GATE ECE 2023 | GA Question: 9

Question

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:

1. Collect saliva samples from all $1000$ individuals and randomly group them into sets of $5$.
2. Mix the samples within each set and test the mixed sample for covid.
3. If the test done in (ii) gives a negative result, then declare all the $5$ individuals to be covid negative.
4. 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.

• A. $700$
• B. $600$
• C. $800$
• D. $1000$

Answer 1

200 groups made =>200 samples(200 testing kit reqd)
WORST CASE, each group has atmost 1 covid+ve individual
so no of such grps =100
Now, people of these grps are tested individually, so 100*5=500 tests(so 500 testing kit reqd)
so in total, 200+500=700 testing kits are reqd.
opt a

Answer 2

Worst case: patient appears in 100 groups out of 200 (Only 100 patients are there to appear so 100 groups)

so first
200 groups will get tested 200*1=200 (multiplied by 1 because we mix all the 5 samples and test only once)

and 100 groups = 100*5 = 500 (each individual needs to be checked. so all 5)

Total = 200+500=700