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GATE 2023 CY – Question 9

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

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.

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

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Correct answer: (A) 700

Explanation

There are1000/5=200 initial pooled tests. At most 100 pools can be positive, because each positive pool needs at least one of the 100 infected individuals. Retesting five people in each adds at most 500 kits. Total worst case=**700, A**, achieved when positives occupy separate pools.