Three of the following number-pairs are alike in some manner and hence form a group. Which number-pair does not belong
to that group?

(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent
digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into
1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)

Question

Three of the following number-pairs are alike in some manner and hence form a group. Which number-pair does not belong
to that group?

(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent
digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into
1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)

Accepted Answer

Let's analyze each pair to find the pattern:

1. Pair (17, 306): Check if 306 is a multiple of 17.
   17 × 18 = 306
   So, 306 = 17 × 18

2. Pair (21, 462): Check if 462 is a multiple of 21.
   21 × 22 = 462
   So, 462 = 21 × 22

3. Pair (14, 196): Check if 196 is a multiple of 14.
   14 × 14 = 196
   So, 196 = 14 × 14

4. Pair (12, 156): Check if 156 is a multiple of 12.
   12 × 13 = 156
   So, 156 = 12 × 13

Now, observe the multipliers:
- For pairs 1, 2, and 4, the second number is the first number multiplied by the next integer (n × (n+1)):
  - 17 × 18
  - 21 × 22
  - 12 × 13

- For pair 3, the second number is the first number multiplied by itself (n × n).

Hence, pair 3 (14 – 196) does not belong to the group because it follows a different pattern.

Answer

Answer

Answer