Which sets of ordered pairs show equivalent ratios? (1, 2), (2, 3), (4, 7) (2, 2), (4, 4), (6, 6) (3, 1), (4, 1), (5, 1) (4, 1), (8, 2), (12, 3) (2, 1), (4, 3), (5, 4)

Given:

The different sets of ordered pairs in the options.

To find:

The sets of ordered pairs that show equivalent ratios

Solution:

The set of ordered pairs show equivalent ratios, if

Where, k is a constant.

For option 1,

(1, 2), (2, 3), (4, 7)

For option 2,

(2, 2), (4, 4), (6, 6)

The set of ordered pairs (2, 2), (4, 4), (6, 6) show equivalent ratios.

For option 3,

(3, 1), (4, 1), (5, 1)

For option 4,

(4, 1), (8, 2), (12, 3)

The set of ordered pairs (4, 1), (8, 2), (12, 3) show equivalent ratios.

For option 5,

(2, 1), (4, 3), (5, 4)

So, sets of ordered pairs in options 1, 3 and 5 does not show equivalent ratios.

Therefore, the correct options are 2 and 4.

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

the answer is c. 23/3