An algebra problem by Paola Ramírez

Algebra Level 3

A positive integer n n meets the following conditions:

  • n n is greater than 1.
  • n n divided by 3 plus 15 is greater than n n divided by 2 plus 1.

How many numbers could be n n ?


The answer is 82.

Paola Ramírez by Paola Ramírez , 24, Mexico

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1 solution

It is given that n > 1 n > 1 and:

n 3 + 15 > n 2 + 1 2 n + 90 > 3 n + 6 n < 84 \begin{aligned} \frac n3 + 15 & > \frac n2 + 1 \\ 2n + 90 & > 3n + 6 \\ n & < 84 \end{aligned}

⟹ n = 2 , 3 , 4 , . . . 83 \implies n = 2,3,4,...83 , therefore, there are: 83 − 1 = 82 n 83-1 = \boxed{82} \ n .

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Same way did ☺

Dipak Prajapati - 5 years ago

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