A group of 630 children is arranged in rows for a group photograph session. Each row contain three fewer children than the row in front of it. What number of rows is not possible ?

Options

A. 3
B. 4
C. 5
D. 6

Answer

D

Explanation

Let the number of rows = x, and the number of children in last row = y. Then, according to the question
`xy + (3(x - 1)(x))/(2) = 630 " " ......(i)`
So, check out all possibilities given in the options.
Put `x = 3` in equation (i), we get `3y +9 = 630 `
or `y = 207 `
So, it is possible.
Put `x = 4` in equation (i), we get `4y + 18 = 630 `or, `y=153 `
So, it is also possible.
Put `x = 5` in equation (i), we get `5y + 30 = 630 `
or, `y = 120 `
So, it is also possible.
Put `x = 6` in equation (i), we get `6y +45 = 630 `
or, `y= 585/6 = 97.5 `
So, it is not possible. [`because` No. of children can.t be in fraction]
Therefore, the number of rows not possible = 6