GATE EC 2023 Set 1 — Question 9
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General Aptitude → Analytical Aptitude → Numerical Relations & Reasoning
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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.
(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.
Correct answer
(A) 700
Solution
1.Total individuals = 1000. Group size = 5. Total groups = .
2.Initial tests: Each group is tested once using a mixed sample. Total initial tests = 200.
3.Additional tests: If a group test is positive, all 5 individuals in that group are tested separately. To find the maximum number of tests required ("no more than"), we consider the worst-case scenario where the 100 positive individuals are distributed such that they trigger the maximum number of additional tests.
4.In the worst case, each of the 100 positive individuals belongs to a different group. This means 100 groups will test positive in the initial phase.
5.For each of these 100 positive groups, 5 additional tests are performed. Total additional tests = .
6.Total tests = Initial tests + Additional tests = .
Thus, no more than 700 testing kits will be required.Continue learning with Success Tracker
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