Question

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? (CAT 2006)

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is D 6

Let there be n rows and a students in the first row.

Number of students in the second row $=a+3$. Number of students in the third row $=a+6$ and so on. The number of students in each row forms an arithmetic progression with common difference = 3. The total number of students = The sum of all terms in the arithmetic progression.

$=\frac{n[2a+3(n-1\left)\right]}{2}=630$

Now consider options:

$1.n=3,a=207$

$2.n=4,a=153$

$3.n=5,a=120$

$4.n=6,a=\frac{195}{2}$

Hence the only option not possible is when n=6.