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If n is an integer and 101n² is less than or equal to 8100, what is th

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If n is an integer and 101n² is less than or equal to 8100, what is th  [#permalink]

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New post 05 Jan 2015, 05:45
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Tough and Tricky questions: Number Properties.



If n is an integer and 101n^2 is less than or equal to 8100, what is the greatest possible value of n?

A. 7
B. 8
C. 9
D. 10
E. 11

Kudos for a correct solution.

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Re: If n is an integer and 101n² is less than or equal to 8100, what is th  [#permalink]

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New post 05 Jan 2015, 16:04
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Bunuel wrote:

Tough and Tricky questions: Number Properties.



If n is an integer and 101n^2 is less than or equal to 8100, what is the greatest possible value of n?

A. 7
B. 8
C. 9
D. 10
E. 11

Kudos for a correct solution.



101 * n^2 <=8100
n^2 <=8100/101 which will be less than 81 since 8100/100 = 81 which is the square of 9

Next closest value of n where n^2<=81 is 8

Ans B
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Re: If n is an integer and 101n² is less than or equal to 8100, what is th  [#permalink]

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New post 05 Jan 2015, 23:55
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Answer = B. 8

\(101n^2 < = 8100\)

\(100n^2 + n^2 < = 8100\)

For n = 9, LHS would be greater than RHS

8100+81 > 8100

So, n = 8

6400 + 64 < 8100
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If n is an integer and 101n² is less than or equal to 8100, what is th  [#permalink]

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New post 20 Mar 2018, 14:39
Bunuel wrote:

Tough and Tricky questions: Number Properties.



If n is an integer and 101n^2 is less than or equal to 8100, what is the greatest possible value of n?

A. 7
B. 8
C. 9
D. 10
E. 11

Kudos for a correct solution.


Dear Bunuel

How come the question is tough and tricky and in same time sub-600?

My approach:

101n^2 < 8100

101n^2 < 81* 100

101n^2 < 9^2 * 10^2

Scanning answer choice

if n =9 , then left side is will be greater as 101 > 100. then we left with only choice below 9

n =8

Answer: B
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Re: If n is an integer and 101n² is less than or equal to 8100, what is th  [#permalink]

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New post 23 Mar 2018, 09:57
Bunuel wrote:

Tough and Tricky questions: Number Properties.



If n is an integer and 101n^2 is less than or equal to 8100, what is the greatest possible value of n?

A. 7
B. 8
C. 9
D. 10
E. 11

Kudos for a correct solution.


I miss read the question first and considered 101n^2 as 1011^2 or 1015^2 etc and thought that "n" is the last digit of a 4 digit integer. But after going through the answer choices got it.

101 * n^2 <= 8100

If we take n = 9, it will become 8101>8100

Therefore C,D, E are out.

It's (B)
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Re: If n is an integer and 101n² is less than or equal to 8100, what is th   [#permalink] 23 Mar 2018, 09:57
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