Question

In a battle $70$% of the combatants lost one eye, $80$% an ear, $75$% an arm, $85$% a leg, $x$% lost all of four body parts. The minimum value of $x$ is

• A. $10$
• B. $12$
• C. $15$
• D. $11$

Answer 1

The correct option is A $10$

People who didn't lose an eye$=100-70$$=30$%
People who didn't lose a ear$=20$%
People who didn't lose an arm$=25$%
People who didn't lose a leg$=15$%
Let us assume that sets described above are distinct subsets without intersection between them

Thus we arrive at the condition of maximum possible number of people who did not lose all four body parts together.

Consecutively, this condition gives the minimum number of people who lost all four body parts.
Minimum number of people who lost all of four body parts$=100-(30+20+25+15)$$=10$