Question

Two brands of hand sanitizers differ in their cleaning powers. How many times does a person have to use brand B to get the same cleaning effect as brand A?

• A. 2 times
• B. 3 times
• C. 4 times
• D. 5 times

Answer 1

The correct option is B 3 times

To make things easy, we take:

$\text{Number of germs before sanitation}=1000$

Checking the cleaning done in each round of use for each hand sanitizer, we find:

$BrandA:Round1$

$\text{Percentage of germs killed}=99.9\%$
$\text{Number of germs killed}=1000\times \frac{99.9}{100}=999$

$\text{Number of germs left alive}=1000–999=1$

$BrandB:Round1$

$\text{Percentage of germs killed}=90\%$
$\text{Number of germs killed}=1000\times \frac{90}{100}=900$

$\text{Number of germs left alive}=1000–900=100$

$BrandB:Round2$

$\text{Percentage of germs killed}=90\%$
$\text{Number of germs killed}=100\times \frac{90}{100}=90$

$\text{Number of germs left alive}=100–90=10$

$BrandB:Round3$

$\text{Percentage of germs killed}=90\%$
$\text{Number of germs killed}=10\times \frac{90}{100}=9$

$\text{Number of germs left alive}=10–9=1$

Hence, using brand B sanitizer for 3 rounds gives the same result as using brand A sanitizer once.