Question

If the sum of the repeating decimals $\mathrm{0.353535...}+\mathrm{0.252525...}$ is written as a fraction in lowest terms, the product of the numerator and denominator is

• A. $3465$
• B. $2475$
• C. $680$
• D. $670$
• E. $660$

Answer 1

The correct option is E $660$

0.353535...+0.252525....=0.6060.....

$Letx=\mathrm{0.6060.....}100x=\mathrm{60.6060....}100x-x=6099x=60x=\frac{60}{99}=\frac{20}{33}$

Numerator $=20$ and Denominator $=33$

Their product $=33\times 20=660$

So correct answer will be option E