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:

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

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.