Understanding Number Analogy Problems

A number analogy question tests your ability to find the relationship between a pair of numbers and apply that same relationship to another number to find a missing term. In the given problem, we have the analogy 14 : 210 :: 16 : ?, which means "14 is to 210 as 16 is to what number?".

Analyzing the Relationship: 14 to 210

We need to figure out how the number 14 is related to the number 210. Let's look for a common mathematical operation or pattern that connects these two numbers.

We can test simple relationships like addition, subtraction, multiplication, division, squaring, or combinations of these.

• Is it addition? $14 + X = 210 \implies X = 210 - 14 = 196$.
• Is it multiplication? $14 \times X = 210 \implies X = 210 \div 14$.

Let's perform the division to find the potential multiplier:

$$ \frac{210}{14} = \frac{21 \times 10}{14} = \frac{3 \times 7 \times 10}{2 \times 7} = \frac{3 \times 10}{2} = 3 \times 5 = 15 $$

So, $14 \times 15 = 210$. This suggests the relationship might be multiplying the first number by 15 to get the second number.

Applying the Pattern: 16 to the Missing Number

Assuming the pattern is indeed "multiply the first number by 15", we apply the same rule to the second pair, 16 : ?.

According to the pattern, the missing number should be $16 \times 15$.

Let's calculate $16 \times 15$:

$$ 16 \times 15 = 16 \times (10 + 5) = (16 \times 10) + (16 \times 5) $$

$$ = 160 + 80 $$

$$ = 240 $$

So, the missing number is 240.

Comparing with Options

Now, let's check the given options to see if 240 is among them:

1. 240
2. 256
3. 212
4. 271

The calculated number, 240, matches option 1.

Conclusion: Finding the Missing Number in Analogy

The relationship between 14 and 210 is that $14 \times 15 = 210$. Applying the same relationship to 16, we find that $16 \times 15 = 240$. Therefore, the missing number in the analogy 14 : 210 :: 16 : ? is 240.

Revision Table: Key Number Analogy Patterns

Additional Information: Related Numerical Reasoning

Number analogy questions are a common type of numerical reasoning problem. They assess your ability to identify underlying rules or patterns. Besides simple arithmetic operations and powers, other patterns can involve:

• Alternating patterns (e.g., add then subtract).
• Patterns based on digits of the number.
• Prime numbers, composite numbers, etc.
• Fibonacci sequence or other series.

Practicing different types of number series and pattern recognition helps improve skills in solving these questions.