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: Number the rows and note the Column I values.
Label the five rows n = 1, 2, 3, 4, 5. The Column I values are 2, 4, 6, 8, 10, fitting the formula Column I = 2n.
Step 2: Express Column II as a function of the row number n.
The known Column II values are 2 (n=1), 14 (n=2), 34 (n=3) and 98 (n=5). Try a quadratic form Column II = a*n^2 + b*n + c and use three known points: from n=1, a + b + c = 2; from n=2, 4a + 2b + c = 14; from n=3, 9a + 3b + c = 34.
Step 3: Solve the system of equations.
Subtracting the first equation from the second gives 3a + b = 12. Subtracting the second from the third gives 5a + b = 20. Subtracting these two results gives 2a = 8, so a = 4. Substituting back, b = 12 - 12 = 0, and c = 2 - 4 - 0 = -2. So the formula is Column II = 4n^2 - 2.
Step 4: Check the formula against the fifth row as an independent test.
For n = 5: Column II = 4(25) - 2 = 100 - 2 = 98, matching the given value exactly, confirming the formula rather than a coincidence from only three points.
Step 5: Apply the formula to the missing fourth row.
For n = 4: Column II = 4(16) - 2 = 64 - 2 = 62.
The missing number is 62, matching the pattern in every other row of the series. \[\boxed{62}\]