Understanding Number Analogy Questions

Number analogy questions test your ability to find the relationship between a pair of numbers and apply that same relationship to another number to find a missing term. The goal is to identify the pattern or rule connecting the first two numbers.

The given analogy is:

12 : 60 :: 16 : ?

This means we need to find how 12 is related to 60 and then use that same relation to find the number that relates to 16 in the same way.

Discovering the Relationship between 12 and 60

Let's examine the relationship between the first pair of numbers, 12 and 60. We need to find an operation or a series of operations that transforms 12 into 60.

• A simple multiplication could be $12 \times 5 = 60$. Let's see if multiplying 16 by 5 gives any of the options: $16 \times 5 = 80$. 80 is not among the options. So, the relationship might be more complex than simple multiplication by a constant.
• Let's look for a relationship that involves the number 12 itself. How can we get the multiplier '5' from '12'?
• Consider operations like division by 2, subtraction, etc.
• What if we divide the first number by 2? $12 / 2 = 6$. If we subtract 1 from this result, we get $6 - 1 = 5$.
• Let's test if multiplying the first number by this result (5) gives the second number: $12 \times 5 = 60$. This works for the first pair!

So, the relationship seems to be: The second number is obtained by multiplying the first number by (half of the first number minus 1).

Mathematically, if the first number is $x$, the second number is $x \times \left(\frac{x}{2} - 1\right)$.

Applying the Relationship to 16

Now, let's apply the same rule to the third number, 16, to find the missing fourth number.

Using the rule $x \times \left(\frac{x}{2} - 1\right)$ with $x = 16$:

First, calculate half of the third number: $\frac{16}{2} = 8$.

Next, subtract 1 from the result: $8 - 1 = 7$.

Finally, multiply the third number (16) by this value (7): $16 \times 7 = 112$.

Therefore, the missing number is 112.

Verifying the Answer with Options

The options provided are 210, 121, 112, and 201. Our calculated missing number is 112, which is present as an option.

The relationship holds true for the given analogy:

• $12 : 12 \times (\frac{12}{2} - 1) = 12 \times (6 - 1) = 12 \times 5 = 60$
• $16 : 16 \times (\frac{16}{2} - 1) = 16 \times (8 - 1) = 16 \times 7 = 112$

Final Answer

Based on the identified relationship, the number that completes the analogy 16 : ? is 112.

Number Analogy Revision Table

Additional Information on Solving Number Analogies

Solving number analogies requires careful observation and systematic thinking. Here are some tips:

• Look for simple arithmetic relationships first (addition, subtraction, multiplication, division).
• Check for squares or cubes of the numbers or numbers near them.
• Consider relationships involving the number itself, like $n \times (n+k)$, $n \times (n-k)$, $n \times (n/k)$, etc.
• Sometimes the relationship involves the sum or product of the digits of the number.
• If the numbers are close, look for addition or subtraction patterns. If they are far apart, look for multiplication, division, squares, or cubes.
• Test your proposed relationship with the given pair before applying it to find the missing term.

Practice with various types of number analogy questions helps in recognizing common patterns quickly.