P, Q, R and S are four types of dangerous microbes recently found in a human habitat. The area of each circle with its diameter printed in brackets represents the growth of a single microbe surviving human immunity system within 24 hours of entering the body. The danger to human beings varies proportionately with the toxicity, potency and growth attributed to a microbe shown in the figure below. [Bubble chart: x-axis = Potency (0-10), y-axis = Toxicity (0-6). Circles: P(1.2) at potency~4, toxicity~5; Q(2) at potency~2, toxicity~2; R(0.5) at potency~7, toxicity~1; S(4) at potency~5, toxicity~4] A pharmaceutical company is contemplating the development of a vaccine against the most dangerous microbe. Which microbe should be the target in its first attempt? A. P B. Q C. R D. S
GATE 2011 · General Aptitude · Data Interpretation · medium
Answer: Microbe S is the most dangerous, with danger score approximately 80 (vs P=7.2, Q=4, R=0.44). The answer is D. S.
- Read chart values for each microbe: From the bubble chart: P: toxicity approx 5, potency approx 4, diameter = 1.2 | Q: toxicity approx 2, potency approx 2, diameter = 2 | R: toxicity approx 1, potency approx 7, diameter = 0.5 | S: toxicity approx 4, potency approx 5, diameter = 4
- Compute relative danger score = toxicity x potency x (d/2)^2 for each microbe: P: 5 x 4 x (0.6)^2 = 5 x 4 x 0.36 = 7.2 | Q: 2 x 2 x (1)^2 = 2 x 2 x 1 = 4 | R: 1 x 7 x (0.25)^2 = 1 x 7 x 0.0625 = 0.4375 | S: 4 x 5 x (2)^2 = 4 x 5 x 4 = 80
- Identify the most dangerous microbe: S has the highest danger score (80) by a large margin. The pharmaceutical company should target microbe S first.