Solving Number Analogy Problems

This question asks us to find a relationship between pairs of numbers and apply that same relationship to a third number to find a missing value. This type of problem is known as a number analogy.

The given analogy is:

\(25 : 125 :: 32 : 160 :: 73 : ?\)

We need to determine how 125 is related to 25, and how 160 is related to 32. Once we find this rule, we apply it to 73 to find the missing number.

Analyzing the Relationship between the First Pair

Let's look at the first pair of numbers: 25 and 125.

We can try different basic arithmetic operations or relationships:

• Addition: \(25 + X = 125 \implies X = 125 - 25 = 100\). Adding 100.
• Subtraction: \(25 - X = 125\) (not applicable as 125 is larger).
• Multiplication: \(25 \times X = 125\). To find X, we divide 125 by 25. \(125 \div 25 = 5\). So, \(25 \times 5 = 125\). Multiplying by 5.
• Division: \(25 \div X = 125\) (not applicable as 125 is larger).

The relationship seems to be multiplication by 5 or addition of 100. Let's check the second pair to confirm the rule.

Verifying the Relationship with the Second Pair

Now, let's examine the second pair: 32 and 160.

Let's test the potential rules found from the first pair:

• Applying Addition of 100: \(32 + 100 = 132\). This is not 160. So, adding 100 is not the rule.
• Applying Multiplication by 5: \(32 \times 5\). Let's calculate this:

Yes, \(32 \times 5 = 160\). This matches the second pair. Therefore, the relationship between the numbers in each pair is that the second number is obtained by multiplying the first number by 5.

Applying the Rule to the Third Pair

The established rule is to multiply the first number by 5 to get the second number in the pair.

Now, we apply this rule to the third pair: 73 and ?

The missing number is \(73 \times 5\).

Calculating the Missing Number

Let's perform the multiplication:

We can calculate this as:

So, the missing number is 365.

Conclusion

The relationship observed in the given number analogy is that the second number is five times the first number. Applying this rule to the third pair (73 : ?) gives us \(73 \times 5 = 365\). Thus, the missing number is 365.

Revision Table: Number Relationships

Additional Information on Number Analogies

Number analogies are common in reasoning tests and quantitative aptitude sections. They require you to identify patterns or relationships between numbers. These relationships can be based on various mathematical operations or properties.

Common types of relationships found in number analogies include:

• Basic arithmetic operations (addition, subtraction, multiplication, division).
• Squares, cubes, or other powers.
• Square roots or cube roots.
• Operations involving the digits of the number (sum of digits, product of digits, reversing digits).
• Combinations of operations.
• Prime numbers, composite numbers, or other number properties.
• Patterns related to sequences or series.

To solve number analogies, it's helpful to systematically test common relationships between the given pairs to find a consistent rule.