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

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kiran120680
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240 students are to be arranged in n rows in the assembly hall [#permalink] New post   14 Mar 2019, 06:14
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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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D
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Re: 240 students are to be arranged in n rows in the assembly hall [#permalink] 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] New post   19 Mar 2019, 21:15
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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] New post   23 Aug 2021, 07:21
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.


From 1 , we know Row 4 has 45 students. therefore, row 1 will have 15, row 2 = 25, row 3 =35 (since its given 10 students are added in subsequent rows). therefore 5th will have 55 and 6th 65 students. When we add all 6 , it sums up to 240. Sufficient

From 2, assuming row 1 has 15 students and there are 6 rows , so row 6 has 65 students. Now we know each subsequent row has 10 students added , therefore by the end of 6th row there will be 240 students. Sufficient.

Answer : D
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Re: 240 students are to be arranged in n rows in the assembly hall [#permalink] New post   30 Aug 2021, 04:48
Answer : Option D

1. Arthematic Series formula :Sn = (n/2) [2a1 + (n-1)d] -
n2(2a+(n−1)d)=240n2(2a+(n−1)d)=240 Sufficient

2. Arthematic Sequence formula : an = a1 + (n-1)d
= a+(n-1)d : n2(2a+(n−1)d)=240 - Sufficient

Each statement is sufficient to predict the answer
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Re: 240 students are to be arranged in n rows in the assembly hall [#permalink] New post   20 Apr 2023, 04:56
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Re: 240 students are to be arranged in n rows in the assembly hall [#permalink]
20 Apr 2023, 04:56
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