Solving Numerical Analogy Problems

This question asks us to find the relationship between the first pair of numbers and apply the same relationship to the third number to find the fourth one. We are given the analogy: 13 ∶ 0.07692 ∶∶ 14 ∶ ?

Analyzing the Relationship

Let's examine the first pair of numbers: 13 and 0.07692. We need to figure out how 0.07692 is related to 13. Common relationships in such problems include addition, subtraction, multiplication, division, squares, cubes, square roots, cube roots, or fractions.

Looking at the numbers, 0.07692 is a small decimal number, while 13 is an integer. This suggests a division or fractional relationship. Let's consider dividing 1 by 13:

$$ \frac{1}{13} $$

Let's calculate the value of $\frac{1}{13}$:

$$ 1 \div 13 \approx 0.07692307... $$

Comparing this calculated value to the second number, 0.07692, we see that they are very close. It appears that the second number is the result of dividing 1 by the first number, possibly rounded or truncated to a few decimal places.

So, the relationship seems to be:

$$ \text{Second Number} = \frac{1}{\text{First Number}} $$

Applying the Relationship to the Third Number

Now, we apply the same relationship to the third number, which is 14. We need to find the number that is related to 14 in the same way. Using the identified relationship:

$$ \text{Fourth Number} = \frac{1}{\text{Third Number}} $$

Here, the third number is 14, so we calculate:

$$ \text{Fourth Number} = \frac{1}{14} $$

Let's calculate the value of $\frac{1}{14}$:

$$ 1 \div 14 \approx 0.07142857... $$

Comparing with Options

Now we compare our calculated value, approximately 0.07142857, with the given options:

• Option 1: 0.07142
• Option 2: 0.08143
• Option 3: 0.07569
• Option 4: 0.7128

Our calculated value, 0.07142857..., is closest to Option 1, 0.07142. This suggests that the result might be rounded or truncated to 5 decimal places.

Conclusion

The relationship established from the first pair (13 and 0.07692) is that the second number is the reciprocal of the first number ($1/13 \approx 0.07692$). Applying this same relationship to the third number (14), we calculate its reciprocal ($1/14 \approx 0.07142857$). Comparing this result with the options, 0.07142 is the closest match, likely obtained by rounding or truncating the exact value.

Revision Table: Key Steps in Solving Analogies

Additional Information on Numerical Reasoning

Numerical reasoning questions often involve finding patterns and relationships between numbers. These relationships can be simple arithmetic operations or more complex sequences and series. Practicing different types of numerical analogies helps improve pattern recognition skills.

Common patterns include:

• Addition/Subtraction: A constant difference between numbers.
• Multiplication/Division: A constant ratio between numbers.
• Squares/Cubes/Roots: Numbers related by powers or roots.
• Fractions/Reciprocals: As seen in this problem, using inverse relationships.
• Sequences: Arithmetic progressions, geometric progressions, or other defined sequences.
• Combinations: A mix of operations, e.g., multiply by 2 and add 1.

Identifying the correct pattern quickly is key to solving these types of problems efficiently.