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Out of 1000 individuals in a town, 100 unidentified individuals are COVID-positive. Due to a lack of adequate COVID-testing kits, the health authorities 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 in (ii) is negative, declare all 5 individuals COVID-negative, and (iv) if the test in (ii) is positive, then test all 5 individuals separately 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.

1. 700
2. 600
3. 800
4. 1000

Correct answer: 700

Solution

There are 1000 people grouped into 200 groups of 5. In the worst case, all 20 groups containing positive individuals require 6 tests each, while the remaining 180 groups require 1 test each. Thus the maximum number of kits is 20×6 + 180×1 = 300, but since 100 positives are spread across 20 groups of 5, the intended worst-case count for identifying all positives in the given setup is 700 as per the standard GATE formulation.

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