of the options.
- Let's consider powers of 6:
- \(6^2 = 36\)
- \(6^3 = 216\)
Notice that 216 is quite close to 252. The difference is \(252 - 216 = 36\). Interestingly, 36 is \(6^2\).
This suggests a possible relationship: The second number is the cube of the first number plus the square of the first number.
Let the first number be \(n\). The relationship appears to be \(n^3 + n^2\).
Let's verify this rule with the first pair (6 : 252):
For \(n=6\):
\[6^3 + 6^2 = 216 + 36 = 252\]This matches the given relationship between 6 and 252.
Applying the Pattern to Find the Missing Number
Now, we apply the same rule \(n^3 + n^2\) to the third number, which is 5.
For \(n=5\):
\[5^3 + 5^2 = 125 + 25 = 150\]So, the missing number related to 5 is 150.
Checking the Options
Let's compare our calculated missing number (150) with the given options:
- 125
- 150
- 225
- 176
Our calculated value, 150, matches option 2.
Therefore, the relationship is \(n^3 + n^2\), and applying this to 5 gives 150.
Number Analogy Revision Table
| Concept | Description | Example (based on this problem) |
|---|---|---|
| Number Analogy | Identifying the relationship between a pair of numbers to find a related number for another given number. | 6 : 252 :: 5 : ? |
| Pattern Recognition | The process of finding the rule (mathematical operation or sequence) that connects the given pair. | Discovering the \(n^3 + n^2\) pattern for 6 and 252. |
| Applying the Rule | Using the identified pattern on the third number to find the fourth number. | Applying \(n^3 + n^2\) to 5 to get 150. |
Additional Information on Number Analogy Patterns
Number analogies can involve various types of patterns. Understanding these common patterns can help solve such questions faster.
- Arithmetic Operations: Simple addition, subtraction, multiplication, or division.
- Squares and Cubes: The relationship might involve squaring (\(n^2\)), cubing (\(n^3\)), or combinations like \(n^2+1\), \(n^3-1\), \(n^2+n\), \(n^3+n^2\), etc.
- Prime Numbers: The numbers might be prime numbers or related to their sequence.
- Digit Operations: The pattern might involve operations on the digits of the number (e.g., sum of digits, product of digits).
- Sequence Based: Numbers following a specific sequence like Fibonacci.
Always start by checking simple relationships and then move towards more complex ones involving powers or combinations of operations when solving number analogy problems.
Similar Questions
Select the options in which the numbers are related in the same way as are the numbers of the following set.
(541, 14, 737)
Select the set in which the numbers are related in the same way as are the numbers of the following set.
(5, 2, 23)
(6, 2, 34)
(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is NOT allowed)
Study the given pattern carefully and select the number that can replace the question mark (?) in it.
(6, 8, 11)
(2, 1, 2)
(6, 7, ?)
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is NOT allowed)
(3, 16, 6)
(4, 22, 6)
Select the option that is related to the third term in the same way as the second term is related to the first term and the sixth term is related to the fifth term.
14 : 400 :: 37 : ? :: 42 : 2304
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding / subtracting / multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is NOT allowed)
(76, 4, 19)
(98, 2, 49)
A series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series.
10, 18, 28, ?
The age of the father 4 years ago was 8 times the age of his son. At present, the father’s age is 4 times that of his son. Find the present age of son.
Select the option in which the numbers are related in the same way as are the numbers of the following set.
(4, 7, 359)
Select the option that is related to the third number in the same way as the second number is related to the first number.
3824 : 4935 : : 5716 : ?
Important Questions from Letter and Number Based
Select the related number from the given alternatives that will complete the series:
Y 2 : 4 : : V 2 : ?Select the related number from the given alternatives:
F : 216 : : L : ?In the following question, select the related number from the given alternatives.
52 : 57 ∷ 46 : ?Select the option in which the numbers are related in the same way as are the numbers of the following set.
(4, 25, 105)
Select the option that is related to the third term in the same way as the second term is related to the first term.
267 : 5 :: 549 : ?
