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

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

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New post 14 Mar 2019, 06:14
3
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (01:47) correct 36% (02:26) wrong based on 53 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.
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Re: 240 students are to be arranged in n rows in the assembly hall  [#permalink]

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New post 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
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Re: 240 students are to be arranged in n rows in the assembly hall  [#permalink]

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New post 19 Mar 2019, 21:15
1
Answer : D
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
Thus answer D
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Re: 240 students are to be arranged in n rows in the assembly hall   [#permalink] 19 Mar 2019, 21:15
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240 students are to be arranged in n rows in the assembly hall

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