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? Choices.
A) 3  B) 4  C) 5  D) 6  E) 7
Explanation :   Let the last row contain x seats. So, the rows in front have x + 3, x + 6 , x + 9 , …   Total no: of students are 630. So, x + (x + 3) + (x + 6) + (x + 9) + ……… = 630.   There are 2 ways of approaching the problem. You can consider it as an Arithmetic Progression, substitute the options and find the answer, else a simple “less time consuming” way explained. We know that the number of students in each row needs to be a “natural number” and not a decimal, since there cannot be 3.5 or 1.2 or any other decimal number of students/row. We exploit this condition to get the solution quickly.   1st option : 3 rows So, x, x + 3, x+ 6 are the students in 3 rows. Sum = 3x + 9 = 630. We get a natural number as value of x. So it is fine.   2nd option : 4 rows x + (x +3) + (x+6) + (x+9) = 630, x = (630 – 18)/4 = natural number.   3rd option : 5 rows x + (x +3) + (x+6) + (x+9) + (x + 12)= 630 x = (630 – 30)/5, again natural number.   4th option : 6 rows x + (x +3) + (x+6) + (x+9) + (x + 12) + (x+15) = 630   x = (630 – 45)/6 is not a natural number, and is a decimal.   Hence, we cannot have 6 rows.   Answer : 6
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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?