Question

Find the missing number in the following set of numbers.

Column I	Column II
2	2
4	14
6	34
8	?
10	98

• A. 30
• B. 62
• C. 42
• D. 78

Hint:

Square the left-hand number in each row and subtract 2 to get the right-hand number.

Answer 1

The Correct Option is B

Step 1: Set up the two columns as given.
The series is arranged in pairs (Column I, Column II): (2, 2), (4, 14), (6, 34), (8, ?), (10, 98). Column I increases by 2 each time (2, 4, 6, 8, 10), so the task is to find the rule connecting each Column I value to its Column II value.
Step 2: Test a simple relationship between the two numbers in each pair.
Try squaring the Column I value and adjusting by a constant. For the first pair, Column I = 2, so 2 squared = 4. Column II is 2, which is 4 - 2 = 2. So try the rule: Column II = (Column I)^2 - 2.
Step 3: Verify the rule against the other known pairs.
For Column I = 4: 4^2 - 2 = 16 - 2 = 14, matching the given 14. For Column I = 6: 6^2 - 2 = 36 - 2 = 34, matching the given 34. For Column I = 10: 10^2 - 2 = 100 - 2 = 98, matching the given 98. Since the rule works for all four known pairs, it is confirmed as the correct pattern.
Step 4: Apply the rule to the missing pair.
For Column I = 8: Column II = 8^2 - 2 = 64 - 2 = 62.
Step 5: Match with the options.
The computed value 62 matches option (2). Options (1) 30, (3) 42 and (4) 78 do not satisfy the rule Column II = (Column I)^2 - 2, so they are incorrect.