Understanding Number Analogy Questions

Number analogy questions test your ability to find the relationship or pattern between pairs of numbers. The same relationship must hold true for all given pairs in the analogy. In this specific problem, we are given three parts: 52 is to 221, 20 is to an unknown number, and 64 is to 272. We need to find the relationship between the first and second numbers (52 and 221) and the fifth and sixth numbers (64 and 272), and then apply that relationship to the third number (20) to find the fourth, or missing, number.

Finding the Pattern in the Number Analogy

Let's look closely at the given pairs:

• Pair 1: 52 and 221
• Pair 3: 64 and 272

We need to find a consistent mathematical operation or relationship that transforms the first number of each pair into the second number.

Let's try division to see if there's a simple ratio:

For the first pair (52 and 221):

\( \frac{221}{52} \)

Let's perform the division:

\( 221 \div 52 \approx 4.25 \)

Let's check if 52 multiplied by 4.25 gives 221:

\( 52 \times 4.25 = 52 \times \frac{17}{4} = \frac{52}{4} \times 17 = 13 \times 17 = 221 \)

This works! The relationship for the first pair seems to be multiplying the first number by 4.25 (or \(\frac{17}{4}\)).

Now let's check this relationship for the third pair (64 and 272):

Is \( 64 \times 4.25 \) equal to 272?

\( 64 \times 4.25 = 64 \times \frac{17}{4} = \frac{64}{4} \times 17 = 16 \times 17 = 272 \)

Yes, the relationship holds true for the third pair as well. The consistent pattern is to multiply the first number by 4.25 (or \(\frac{17}{4}\)) to get the second number.

Applying the Pattern to Find the Missing Number

Now we need to apply this same pattern to the third number in the analogy, which is 20, to find the missing fourth number.

The relationship is: Missing Number = \( 20 \times 4.25 \)

Let's calculate:

\( 20 \times 4.25 = 20 \times \frac{17}{4} \)

We can simplify this calculation:

\( \frac{20}{4} \times 17 = 5 \times 17 = 85 \)

So, the missing number is 85.

Verifying the Solution

The analogy can be completed as: 52 : 221 :: 20 : 85 :: 64 : 272

This fits the pattern we discovered where the second number is obtained by multiplying the first number by 4.25.

Let's check the given options:

• 170
• 255
• 84
• 85

Our calculated missing number, 85, matches one of the options.

Summary of the Analogy Pattern

Revision Table: Number Analogy Concepts

Additional Information: Types of Number Patterns

Number analogy problems can use various types of patterns. Here are some common ones:

• Arithmetic Operations: Addition, subtraction, multiplication, division, or a combination of these.
• Squares and Cubes: Numbers related to squares or cubes (e.g., \(n^2\), \(n^2+1\), \(n^3\), \(n^3-1\)).
• Digit Operations: Sum, difference, product, or other operations on the digits of the numbers.
• Prime Numbers: Patterns involving prime numbers.
• Series Logic: The numbers might be part of a sequence or series with a specific rule.

Practicing different types of patterns helps improve your ability to quickly identify the rule in number analogy questions.