Question

Select the option that is related to the third number in the same way as the second number is related to the first number.
99 : 120 :: 143 : ?

• A. 168
• B. 361
• C. 289
• D. 189

Hint:

When you see numbers like 99, 120, 143, which are one less than a perfect square, immediately test the pattern \(n^2 - 1\). This is a very common pattern in analogy questions.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
We need to identify the logical relationship between the first pair of numbers (99 and 120) and apply the same logic to the second pair (143 and ?) to find the missing number.
Step 2: Key Formula or Approach:
The approach is to analyze the numbers to find a mathematical pattern. Often, these patterns involve squares, cubes, or simple arithmetic operations. Let's express the given numbers in terms of nearby perfect squares.
Step 3: Detailed Explanation:
Let's analyze the first number in the first pair, 99.
99 can be written as \(100 - 1\), which is \(10^2 - 1\).
Now let's analyze the second number in the first pair, 120.
120 can be written as \(121 - 1\), which is \(11^2 - 1\).
So, the relationship is \(n^2 - 1 : (n+1)^2 - 1\), where n = 10.
Now, let's apply this same logic to the second pair.
The first number is 143.
143 can be written as \(144 - 1\), which is \(12^2 - 1\).
Here, n = 12.
Following the pattern, the missing number should be \((n+1)^2 - 1 = (12+1)^2 - 1\).
\[ (13)^2 - 1 = 169 - 1 = 168 \] Step 4: Final Answer:
The missing number is 168.