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

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Intern
Joined: 20 May 2012
Posts: 15
Concentration: General Management, Finance
GRE 1: Q168 V162
GPA: 3.82
WE: Research (Health Care)
A group of 630 children is arranged in rows for a group photograph  [#permalink]

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02 Aug 2015, 05:41
1
5
00:00

Difficulty:

95% (hard)

Question Stats:

49% (02:22) correct 51% (02:34) wrong based on 158 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)
CEO
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: A group of 630 children is arranged in rows for a group photograph  [#permalink]

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02 Aug 2015, 05:48
1
1
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

Kudos if you like

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.

Intern
Joined: 02 Aug 2015
Posts: 1
Re: A group of 630 children is arranged in rows for a group photograph  [#permalink]

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02 Aug 2015, 05:53

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.
CEO
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: A group of 630 children is arranged in rows for a group photograph  [#permalink]

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02 Aug 2015, 05:56
1
Gmatkor1987 wrote:
: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.
Manager
Joined: 29 Sep 2017
Posts: 113
Location: United States
GMAT 1: 720 Q49 V39
GPA: 3.3
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Re: A group of 630 children is arranged in rows for a group photograph  [#permalink]

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02 Jul 2018, 08:24
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.
_________________

If this helped, please give kudos!

Intern
Joined: 14 Nov 2017
Posts: 1
Re: A group of 630 children is arranged in rows for a group photograph  [#permalink]

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08 Aug 2018, 05:13
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.

Posted from my mobile device
Re: A group of 630 children is arranged in rows for a group photograph &nbs [#permalink] 08 Aug 2018, 05:13
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