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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:
(i) Collect saliva samples from all 1000 individuals and randomly group them into sets of 5.
(ii) Mix the samples within each set and test the mixed sample for covid.
(iii) If the test done in (ii) gives a negative result, then declare all the 5 individuals to be covid negative.
(iv) 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
To understand why the answer is 700, we need to break down the testing process and calculate the maximum number of tests required.
Step (i): Collect saliva samples from all 1000 individuals and randomly group them into sets of 5.
To group 1000 individuals into sets of 5, we need 
sets.
Step (ii): Mix the samples within each set and test the mixed sample for covid.
We will test 200 mixed samples, each containing 5 individual samples. If all 5 individuals in a set are negative, we can declare all 5 individuals as negative without further testing. If any of the 5 individuals in a set are positive, we move to step (iv).
Step (iii): If the test done in (ii) gives a negative result, then declare all 5 individuals to be covid negative. If all 5 individuals in a set are negative, we can declare all 5 individuals as negative without further testing. Therefore, we do not need any additional tests for that set.
Step (iv): If the test done in (ii) gives a positive result, all 5 individuals are separately tested for covid.
If any of the 5 individuals in a set are positive, we must test each separately.
Therefore, we need 5 additional tests for that set. So, the maximum number of tests required to identify all 100 covid positive individuals is: 200 (mixed sample tests) 
(individual tests for positive sets) 
tests
Therefore, no more than 700 testing kits will be required to identify all the 100 covid positive individuals irrespective of how they are grouped."