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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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07 Mar 2018, 02:31
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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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07 Mar 2018, 02:37
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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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24 Mar 2018, 17:29

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.

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