Question

For what value of n will $\frac{4}{16-5n}$achieve maximum value if $nϵN.$

• A. 3
• B. 4
• C. 6
• D. 7

Answer 1

The correct option is A

3

$\frac{4}{16-5n}$ gets maximum value if 16-5n is least

As n ∈ N, for n = 1 16 - 5n = 11

n = 2 16 - 5n = 6

n = 3 16 - 5n = 1

n = 4 16 - 5n = -4

. .

. .

. .

. .

The sequence is $\frac{4}{11}$, $\frac{4}{6}$, $\frac{4}{1}$, $\frac{4}{-4}$, -----------

Observe that after n = 3, all the terms are negative and maximum value among positive terms occurs

for n = 3.

So, given expression $\frac{4}{16-5n}$ achieves maximum value for n = 3.