Understanding the Number Analogy Question

This question asks us to find a relationship between two numbers in the first pair (-13/11 and 11/13) and then apply the same relationship to the first number in the second pair (7/5) to find the missing second number.

This type of question is common in reasoning tests and assesses our ability to identify patterns and apply them consistently.

Identifying the Relationship between -13/11 and 11/13

Let's look closely at the first pair of numbers: \(- \frac{13}{11}\) and \(\frac{11}{13}\).

We can observe two things:

• The fraction is inverted. The numerator becomes the denominator and the denominator becomes the numerator. This operation is called taking the reciprocal of the number.
• The sign of the number changes. The first number is negative (\(- \frac{13}{11}\)), and the second number is positive (\(\frac{11}{13}\)).

So, the relationship between the first number and the second number in the first pair appears to be: Take the reciprocal of the first number and then change its sign.

Let's verify this:

The reciprocal of \(- \frac{13}{11}\) is \(- \frac{11}{13}\).

Now, change the sign of \(- \frac{11}{13}\). This gives us \(\frac{11}{13}\).

This matches the second number in the first pair.

Applying the Relationship to 7/5

Now we apply the same relationship to the first number in the second pair, which is \(\frac{7}{5}\).

The relationship is: Take the reciprocal of the number and then change its sign.

Step 1: Take the reciprocal of \(\frac{7}{5}\).

The reciprocal of \(\frac{7}{5}\) is found by swapping the numerator and the denominator, which gives \(\frac{5}{7}\).

Step 2: Change the sign of the result from Step 1.

The result from Step 1 is \(\frac{5}{7}\), which is a positive number. Changing its sign makes it negative.

So, changing the sign of \(\frac{5}{7}\) gives \(- \frac{5}{7}\).

Conclusion

Following the established relationship, the number related to \(\frac{7}{5}\) in the same way as \(- \frac{13}{11}\) is related to \(\frac{11}{13}\) is \(- \frac{5}{7}\).

Let's check the given options to find \(- \frac{5}{7}\).

The number \(- \frac{5}{7}\) is listed as option 4.

Revision Table: Key Concepts

Additional Information: Types of Number Relationships

Number analogy questions can involve various types of relationships. Here are a few common ones:

• Arithmetic Operations: Addition, subtraction, multiplication, division. (e.g., 5:10 :: 6:12 - relationship is multiplication by 2)
• Squares and Cubes: Squaring or cubing the number. (e.g., 3:9 :: 4:16 - relationship is squaring)
• Square Roots and Cube Roots: Taking the root of the number. (e.g., 16:4 :: 25:5 - relationship is square root)
• Digit Operations: Sum of digits, product of digits, rearranging digits. (e.g., 12:3 :: 23:5 - relationship is sum of digits)
• Specific Sequences: Prime numbers, Fibonacci series, etc.
• Reciprocals: As seen in this question.
• Combinations of Operations: More complex relationships involving multiple steps.

To solve number analogy questions, it's important to carefully analyze the first pair to determine the exact relationship before applying it to the second pair.