Solving Number Analogy Problems

Number analogy questions test your ability to find the relationship or pattern between two numbers and apply that same relationship to a different pair of numbers to find a missing value. In this specific problem, we are given three pairs, with the last number in the third pair missing:

\(129 : 32 :: 109 : 27 :: 289 : ?\)

The task is to determine how the second number relates to the first number in the first two pairs, and then use that rule to find the number related to 289.

Analyzing the First Number Pair: 129 and 32

Let's examine the relationship between 129 and 32. We look for mathematical operations or patterns. Common relationships involve addition, subtraction, multiplication, division, squares, cubes, roots, or digit manipulation.

If we divide 129 by a small number, say 4, we get \(129 \div 4 = 32.25\). This is very close to 32. Perhaps there's an adjustment before dividing, or rounding involved. Let's consider subtracting a small number from 129 first.

What if we subtract 1 from 129? We get \(129 - 1 = 128\). Now, if we divide 128 by 4, we get \(128 \div 4 = 32\). This exactly matches the second number in the pair!

So, a potential rule is: \(\text{Second Number} = (\text{First Number} - 1) \div 4\).

Analyzing the Second Number Pair: 109 and 27

Let's test if the rule we found from the first pair applies to the second pair, 109 and 27.

Using the rule: \(\text{Second Number} = (\text{First Number} - 1) \div 4\).

Substitute the first number, 109:

\((\text{109} - 1) \div 4 = 108 \div 4\)

\(108 \div 4 = 27\)

This result, 27, matches the second number in the second pair. The rule seems consistent.

Identifying the Pattern or Rule

Based on the analysis of the first two pairs, the pattern is clearly established: the second number is obtained by subtracting 1 from the first number and then dividing the result by 4.

The rule is: \(\text{Related Number} = (\text{Given Number} - 1) / 4\)

Applying the Pattern to Find the Missing Number: 289 : ?

Now, we apply this rule to the third pair, 289 : ?. The given number is 289.

Using the rule: \(\text{Missing Number} = (\text{289} - 1) \div 4\)

Step 1: Subtract 1 from the given number.

\(289 - 1 = 288\)

Step 2: Divide the result by 4.

\(288 \div 4\)

To calculate \(288 \div 4\):

• Divide 28 by 4: \(28 \div 4 = 7\)
• Divide 8 by 4: \(8 \div 4 = 2\)
• Combine the results: 72

So, \(288 \div 4 = 72\).

The missing number is 72.

Conclusion

The number related to 289 using the same pattern as the first two pairs is 72.

Revision Table: Number Analogy Pattern

Additional Information on Number Analogy

Number analogy questions are a common type in logical reasoning tests. They require you to identify the underlying rule that transforms the first number into the second number in a pair. This rule can be based on various mathematical operations or properties.

Common types of patterns found in number analogy problems include:

• Arithmetic operations (addition, subtraction, multiplication, division)
• Operations involving squares, cubes, square roots, or cube roots
• Operations based on digits of the number (sum of digits, product of digits, reversing digits)
• Combinations of multiple operations
• Prime numbers, composite numbers, or specific number series

To solve these problems effectively, it's helpful to:

• Start by examining simple relationships (addition/subtraction, multiplication/division).
• Consider squares and cubes of numbers near the given values.
• Look at digit-based operations.
• Test the identified pattern on all given pairs to ensure consistency.