Select the option that is related to the fourth term in the same way as the first term is related to the second term.
340
Solving Numerical Analogy Questions
Numerical analogy questions test your ability to find the relationship between numbers and apply that relationship to a new pair. In this question, we need to determine the relationship between 213 and 7, and then apply that same relationship to find the number that corresponds to 8.
Analyzing the Relationship between 213 and 7
Let's look at the first pair of numbers: 213 and 7. We need to find a logical connection or pattern between them. Common patterns involve arithmetic operations, digit manipulation, or sequences.
Let's try manipulating the digits of 213:
- Sum of the digits: \(2 + 1 + 3 = 6\)
- Product of the digits: \(2 \times 1 \times 3 = 6\)
Neither the sum nor the product of the digits directly gives 7. However, 6 is very close to 7. What if the pattern involves adding 1 to the sum of the digits?
Sum of digits of 213 + 1 = \( (2 + 1 + 3) + 1 = 6 + 1 = 7 \).
This matches the second number in the first pair. So, the relationship appears to be: The second number is equal to the sum of the digits of the first number plus 1.
Applying the Pattern to Find the Missing Term
Now, we apply this pattern to the second pair: _______ : 8. Let the missing term be \(X\).
According to our identified pattern, the second number (8) is equal to the sum of the digits of the first number (\(X\)) plus 1.
So, we have the equation:
\( \text{Sum of digits of } X + 1 = 8 \)
Subtracting 1 from both sides, we get:
\( \text{Sum of digits of } X = 8 - 1 = 7 \)
We are looking for a number among the options whose digits add up to 7.
Checking the Options
Let's examine the sum of the digits for each given option:
| Option | Number | Sum of Digits | Matches 7? |
|---|---|---|---|
| 1 | 343 | \(3 + 4 + 3 = 10\) | No |
| 2 | 512 | \(5 + 1 + 2 = 8\) | No |
| 3 | 340 | \(3 + 4 + 0 = 7\) | Yes |
| 4 | 509 | \(5 + 0 + 9 = 14\) | No |
From the table, we can see that only the number 340 has a sum of digits equal to 7. Therefore, 340 is the missing term that fits the established pattern.
Conclusion
The relationship between 213 and 7 is that 7 is the sum of the digits of 213 plus 1. Applying this same relationship to the second pair, we found that the missing number should have digits that sum up to 7. The option that satisfies this condition is 340.
Therefore, 213 : 7 :: 340 : 8.
Revision Table: Key Concepts
| Concept | Description | Relevance to Question |
|---|---|---|
| Numerical Analogy | Finding a pattern or relationship between a pair of numbers and applying it to another pair. | This question is a classic example of a numerical analogy. |
| Digit Manipulation | Using operations on the individual digits of a number (sum, product, etc.) to find a relationship. | The pattern in this question involves the sum of the digits. |
| Pattern Recognition | Identifying the rule that connects the numbers in the first pair. | Crucial first step to solving the analogy. |
Additional Information: Types of Numerical Patterns
Numerical analogy questions can involve various types of patterns. Recognizing these common types can help you solve problems faster.
- Arithmetic Operations: Addition, subtraction, multiplication, or division between the two numbers. Sometimes involves squaring, cubing, or taking roots.
- Digit Operations: Sum of digits, product of digits, reversal of digits, or other manipulations of the individual digits.
- Sequence Based: The numbers might be terms in a known sequence (e.g., prime numbers, squares, cubes) or follow a simple arithmetic or geometric progression.
- Positional Value: The relationship might depend on the place value of the digits.
- Logical Rules: Sometimes the pattern is a specific rule or condition, like being an even/odd number, or based on the number of factors.
Always start by exploring simple relationships (like arithmetic operations) and then move to digit manipulations if the initial attempts are unsuccessful.
Similar Questions
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)
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 option that is related to the third number in the same way as the second number is related to the first number and the sixth number is related to the fifth number.
24 : 15 : : 32 : ? : : 46 : 26
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.)
(12, 9, 4)
(18, 9, 6)
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.)
(8, 8, 128)
(11, 7, 162)
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.)
(20, 16, 8)
(10, 13, 12)
Select the option that is related to the third number in the same way as the second number is related to the first number and the sixth number is related to the fifth number.
8 : 49 : : 16 : ? : : 12 : 121
Select the number that is related to the third number in the same way as the second number is related to the first number.
12 : 36 :: 18 : ?
Study the given pattern carefully and find the missing number.
(9, 9, 2) (8, __, 1) (4, 8, 8)
Study the given pattern carefully and select the number that can replace the question mark (?) in it.
(17, 9, 4) (13, ?, 7) (14, 3, 13)
Important Questions from Letter and Number Based
Select the option that is related to the third number in the same way as the second number is related to the first number.
22 : 441 :: 13 : ?Select the option that is related to the third number in the same way as the second number is related to the first number.
31 : 90 :: 43 : ?
Select the option which is related to the third number in the same way as the second number is related to the first number.
7 : 56 :: 13 : ?
Select the option that is related to the third number in the same way as the second number is related to the first number.
77 : 11 :: 259 : ?
Select the option that is related to the third number in the same way as the second number is related to the first number.
15 : 270 :: 13 : ?
