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.
iii. If the test done in (ii) gives a negative result, then declare all 5 individuals to be covid negative.
iv. If the test done in (ii) gives a positive result, then all 5 individuals to be covid positive.
If the test done in (iii) gives a negative result, how many more ______ testing kits will be required to identify the 100 covid-positive individuals irrespective of how they are grouped?
A. 700
B. 600
C. 800
D. 1000
GATE 2023 · General Aptitude · Logical Reasoning · medium
Answer: 700 testing kits are required in total. Answer: A. 700
Count Phase 1 pooled tests: 1000 individuals / 5 per group = 200 groups. Phase 1 requires 200 pooled tests.
Determine groups testing positive (worst case): 100 infected individuals spread across 100 different groups means all 100 groups test positive in Phase 1.
Count Phase 2 individual tests: 100 positive groups x 5 individuals per group = 500 individual tests in Phase 2.
Calculate total tests required: Total = 200 (Phase 1 pooled) + 500 (Phase 2 individual) = 700 testing kits.