Question

The missing numbers in the below series would be
1 : 1, 8 : 4, 9 : 27, 64 : 16, 25 : 125, ? : ?, 49 : 343

• A. 36 : 316
• B. 216 : 36
• C. 316 : 16
• D. 32 : 316

Answer 1

The Correct Option is B

The given series is a pattern-based numerical sequence: 1 : 1, 8 : 4, 9 : 27, 64 : 16, 25 : 125, ? : ?, 49 : 343. Our task is to identify the missing pair.

The sequence consists of pairs of numbers in the form x : y. Observe that in each pair, the x values are either perfect squares or perfect cubes, and the y values follow a specific relationship with the x values. Let's establish the pattern:

1. 1:1 - Here, 1²=1 and 1³=1. 
2. 8:4 - Note that 8=2³, and 4=2².
3. 9:27 - Here, 9=3², and 27=3³.
4. 64:16 - 64=4³, and 16=4².
5. 25:125 - 25=5², and 125=5³.

The pattern alternates between a perfect cube paired with a perfect square and vice-versa.

1. 216:36 - Following the pattern, 216 is 6³, and 36 is 6². This fits the established pattern perfectly.
2. 49:343 - 49=7², and 343=7³.

Thus, the missing pair, following the pattern, is 216:36.