Understanding Number Pair Analogies

In number pair analogy questions, we need to find the mathematical relationship or pattern that connects the two numbers in a given pair. Once the rule is discovered, we apply it to the options to find the pair that follows the same rule. It's important to remember that the operations should be performed on the whole number itself, not on its individual digits.

Finding the Pattern in the Given Number Pairs

We are given two number pairs: (12, 57) and (16, 77). Let's analyze these pairs to find the mathematical operation connecting the first number to the second.

Consider the first pair (12, 57). We need to figure out how to get 57 from 12.

• Let's try multiplying the first number by a value and then adding or subtracting something.
• If we multiply 12 by 4, we get $12 \times 4 = 48$. To reach 57, we need to add $57 - 48 = 9$. So, the rule could be $x \times 4 + 9$. Let's test this on the second pair.
• For the second pair (16, 77), applying this rule gives $16 \times 4 + 9 = 64 + 9 = 73$. This is not 77, so this rule is incorrect.

Let's try multiplying the first number by a different value.

• If we multiply 12 by 5, we get $12 \times 5 = 60$. To reach 57, we need to subtract $60 - 57 = 3$. So, the rule could be $x \times 5 - 3$. Let's test this on the second pair.
• For the second pair (16, 77), applying this rule gives $16 \times 5 - 3 = 80 - 3 = 77$. This matches the second number!

So, the pattern found is: Second Number = (First Number $\times$ 5) - 3.

Applying the Pattern to the Options

Now, let's apply the rule (First Number $\times$ 5) - 3 to each of the given options to find the pair that follows the same pattern.

• Option 1: (11, 49)

  Apply the rule to the first number, 11:

  $\text{Calculated second number} = 11 \times 5 - 3 = 55 - 3 = 52$

  The calculated second number (52) does not match the given second number (49).

• Option 2: (4, 14)

  Apply the rule to the first number, 4:

  $\text{Calculated second number} = 4 \times 5 - 3 = 20 - 3 = 17$

  The calculated second number (17) does not match the given second number (14).

• Option 3: (8, 37)

  Apply the rule to the first number, 8:

  $\text{Calculated second number} = 8 \times 5 - 3 = 40 - 3 = 37$

  The calculated second number (37) matches the given second number (37).

• Option 4: (21, 106)

  Apply the rule to the first number, 21:

  $\text{Calculated second number} = 21 \times 5 - 3 = 105 - 3 = 102$

  The calculated second number (102) does not match the given second number (106).

Identifying the Matching Pair

Based on the calculations above, only Option 3, (8, 37), follows the pattern (First Number $\times$ 5) - 3 established by the initial pairs (12, 57) and (16, 77).

Revision Table: Number Pair Pattern

Let's quickly summarize the pattern identified and how it applies.

• The core operation is multiplying the first number by 5.
• After multiplication, 3 is subtracted from the result.
• This rule, $x \rightarrow 5x - 3$, successfully connects the numbers in the initial pairs.
• We then tested this exact rule on all the provided options.

Additional Information: Solving Analogy Questions

Number analogy questions are a common type of logical reasoning problem. They test your ability to find relationships between numbers. Here are some tips for solving them:

• Look for basic arithmetic operations: addition, subtraction, multiplication, division.
• Consider combinations of operations, like multiply and then add/subtract, or divide and then add/subtract.
• Check for powers or roots (squares, cubes, square roots, etc.).
• Sometimes the pattern involves sequences or progressions.
• Always test your hypothesized rule on all the given examples (if more than one pair is provided) before applying it to the options.
• Pay close attention to any specific constraints mentioned in the question, such as operating only on whole numbers.