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GATE 2023 EC – Question 9

General Aptitude · Quantitative Aptitude: Probability and Combinatorics · 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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Show answer and explanation

Correct answer: (A) 700

Explanation

There are $1000/5=200$ groups, so 200 group tests. In the worst case the 100 positives fall in 100 different groups; each of those groups needs 5 individual tests. Total $=200+100\times5=700$.