GMATnavigator wrote:

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

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7

Kudos if you like

Source: GMAT notes (China Maths bible)

Let n be the number of children in the least populated row. The subsequent rows will have n+3, n+6, n+9 ... etc children.

Start by POEing the options.

Option A, the distribution will be n, n+3, n+6 ---> n+n+3+n+6 = 630 --> n = Integer. Possible

Option B, the distribution will be n, n+3, n+6, n+9 ---> n+n+3+n+6+n+9 = 630 --> n = Integer. Possible

Option C, the distribution will be n, n+3, n+6, n+9, n+12 ---> n+n+3+n+6+n+9+ n+12 = 630 --> n = Integer. Possible

Option D, the distribution will be n, n+3, n+6, n+9, n+12, n+15 ---> n+n+3+n+6+n+9+ n+12+n+15 = 630 --> n \(\neq\) Integer. NOT POSSIBLE.

Option E, the distribution will be n, n+3, n+6, n+9, n+12, n+15, n+18 ---> n+n+3+n+6+n+9+ n+12+n+15+n+18 = 630 --> n = Integer. possible.

D is the correct answer.