Which of the following set of numbers is analogous to thegiven set of numbers? 21 : 462 :: ?31 : 98241 : 173227 : 76639 : 1560

To determine the analogous set of numbers, let's analyze the relationship between the numbers in the first pair (21 and 462) and then apply the same pattern to find the missing number corresponding to 31.

Step 1: Break Down the Problem

• The given pair is 21 and 462.
• We need to identify the rule or relationship that links these two numbers.

Step 2: Relevant Concepts

• We can look for arithmetic or multiplicative relationships. A common approach is to check if one number is a multiple of the other or if there are any operations involved, such as exponentiation or factorials.

Step 3: Analysis and Detail

1. Calculate $21 \times 21 = 441$ (a perfect square)
2. Check $441 + 21 = 462$
3. This indicates that the second number (462) is the result of squaring the first number (21) and then adding the first number.

Now we apply this relationship to the number 31 to find the analogous number.

Step 4: Verify and Summarize

1. Calculate $31 \times 31 = 961$
2. Then add $31$: $961 + 31 = 992$

Final Answer

The analogous number for 31 is 992.