SOLUTION: a group of 630 children is seated in row for a group photo session. each row contains three less children than the row in front of it which one of the following number of row is n

Question 909251: a group of 630 children is seated in row for a group photo session. each row contains three less children than the row in front of it which one of the following number of row is not possible??
a 2
b 3
c 5
d 6
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
Your problem states that there is only one correct answer listed,
but there are two correct answers.
--------------------------------------
We'll try them all:
The formula for the sum of an arithmetic series is

where n = the number of terms and a₁ = the first term.
We will set S_n = 630 and d=3 in every case.
n will be the number of rows and a₁ will be the number
of children in the first, shortest, row.
--------------------------------------
We try n = 2

That would be children in one row and
3 less or is the second row.
That would add up to 630 children, but it's not nice to
cut children in half, :) so you can't have 2 rows.
That's one answer.
--------------------------------------
We try n = 3

Multiply both sides by 2 to clear the fraction

You have 3 rows with 207, 210, and 213
and 207+210+213 = 630. That's possible so it isn't a
correct answer
--------------------------------------
We try n = 5

Multiply both sides by 2 to clear the fraction

You have 4 rows with 120, 123, 126, 129 and 132
and 120+123+126+129 = 630. That's possible so it isn't a
correct answer.
--------------------------------------
We try n = 6

Divide both sides by 3

You have 6 rows of ,,,,,. That adds to 630, but we'd have to cut
3 children in half. So that's not a possibility either. So 6 is a
correct answer also.
So two of the choices are correct, 2 and 6.
Edwin
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