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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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Math Expert
Joined: 02 Sep 2009
Posts: 50619
If n is an integer and 101n² is less than or equal to 8100, what is th  [#permalink]

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05 Jan 2015, 05:45
1
3
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:23) correct 21% (01:46) wrong based on 162 sessions

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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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Posts: 175
Location: United States
GMAT 1: 700 Q49 V35
Re: If n is an integer and 101n² is less than or equal to 8100, what is th  [#permalink]

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05 Jan 2015, 16:04
2
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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05 Jan 2015, 23:55
2

$$101n^2 < = 8100$$

$$100n^2 + n^2 < = 8100$$

For n = 9, LHS would be greater than RHS

8100+81 > 8100

So, n = 8

6400 + 64 < 8100
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Joined: 26 Mar 2013
Posts: 1880
If n is an integer and 101n² is less than or equal to 8100, what is th  [#permalink]

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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

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

n =8

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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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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 &nbs [#permalink] 23 Mar 2018, 09:57
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