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: 
(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.

• A. 700
• B. 600
• C. 800
• D. 1000

Hint:

Pooling strategy reduces test kits drastically. Worst-case analysis assumes maximum groups testing positive, which determines the upper bound.

Answer 1

The Correct Option is A

Step 1: Grouping.
There are $1000$ individuals, grouped into sets of 5.
Thus, total groups $=1000/5=200$.
Each group is tested once (200 tests).
Step 2: Worst-case scenario.
Worst case: All $100$ covid positives are in distinct groups (so that maximum groups turn positive).
Then $100$ groups test positive.
Step 3: Individual testing.
For each positive group, all 5 individuals are separately tested.
So, additional tests $=100 \times 5=500$.
Step 4: Total tests.
Initial group tests $=200$, plus individual tests $=500$.
Total $=200+500=700$.
\[ \boxed{700} \]