the-greatest-value-of-n-so-that-only-one-value-of-k-satisfies-8-15-lt-n-n-k-lt-7-13-is-

Question Number 77459 by jagoll last updated on 06/Jan/20

t h e g r e a t e s t v a l u e o f n s o t h a t

o n l y o n e v a l u e o f k s a t i s f i e s

\frac{8}{15} < \frac{n}{n + k} < \frac{7}{13} i s

Answered by MJS last updated on 06/Jan/20

\frac{8}{15} < \frac{n}{n + k} \Rightarrow k < \frac{7}{8} n

\frac{n}{n + k} < \frac{7}{13} \Rightarrow k > \frac{6}{7} n

\Rightarrow

\frac{6}{7} n < k < \frac{7}{8} n

to get at least m possible values for k

n ⩾ 7 \times 8 \times m + 1

\Rightarrow answer is n = 7 \times 8 \times 2 = 112

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