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# 240 students are to be arranged in n rows in the assembly hall

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Director
Joined: 18 Feb 2019
Posts: 607
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
240 students are to be arranged in n rows in the assembly hall  [#permalink]

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14 Mar 2019, 06:14
5
00:00

Difficulty:

45% (medium)

Question Stats:

64% (01:50) correct 36% (02:28) wrong based on 59 sessions

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240 students are to be arranged in n rows in the assembly hall of a school. If the first row is the closest to the stage and each subsequent row has 10 more students than the row ahead of it, what is the value of n?

I. There are 45 students in the 4th row from the stage.
II. The number of students in the nth row is 10 less than 5 times the number of students in the first row.
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5483
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: 240 students are to be arranged in n rows in the assembly hall  [#permalink]

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19 Mar 2019, 12:35
kiran120680 wrote:
240 students are to be arranged in n rows in the assembly hall of a school. If the first row is the closest to the stage and each subsequent row has 10 more students than the row ahead of it, what is the value of n?

I. There are 45 students in the 4th row from the stage.
II. The number of students in the nth row is 10 less than 5 times the number of students in the first row.

I am not sure how answer is D
IMO A is sufficinet
#2
i am not able to make the relation as its given
Director
Joined: 28 Jul 2016
Posts: 679
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)
Re: 240 students are to be arranged in n rows in the assembly hall  [#permalink]

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19 Mar 2019, 21:15
1
Explanation:
Le the number of students in row 1 =a
I : A.P question 45 students in 4th row = a+3*10 = 45 . thus a=15
Total students = 240 hence
$$\frac{n}{2}(2a+(n-1)d)= 240$$
Solve for n . Hence sufficient

II: Students in last row(nth row) = a+(n-1)d
given a+(n-1)d +10 = 5a
solve the above equation:
4a= 10n
thus a= 5/2 n

Now as per A.P sum
$$\frac{n}{2}(2a+(n-1)d)= 240$$
substitute value of a
and simplify the equation
$$\frac{25n^2}{4}=850$$
thus n = 12
Hence II is also sufficient
Re: 240 students are to be arranged in n rows in the assembly hall   [#permalink] 19 Mar 2019, 21:15
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