Solving the Number Analogy: 52 : 57 ∷ 46 : ?

This question asks us to find a number that has the same relationship with 46 as 57 has with 52. This is a classic number analogy problem where we need to identify the pattern or rule connecting the first pair of numbers and apply it to the third number to find the fourth.

Analyzing the Relationship Between 52 and 57

Let's look at the first pair of numbers, 52 and 57. We need to figure out how we can get from 52 to 57 using a simple mathematical operation or pattern.

• Is it addition? Let's check: $57 - 52 = 5$. So, adding 5 to 52 gives 57.
• Is it subtraction? No, 57 is greater than 52.
• Is it multiplication or division? Multiplying or dividing 52 would not easily result in 57.
• Is there a pattern involving digits? $5+2=7$, $5+7=12$. No obvious pattern here connecting the sum of digits directly to the relationship.

The simplest and most direct relationship appears to be addition. Adding 5 to 52 gives 57.

Pattern identified: Add 5 to the first number to get the second number.

Applying the Pattern to 46

Now, we apply the same pattern to the third number, 46. We need to add 5 to 46 to find the missing number.

Missing number = $46 + 5$

Calculation: $46 + 5 = 51$

Verifying the Analogy

The analogy is 52 : 57 ∷ 46 : 51.

Let's check if the relationship holds:

• First pair: 52 and 57 ($52 + 5 = 57$) - The relationship holds.
• Second pair: 46 and 51 ($46 + 5 = 51$) - The relationship holds.

The pattern of adding 5 is consistent across both pairs.

Resulting Number

The number related to 46 in the same way that 57 is related to 52 is 51.

Conclusion

Following the pattern identified in the first pair (52 : 57), where 5 is added to the first number to get the second, applying the same logic to 46 gives us 51 ($46 + 5 = 51$).

Revision Table: Understanding Number Analogies

Additional Information: Common Number Analogy Patterns

Number analogies can use various mathematical relationships. Some common patterns include:

• Addition or Subtraction of a constant number (like in this question).
• Multiplication or Division by a constant number.
• Squares or Cubes of the number (e.g., $N : N^2$ or $N : N^3$).
• Operations involving digits of the number (e.g., sum of digits, product of digits).
• Sequential patterns (e.g., $N : N+1$, $N : N+2$, etc.).
• Combination of operations (e.g., $N : 2N+1$).

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