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)
Answer: Option D
:
D
Let there be n rows and a students in the first row.
Number of students in the second row = + 3a Number of students in the third row = a+ 6 and so on. aThe 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.
=n[2a+3(n−1)]2=630
Now consider options.
1.n=3,a=207
2.n=4,a=153
3.n=5,a=120
4.n=6,a=1952
5.n=7,a=8
Hence the only option not possible is when n=6
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:
D
Let there be n rows and a students in the first row.
Number of students in the second row = + 3a Number of students in the third row = a+ 6 and so on. aThe 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.
=n[2a+3(n−1)]2=630
Now consider options.
1.n=3,a=207
2.n=4,a=153
3.n=5,a=120
4.n=6,a=1952
5.n=7,a=8
Hence the only option not possible is when n=6
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