In the following question, select the related number from the given alternatives.
11 : 120 : : 13 : ?

Question

In the following question, select the related number from the given alternatives.11 : 120 : : 13 : ?

Prepp Team · Accepted Answer

Understanding Number Analogy Questions

Number analogy questions test your ability to find a relationship between a given pair of numbers and then apply that same relationship to another number to find the missing term. In the question 11 : 120 : : 13 : ?, we need to figure out the link between 11 and 120 and use it for 13.

Analyzing the Relationship in the First Pair (11 : 120)

Let's look closely at the first pair of numbers, 11 and 120. We need to find a mathematical operation or pattern that connects 11 to 120.

Could it be simple addition or subtraction? $120 - 11 = 109$. Adding 109 to 13 would give $13 + 109 = 122$, which is not among the options.
Could it involve multiplication? $11 \times \text{something} \approx 120$. $11 \times 10 = 110$, $11 \times 11 = 121$. This looks promising.
Let's consider squaring the number 11. $11^2 = 11 \times 11 = 121$.
Now, compare 121 with 120. The difference is $121 - 120 = 1$.

So, the pattern seems to be: Square the first number and subtract 1 to get the second number.

Let's verify this pattern with the first pair:

$\text{First Number} = 11$

$\text{Relationship} = (\text{First Number})^2 - 1$

$\text{Second Number} = 11^2 - 1 = 121 - 1 = 120$

This matches the given second number in the first pair (120).

Applying the Pattern to Find the Related Number for 13

Now we apply the same pattern to the second part of the analogy, starting with the number 13. We need to find the number that relates to 13 in the same way that 120 relates to 11.

Using the pattern: Square the number and subtract 1.

$\text{First Number in Second Pair} = 13$

$\text{Related Number} = (13)^2 - 1$

Calculate the square of 13:

$13^2 = 13 \times 13 = 169$

Now, apply the subtraction:

$\text{Related Number} = 169 - 1 = 168$

The related number for 13 is 168.

Verifying the Options

Let's look at the given options to see if 168 is present:

165
168
170
169

The calculated number, 168, matches option 2.

Therefore, the correct answer is 168.

Summary of the Analogy Pattern
Pair	First Number	Pattern Applied	Result
First Pair	11	$11^2 - 1$	$121 - 1 = 120$
Second Pair	13	$13^2 - 1$	$169 - 1 = 168$

Revision Table: Key Concepts in Number Analogy

Concept	Explanation	Example Pattern
Basic Operations	Addition, Subtraction, Multiplication, Division	$n : n+k$, $n : n \times k$
Squares and Cubes	Relating numbers using their squares ($n^2$) or cubes ($n^3$)	$n : n^2$, $n : n^2+k$, $n : n^3$, $n : n^3-k$
Prime Numbers	Relating numbers based on their prime nature or position in the prime sequence	$p_n : p_{n+k}$
Digit Operations	Operations on the digits of the number	$n : \text{sum of digits of } n$

Additional Information on Number Reasoning

Number reasoning questions, including analogies, are common in competitive exams. To excel in these types of questions, it's helpful to be familiar with common patterns and relationships between numbers.

Practice: Regularly practicing different types of number series and analogy questions helps in quickly identifying patterns.
Squares and Cubes: Memorizing squares up to at least 20 and cubes up to at least 10 can save time.
Prime Numbers: Be able to recognise prime numbers quickly.
Observation: Carefully observe the difference, ratio, or relationship between the numbers in the first pair. Look for common mathematical operations or sequences.
Break Down: If the numbers are large, sometimes the pattern might involve operations on the digits themselves.

Understanding these basic concepts and practicing regularly will significantly improve your ability to solve number analogy and other logical reasoning questions.