Out of $1000$ individuals in a town, $100$ unidentified individuals are covid positive. Due to lack of adequate covid-testing kits, the health authorities of the town devised a strategy to identify these covid-positive individuals. The strategy is to:
- Collect saliva samples from all $1000$ individuals and randomly group them into sets of $5$.
- Mix the samples within each set and test the mixed sample for covid.
- If the test done in (ii) gives a negative result, then declare all the $5$ individuals to be covid negative.
- If the test done in (ii) gives a positive result, then all the $5$ individuals are separately tested for covid.
Given this strategy, no more than _______ testing kits will be required to identify all the $100$ covid positive individuals irrespective of how they are grouped.
- $700$
- $600$
- $800$
- $1000$