GMATinsight wrote:A group of 630 children is arranged in rows for a photograph session. Each row contains 3 fewer children than the row in front of it. What number of rows from the following numbers is not a possible number of rows.

A) 3
B) 4
C) 5
D) 6
E) 7

ANS: B

The correct answer is D (6 number of rows), not 4.

Let us start with option A.

There are 3 rows.

Say, the first row has x, the second row has (x-3), and the third row has (x-6) number of children.

Thus, x + (x-3) + (x-6) = 630

3x - 9 = 630

3x = 630 + 9

3x = 639

x = 213 (A positive integer); thus, 3 number of rows is possible.

Option B:

For 3 number of rows, we had 3x = 639, thus for 4 rows, we would have 4x = 639 + (4-1)*3

4x = 639 + 3*3 = 639 + 9 = 648

x = 648/4 = 162 (A positive integer); thus, 4 number of rows is possible.

Option C:

For 4 number of rows, we had 4x = 648, thus for 5 rows, we would have 5x = 648 + (5-1)*3

5x = 648 + 4*3 = 648 + 12 = 660

x = 660/5 = 132 (A positive integer); thus, 5 number of rows is possible.

Option D:

For 5 number of rows, we had 5x = 660, thus for 6 rows, we would have 6x = 660 + (6-1)*3

6x = 660 + 5*3 = 660 + 15 = 675

x = 675/6 = A decimal number; thus, 6 number of rows is not possible.

The correct answer: D

Hope this helps!

-Jay
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GMATinsight wrote: ↑

Sat May 20, 2017 7:20 pm

A group of 630 children is arranged in rows for a photograph session. Each row contains 3 fewer children than the row in front of it. What number of rows from the following numbers is not a possible number of rows.

A) 3
B) 4
C) 5
D) 6
E) 7

ANS: B

Solution:

Since each row contains three fewer children than the row in front of it, the number of children form an evenly spaced set. In other words, if there are an odd number of rows, the middle row has the median, or average, number of children. Of course, that number has to be an integer because the number of children has to be a whole number. Since 630 is divisible by 3, 5, and 7, we see the middle row will indeed have an integer number of children. If any of these numbers of rows is not possible, the number of children in the middle row will not be an integer. However, since they are, they can’t be the correct answer and we are only left with either choice B or D as the correct answer.

Let’s examine choice B first. We can let x = the number of children in the first row. Therefore, the number of children in the second, third and fourth rows are x - 3, x - 6, and x - 9, respectively. We can create the equation:

x + x - 3 + x - 6 + x - 9 = 630

4x - 18 = 630

4x = 648

x = 162

Since x is an integer, we see that the number of rows can be 4. Since we are looking for the number of rows that is not possible, we are left with choice D as the correct answer.

Answer: D