Solving Number Analogy Problems

Number analogy questions test your ability to find the relationship between a pair of numbers and apply that same relationship to another number to find a missing term. In this specific problem, we are given the analogy: 83 : 121 :: 12 : ? We need to determine the relationship between 83 and 121 and then apply it to 12 to find the corresponding number.

Analyzing the Relationship in the First Pair (83 : 121)

Let's look closely at the numbers 83 and 121. We need to find a mathematical operation or pattern that connects 83 to 121.

• Consider the digits of 83. The digits are 8 and 3.
• Let's try summing the digits: \(8 + 3 = 11\).
• Now, look at the second number, 121. We know that 121 is a perfect square: \(11^2 = 121\).
• It seems the relationship is: Take the sum of the digits of the first number and square the result to get the second number.

Applying the Relationship to the Second Pair (12 : ?)

Now, we will use the same rule we found for the first pair and apply it to the number 12.

• Consider the digits of 12. The digits are 1 and 2.
• Sum the digits: \(1 + 2 = 3\).
• According to the pattern, we need to square this sum: \(3^2 = 9\).
• Therefore, the number related to 12 in the same way that 121 is related to 83 is 9.

Verifying the Solution

Let's double-check the pattern and our result:

• For 83 : 121: Sum of digits of 83 is \(8+3=11\). Squaring 11 gives \(11^2=121\). This holds true.
• For 12 : ?: Sum of digits of 12 is \(1+2=3\). Squaring 3 gives \(3^2=9\).

The pattern is consistent, and the calculated missing number is 9.

Evaluating the Options

Let's compare our result with the given options:

• Option 1: 9
• Option 2: 3
• Option 3: 76
• Option 4: 54

Our calculated number, 9, matches Option 1.

The final answer is 9.

Revision Table: Number Analogy Pattern

Additional Information: Types of Number Analogies

Number analogy questions can involve various mathematical relationships. Some common patterns include:

• Arithmetic Operations: Addition, subtraction, multiplication, division.
• Squares and Cubes: The second number is the square or cube of the first number, or related to it by squaring/cubing.
• Digit Manipulation: Sum, difference, product, or rearrangement of digits.
• Consecutive Numbers: The second number is the next prime, next composite, etc., after the first.
• Mathematical Formulas: Applying a specific formula to the first number to get the second.
• Mixed Operations: A combination of the above, such as sum of digits then squaring, as seen in this problem.

Practicing different types of number analogies helps in quickly identifying the pattern during exams.