Understanding the Number Analogy Problem

The question presents a number analogy where the relationship between the first pair of numbers is the same as the relationship between the second pair. We need to find the number related to the fifth number based on this consistent relationship.

The analogy is given as: 7 ∶ 35 ∶∶ 21 ∶ 399 ∶∶ 4 ∶ ?

This means 7 is related to 35 in the same way that 21 is related to 399, and 4 is related to the missing number.

Analyzing the First Pair: 7 ∶ 35

Let's look at the relationship between 7 and 35. We can see that 35 is a multiple of 7.

If we divide 35 by 7, we get: $35 \div 7 = 5$.

So, the relationship could be multiplication by 5: $7 \times 5 = 35$.

Analyzing the Second Pair: 21 ∶ 399

Now let's examine the relationship between 21 and 399. We look for a similar pattern or a consistent relationship.

If we consider multiplication, what do we multiply 21 by to get 399?

Let's divide 399 by 21: $399 \div 21$.

We can estimate: $21 \times 10 = 210$. $399 - 210 = 189$.

What do we multiply 21 by to get 189? $21 \times 9 = 189$.

So, $21 \times (10 + 9) = 21 \times 19 = 399$.

The relationship here is multiplication by 19: $21 \times 19 = 399$.

Identifying the Number Pattern

We have found the multipliers for the first two pairs:

• For 7 ∶ 35, the multiplier is 5.
• For 21 ∶ 399, the multiplier is 19.

Now, let's look for a pattern between the first number in each pair (7 and 21) and the corresponding multiplier (5 and 19).

Consider the first pair: The first number is 7, the multiplier is 5. Notice that $5 = 7 - 2$.

Consider the second pair: The first number is 21, the multiplier is 19. Notice that $19 = 21 - 2$.

It appears the pattern is: the second number is obtained by multiplying the first number by (the first number minus 2).

Relationship Pattern: Second Number = First Number $\times$ (First Number - 2)

Applying the Pattern to the Third Pair: 4 ∶ ?

The third pair is 4 ∶ ?. Here, the first number is 4.

Following the pattern we identified:

The multiplier should be (First Number - 2) = $4 - 2 = 2$.

The missing number should be First Number $\times$ Multiplier = $4 \times 2$.

Step-by-Step Calculation for the Missing Number

Let the missing number be $x$. We have the pair 4 ∶ $x$.

1. Identify the first number in the pair: The first number is 4.
2. Determine the multiplier based on the pattern: Multiplier = First Number - 2 = $4 - 2 = 2$.
3. Calculate the second number by multiplying the first number by the multiplier: $x = 4 \times 2$.
4. Perform the multiplication: $4 \times 2 = 8$.

So, the missing number is 8.

Conclusion: The Number Related to 4

Based on the consistent pattern observed in the first two pairs of the analogy, the number related to 4 is 8.

The completed analogy is: 7 ∶ 35 ∶∶ 21 ∶ 399 ∶∶ 4 ∶ 8.

Revision Table: Number Analogy Relationships

Additional Information: Strategies for Solving Number Analogies

Number analogies require you to find a logical rule or pattern connecting the numbers in one pair and apply it to another pair. Here are some strategies:

• Basic Operations: Check for addition, subtraction, multiplication, or division between the numbers.
• Squares and Cubes: See if the numbers are squares or cubes, or related to squares/cubes ($n^2 \pm k$, $n^3 \pm k$).
• Differences/Ratios: Look at the difference or ratio between the numbers. Is it a constant value or a sequence?
• Digit Operations: Sometimes the pattern involves the digits of the numbers (sum of digits, product of digits, etc.).
• Prime Numbers: The relationship might involve prime numbers.
• Combinations: The pattern can be a combination of different operations.

Always verify the pattern with all the given pairs before applying it to find the missing number.