Solving the Number Analogy Question: 31 : 90 :: 43 : ?

This question is a number analogy problem. We are given the relationship between the first pair of numbers (31 and 90) and we need to find the number that has the same relationship with the third number (43).

Let's analyze the relationship between the first pair: 31 and 90.

We need to find a mathematical operation or pattern that transforms 31 into 90.

• One possible relationship is simple addition or subtraction. What is the difference between 90 and 31?

Calculation for the difference:

$$90 - 31 = 59$$

So, adding 59 to 31 gives 90:

$$31 + 59 = 90$$

Let's test if this relationship holds for the third number, 43. We apply the same operation (adding 59) to 43.

Calculation for the missing number:

$$43 + 59 = 102$$

Now, let's check the given options to see if 102 is present.

• Option 1: 130
• Option 2: 125
• Option 3: 102
• Option 4: 75

The calculated value, 102, matches Option 3.

Therefore, the relationship between 31 and 90 is adding 59, and applying the same rule to 43 gives 102.

Step-by-Step Solution

1. Identify the first pair of numbers: 31 and 90.
2. Find the relationship between 31 and 90. We found that $31 + 59 = 90$.
3. Identify the third number: 43.
4. Apply the same relationship (adding 59) to the third number.
5. Calculate $43 + 59$.
6. $43 + 59 = 102$.
7. Match the result with the given options. The result 102 matches Option 3.

The missing number in the analogy 31 : 90 :: 43 : ? is 102.

Revision Table: Number Analogy Key Concepts

Additional Information on Number Reasoning

Number reasoning questions test your ability to identify patterns and relationships between numbers. These patterns can be simple arithmetic operations, sequences, ratios, or more complex rules involving digits or positions.

• Common Relationships: Look for addition, subtraction, multiplication, division, or a combination of these. Squaring, cubing, square roots, and cube roots are also frequent.
• Digit Operations: Sometimes the relationship involves the individual digits of the numbers (e.g., sum of digits, product of digits, reversing digits).
• Position-based Rules: In number series, the position of the number can be part of the rule.
• Prime or Composite Numbers: The pattern might be based on properties of numbers like being prime or composite.
• Trial and Error: Often, you need to try out different possible relationships between the first pair to see which one works and produces one of the given options when applied to the third number. Start with simple arithmetic operations as they are most common.

Practice with various types of number reasoning questions helps in quickly recognizing patterns and applying the correct logic.