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A group of 630 children is arranged in rows for a group photograph

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A group of 630 children is arranged in rows for a group photograph  [#permalink]

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New post 02 Aug 2015, 06:41
1
5
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

48% (02:22) correct 52% (02:34) wrong based on 159 sessions

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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?

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


Source: GMAT notes (China Maths bible)
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Re: A group of 630 children is arranged in rows for a group photograph  [#permalink]

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New post 02 Aug 2015, 06:48
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GMATnavigator wrote:
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?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

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Source: GMAT notes (China Maths bible)



Let n be the number of children in the least populated row. The subsequent rows will have n+3, n+6, n+9 ... etc children.

Start by POEing the options.

Option A, the distribution will be n, n+3, n+6 ---> n+n+3+n+6 = 630 --> n = Integer. Possible

Option B, the distribution will be n, n+3, n+6, n+9 ---> n+n+3+n+6+n+9 = 630 --> n = Integer. Possible

Option C, the distribution will be n, n+3, n+6, n+9, n+12 ---> n+n+3+n+6+n+9+ n+12 = 630 --> n = Integer. Possible

Option D, the distribution will be n, n+3, n+6, n+9, n+12, n+15 ---> n+n+3+n+6+n+9+ n+12+n+15 = 630 --> n \(\neq\) Integer. NOT POSSIBLE.

Option E, the distribution will be n, n+3, n+6, n+9, n+12, n+15, n+18 ---> n+n+3+n+6+n+9+ n+12+n+15+n+18 = 630 --> n = Integer. possible.

D is the correct answer.
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Re: A group of 630 children is arranged in rows for a group photograph  [#permalink]

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New post 02 Aug 2015, 06:53
:cry: :cry: :cry:


Moderators please rate the difficulty level of this question. I am doubtful about getting this this problem solved easily and want to guage my level of preparation.
Very good question.
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Re: A group of 630 children is arranged in rows for a group photograph  [#permalink]

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New post 02 Aug 2015, 06:56
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Gmatkor1987 wrote:
:cry: :cry: :cry:


Moderators please rate the difficulty level of this question. I am doubtful about getting this this problem solved easily and want to guage my level of preparation.
Very good question.


I would say 600-700 level question.
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Re: A group of 630 children is arranged in rows for a group photograph  [#permalink]

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New post 02 Jul 2018, 09:24
I would say this is 600 level.

Say row 1 has x children, then row 2 has x-3 and row 3 has x-6 and so forth. Hence, with plug and play, we get D as the answer since:

Row 1: x
Row 2: x - 3
Row 3: x - 6
Row 4: x - 9
Row 5: x - 12
Row 6: x- 15

This adds to 6x - 45 = 630 or 6x = 675. For a number to be divisible by 6, it must be divisible by both 2 and 3. 675 is not divisible by 2. All the rest of the answers result in an integer for x.
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Re: A group of 630 children is arranged in rows for a group photograph  [#permalink]

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New post 08 Aug 2018, 06:13
I would rate this question easy.
If you place 1 student in the first row.
Then you’ll have 4 in the next and so on.
So you can see a pattern.
each row is having 2n-1 students.
And since we need an integral value. Thus the only value of n that doesn’t divide 630 is 6.

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Re: A group of 630 children is arranged in rows for a group photograph   [#permalink] 08 Aug 2018, 06:13
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