Select the option that is related to the fourth number in the same way as the first number is related to the second number and the fifth number is related to the sixth number. 216 ∶ 3 ∶∶ ? ∶ 4 ∶∶ 1728 ∶ 6
512
Number Analogy Reasoning: Solving the Pattern
This question asks us to identify the relationship between pairs of numbers in an analogy and apply that relationship to find a missing number. The given analogy is: 216 ∶ 3 ∶∶ ? ∶ 4 ∶∶ 1728 ∶ 6.
We have three pairs of numbers implied by the analogy structure:
- Pair 1: 216 and 3
- Pair 2: ? and 4
- Pair 3: 1728 and 6
The symbol '∶' means "is to", and '∶∶' means "as". So, the analogy reads: 216 is to 3, as ? is to 4, as 1728 is to 6.
Analyzing the Given Number Pairs to Find the Relationship
Let's examine the first and third pairs to find a consistent rule connecting the two numbers in each pair. The pairs are (216, 3) and (1728, 6).
We can look for various mathematical relationships, such as addition, subtraction, multiplication, division, powers, or roots.
Let's consider powers. We notice that 216 and 1728 are common cubic numbers:
- \(6^3 = 6 \times 6 \times 6 = 36 \times 6 = 216\)
- \(12^3 = 12 \times 12 \times 12 = 144 \times 12 = 1728\)
So, 216 is the cube of 6, and 1728 is the cube of 12.
Now let's see how the second number in each pair (3 and 6) relates to the base of the cube (6 and 12):
- For the first pair (216, 3), the base is 6, and the second number is 3. We can see that \(6 = 3 \times 2\).
- For the third pair (1728, 6), the base is 12, and the second number is 6. We can see that \(12 = 6 \times 2\).
The pattern appears to be that the first number is the cube of twice the second number. Let's express this as a formula:
\(N_1 = (N_2 \times 2)^3\)
Where \(N_1\) is the first number and \(N_2\) is the second number in a pair.
Applying the Pattern to Find the Missing Number
The missing number is in the second pair, which is (? : 4). Here, \(N_2 = 4\), and we need to find \(N_1\) (the missing number).
Using the pattern \(N_1 = (N_2 \times 2)^3\):
- Substitute the value of \(N_2\): \(N_1 = (4 \times 2)^3\)
- Perform the multiplication inside the parentheses: \(N_1 = (8)^3\)
- Calculate the cube: \(N_1 = 8 \times 8 \times 8\)
- \(N_1 = 64 \times 8\)
- \(N_1 = 512\)
So, the missing number is 512.
Confirming the Answer
The calculated missing number is 512. Let's check the given options:
- Option 1: 512
- Option 2: 864
- Option 3: 728
- Option 4: 946
Our calculated value, 512, matches Option 1.
Revision Table: Number Analogy Patterns
| Pattern Type | Description | Example |
|---|---|---|
| Arithmetic Operation | A constant difference or sum relates the numbers. | 5 : 8 :: 10 : 13 (Add 3) |
| Multiplication/Division | A constant multiplier or divisor relates the numbers. | 4 : 12 :: 7 : 21 (Multiply by 3) |
| Squares/Cubes | One number is the square or cube of the other or a number related to it. | 9 : 3 :: 25 : 5 (\(N_1 = N_2^2\)) |
| Combined Operations | A mix of operations (e.g., multiply and add). | 3 : 10 :: 5 : 16 (Multiply by 3, Add 1) |
| Pattern in Digits | Relationship based on the digits of the numbers. | 12 : 3 :: 23 : 5 (Sum of digits) |
| Based on \(N_2 \times K\) | First number is a power of \(N_2\) times a constant (as in this question). | 216 : 3 (\((3 \times 2)^3 = 6^3 = 216\)) |
Additional Information: Strategies for Solving Analogy Questions
Number analogy questions test your ability to find logical relationships between numbers. Here are some tips for tackling them:
- Look for common relationships: Start with simple arithmetic (add, subtract, multiply, divide), then consider powers and roots (squares, cubes).
- Check both pairs: The relationship you find must hold true for all given pairs in the analogy.
- Think about digits: Sometimes the pattern involves the digits of the numbers (sum of digits, product of digits, reversing digits).
- Consider position: In longer series, the position of the number might be relevant.
- Break down complex numbers: Large numbers might be products or powers of smaller numbers.
- Test your hypothesis: Once you think you've found the pattern, apply it to the known pairs to ensure it fits before calculating the missing number.
- Review options: The options can sometimes give you clues or help you verify your calculated answer.
Practice with different types of analogy questions will help you recognize common patterns more quickly.
Similar Questions
Select the option that is related to the third number in the same way as the second number is related to the first number.
5 : 150 :: 8 : ?
Select the set in which the numbers are related in the same way as are the numbers of the following set.
(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)
(52, 34, 43)
(61, 33, 47)
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)
(221, 144, 73)
(222, 153, 75)
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.)
(13, 52, 91)
(19, 76, 133)
Select the set in which the numbers are related in the same way as the numbers of the given 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.)
(111, 117, 123)
(169, 200, 231)
Select the set in which the number are related in the same way as the numbers of the given 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.)
(7, 9, 257)
(10, 3, 170)
Select the set in which the numbers are related in the same way as are the numbers of the following set.
(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)
(137, 95, 67)
(246, 204, 176)
Select the set in which the number are related in the same way as the numbers of the given 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.)
(17, 87, 104)
(20, 102, 122)
Select the set in which the number are related in the same way as the numbers of the given 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.)
(9, 7, 189)
(4, 13, 156)
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.)
(4, 60, 5)
(5, 90, 6)
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 : ?Select the option in which the numbers are related in the same way as are the numbers of the following set.
(12, 60, 84)
Three of the following four number-pairs ale alike in a certain way and one is different. Find the odd one out.
In the following question, select the related number from the given alternatives.
52 : 57 ∷ 46 : ?
