Solving the Number Analogy Question

This question asks us to find the relationship between pairs of numbers and apply the same relationship to a third pair to find the missing number. We are given three parts to the analogy:

• First pair: 14 ∶ 85
• Second pair: 20 ∶ 121
• Third pair: 11 ∶ ?

We need to determine how the second number in the first two pairs is related to the first number, and then use that same rule for the third pair.

Finding the Pattern

Let's examine the first pair, 14 and 85. We look for a mathematical relationship, such as multiplication, addition, subtraction, division, squaring, etc., or a combination of these operations.

Consider multiplication: What multiple of 14 is close to 85? \(14 \times 5 = 70\), \(14 \times 6 = 84\), \(14 \times 7 = 98\).

The number 84 is very close to 85. It is \(14 \times 6\). If we add 1 to 84, we get 85.

So, a possible pattern is: Second number = (First number \(\times\) 6) + 1.

Let's test this pattern with the first pair:

\((14 \times 6) + 1 = 84 + 1 = 85\)

This works for the first pair.

Now, let's test this proposed pattern with the second pair, 20 and 121. According to the pattern, the second number should be (20 \(\times\) 6) + 1.

\((20 \times 6) + 1 = 120 + 1 = 121\)

This also works for the second pair. The pattern seems to be consistent: the second number is obtained by multiplying the first number by 6 and then adding 1.

The established pattern is: Second number = (First number \(\times\) 6) + 1.

Applying the Pattern to the Third Pair

Now we apply this pattern to the third pair, 11 ∶ ?. Let the missing number be \(x\).

According to the pattern, \(x\) should be (11 \(\times\) 6) + 1.

Let's calculate:

\((11 \times 6) + 1 = 66 + 1 = 67\)

So, the missing number is 67.

Verifying the Options

We compare our calculated number, 67, with the given options:

1. 65
2. 76
3. 77
4. 67

Our calculated value matches option 4.

The complete analogy is 14 ∶ 85 ∶∶ 20 ∶ 121 ∶∶ 11 ∶ 67.

Conclusion

The pattern connecting the numbers in each pair is to multiply the first number by 6 and add 1. Applying this rule to the number 11 gives us 67.

The final answer is 67.

Revision Table: Number Analogy Pattern

Additional Information: Types of Number Analogy Patterns

Number analogy questions test your ability to identify mathematical relationships between numbers. Common patterns include:

• Arithmetic Operations: Simple addition, subtraction, multiplication, or division.
• Multiple Operations: Combinations like multiply and add/subtract, divide and add/subtract.
• Squaring or Cubing: The second number might be the square or cube of the first number, or related to the square/cube with addition/subtraction.
• Square Roots or Cube Roots: The relationship might involve roots.
• Consecutive Numbers: The pattern might relate to consecutive integers or their properties.
• Digit Operations: Sometimes the pattern involves operations on the digits of the number (e.g., sum of digits, product of digits).
• Prime or Composite Numbers: The relationship might be based on number properties like being prime or composite.

Solving these questions requires careful observation and systematic testing of possible relationships.