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If N is a positive integer, what is the value of N? (1) N^2 < 130

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If N is a positive integer, what is the value of N? (1) N^2 < 130  [#permalink]

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New post 07 Mar 2018, 01:31
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If N is a positive integer, what is the value of N?

(1) N^2 < 130

(2) N is the smallest integer for which 3^N > 9^5
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If N is a positive integer, what is the value of N? (1) N^2 < 130  [#permalink]

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New post 07 Mar 2018, 01:37
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N is a positive integer. This means N > 0 and N is integer.


Statement 1: \(N^2\) < 130 could mean N = 1,2,3,4,....11. Hence, insufficient

Statement 2: \(3^N\) > \(9^5\)

=> \(3^N\) > \(3^10\)

=> N being the smallest integer satisfying the above relation could only be 11.

Hence, Statement 2 is sufficient. Answer is B.
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If N is a positive integer, what is the value of N? (1) N^2 < 130  [#permalink]

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New post 24 Mar 2018, 16:29

Solution



We are given:
N is a positive integer.

We need to find the value of N.

Statement-1 “\(N^2 < 130\)”

    Perfect squares less than 130 are 1,4,9,16,25,36,49,64,81,100,121.
    And for different values of \(N^2\), the value of \(N\) is also different.

Thus, Statement 1 alone is NOT sufficient to answer the question.



Statement-2N is the smallest integer for which \(3^N > 9^5\)

    =\(3^N >9^5\)
    \(=3^N > {(3^2)}^5\)
    \(=3^N > 3^{10}\)

\(3^N\) is greater than\(3^{10}\) for\(N>10\). Thus, the smallest value of N is 11.
Statement 2 alone is sufficient to answer the question.

Answer: B
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If N is a positive integer, what is the value of N? (1) N^2 < 130 &nbs [#permalink] 24 Mar 2018, 16:29
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