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:

For worst-case counts in pooled testing, spread positives across groups to maximize the number of positive pools (each triggers extra individual tests).

Answer 1

The Correct Option is A

Step 1: The 1000 people are split into \(1000/5=200\) groups. Testing each pooled sample needs \(200\) kits.
Step 2: Any group that tests positive requires 5 additional tests (one per individual). To \emph{maximize} the total number of tests regardless of grouping, distribute the 100 positives so that the number of positive groups is as large as possible—i.e., one positive in each group. This yields \(100\) positive groups.
Step 3: Additional individual tests \(= 100 \times 5 = 500\). Hence, maximum total kits required \[ 200 + 500 = 700. \] Therefore, no more than \(\boxed{700}\) kits are needed.