Suppose a, b, c are positive integers such that 2^a+4^b+8^c=328 . Then, frac{a+2 b+3 c}{a b c} is eq

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4-2.Quadratic Equations and Inequations

hard

Suppose $a, b, c$ are positive integers such that $2^a+4^b+8^c=328$. Then, $\frac{a+2 b+3 c}{a b c}$ is equal to

A

$\frac{1}{2}$

B

$\frac{5}{8}$

C

$\frac{17}{24}$

D

$\frac{5}{6}$

(KVPY-2015)

Solution

(c)

We have,

$2^a+4^b+8^c=328$

$\Rightarrow 2^a\left(1+2^{2 b-c}+2^{3 c-a}\right)=2^3 \times 41$

$\therefore \quad a=3$

$\Rightarrow \quad 2^{2 b-3}+2^{3 c-3}=40$

$\Rightarrow \quad 2^{2 b-3}+2^{3 c-3}=2^3 \cdot 5$

$\Rightarrow \quad 3 c-3=3 \Rightarrow c=2, b=4$

$\frac{a+2 b+3 c-3+8+6}{a b c}=\frac{17}{24}$

Standard 11

Mathematics

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