# Worked Examples Type-III

In the following examples, five pairs of numbers are given. Out of these, four pairs are alike in a certain way. Identify the pair which is different from others.

Example-1
(1) 2, 90 (2) 89, 12 (3) 72, 56 (4) 30, 20 (5) 6, 110
Analysis:
Observe the pair of numbers in (1), (3), (4) and (5).

Both the numbers in these pairs are of the form n2 + n, where n is a natural number.

In pair (2) only one number 12 follow this pattern (12 = 32 + 3).

But 89 does not follow this pattern.

Example-2
(1) 2, 8 (2) 1010, 720 (3) 10, 24 (4) 68, 120 (5) 350, 504
Solution
The first number of each pair is of the form n3 + n.

The second number of each pair except pair (1) is of the form n3 - n.

Hence, pair (1) is an odd man.

Example-3
(1) 334, 36 (2) 433, 36 (3) 822, 36 (4) 632, 36 (5) 914, 36
Solution
The product of digits of the first number is equal to the second number in each of the pairs, except in pair (3).

Pair (3) does not follow this pattern.

Example-4
(1) 273, 12 (2) 329, 14 (3) 457, 16 (4) 567, 18 (5) 679, 20
Solution
The sum of digits of the first number is the second number in all the pairs, except in pair (5).

In pair (5), the sum of digits of the first number is 22, where as the second number is 20.

Example-5
(1) 7, 743 (2) 6, 612 (3) 5, 521 (4) 4, 46 (5) 3, 72
Solution
Consider the first number of each pair.

Find the cube of the said number.

Write the digits of this cube in the reverse order.

We get the second number in all the pairs except in pair (1).