Question

Directions for Q125-129: The following set of questions is based on a decision-making situation described below. Read the passage and answer the questions that follow.

Ram Kumar, an overworked executive in Delhi, has to decide on the travel plan for attending his friend's marriage in Ajmer, Rajasthan. He has barely managed to get leave from his boss, so he must make sure he reaches Ajmer at least on the day of the marriage. Since it had been a while since his last break, he also planned to visit a few tourist spots along the way to de-stress after a year of demanding work.

As per his plan, Ram would start from Delhi and first visit the Bharatpur bird sanctuary, staying at the forest guest house for some time. He would then travel to Jodhpur for a day or two of sightseeing, and from Jodhpur move to Jaipur to spend a few days visiting the city. After that he would travel on to Ajmer, where his friend's wedding would take place.

Leg 1, Delhi to Bharatpur (bus, taxi or train, all three taking 12 hours): the probability of reaching on time is 0.65 by bus, 0.75 by taxi and 0.9 by train.
Leg 2, Bharatpur to Jodhpur (train, bus or private taxi): the probability of reaching on time is 0.9 by train (12 hours), 0.8 by bus (16 hours) and 0.85 by taxi (14 hours).
Leg 3, Jodhpur to Jaipur (flight, train, bus or taxi): the probability of reaching on time is 0.85 by flight (2 hours), 0.9 by train (10 hours), 0.65 by bus (15 hours) and 0.7 by taxi (15 hours).
Leg 4, Jaipur to Ajmer (train, bus or taxi): the probability of reaching on time is 0.75 by train (4 hours), 0.55 by bus (5 hours) and 0.55 by taxi (5 hours).

Since both Jaipur and Jodhpur have airports, Ram could also fly directly from Delhi to either city, or use a flight partway along with a combination of land transport.

Ram's statistically minded friend Rocky feels that Ram should not use just one criterion to decide on a plan. "Decision making has to bring in all the criteria together. That is what makes a decision sound," Rocky said.

"How do I do that?" Ram asked. "Simple," said Rocky. "Give a weight to each criterion, multiply the value of each criterion by its weight, and add up the products for each option."

Rocky explained with an example: "For each option there are two criteria, the probability of not making it to the wedding and the travel time. The probability of not reaching on time is 1 minus the probability of reaching on time. Say you hate the thought of missing the wedding after all this effort, so give that criterion a weight of 80%. You also want to keep the travel time low, so give that a weight of 20%. For each option, add up (value of each criterion times its weight) and compare the totals across options. Pick the option with the lowest total."

"That simple?" Ram asked. "Well, it is, for a start," Rocky admitted.

For reference, the five itineraries under discussion (labelled A to E on the x-axis of each bar chart) are:
A: Delhi to Bharatpur by train; Bharatpur to Jodhpur by taxi; Jodhpur to Jaipur by bus; Jaipur to Ajmer by train
B: Delhi to Bharatpur by taxi; Bharatpur to Jodhpur by train; Jodhpur to Jaipur by flight; Jaipur to Ajmer by train
C: Delhi to Bharatpur by train; Bharatpur to Jodhpur by train; Jodhpur to Jaipur by train; Jaipur to Ajmer by train
D: Delhi to Bharatpur by train; Bharatpur to Jodhpur by taxi; Jodhpur to Jaipur by train; Jaipur to Ajmer by train
E: Delhi to Bharatpur by train; Bharatpur to Jodhpur by bus; Jodhpur to Jaipur by flight; Jaipur to Ajmer by train

Q129. Of the diagrams given as options, which one best represents the contribution of each of the two criteria to the overall score, for each of the five itineraries A to E listed above, where the bottom portion of each bar shows the contribution of the probability of NOT reaching the destination on time, and the top portion shows the contribution of travel time?

• A.

  

• B.

  

• C.

  

• D.

  

Hint:

Rank the five itineraries by failure probability and by scaled travel time first, then look for the diagram where bar A is tallest, bar C is shortest, and every bar's bottom segment outweighs its top segment.

Answer 1

The Correct Option is D

Step 1: Work out both criteria for all five itineraries.
Using the same method as Rocky's framework, each itinerary A through E gets a failure probability, one minus the product of its leg probabilities, and a travel time scaled against the longest option in the group. Itinerary A gives a failure chance of about 0.627 with the longest time, scaling to 1.0. Itinerary B gives about 0.570 with a scaled time of about 0.667. Itinerary C, all train, gives about 0.453 with a scaled time of about 0.844. Itinerary D gives about 0.484 with a scaled time of about 0.889. Itinerary E gives about 0.541 with a scaled time of about 0.756.

Step 2: Split each score into its two bar segments.
The bottom segment of each bar, the failure probability's contribution, is eighty percent of that itinerary's failure chance. The top segment, the travel time's contribution, is twenty percent of the scaled time. Since the eighty percent weight always dominates the twenty percent weight, the bottom segment of every bar is bigger than its top segment, and itinerary A carries both the tallest bar overall and the largest bottom segment, while itinerary C carries the shortest bar overall and the smallest bottom segment.

Step 3: Rank the total bar heights.
Adding both segments together for each itinerary gives A as the tallest bar, followed by B, then E, then D, with C standing as the shortest bar of the five, matching the order in which these itineraries rank from least reliable to most reliable overall.

Step 4: Match this pattern to the diagrams.
Checking the four diagrams against this pattern, the one where bar A is clearly the tallest with the largest bottom portion, bar C is clearly the shortest with the smallest bottom portion, and every bar's bottom segment sits visibly larger than its top segment, is the diagram that correctly represents the two criteria's contribution across all five itineraries.

Final Answer:
The fourth diagram is the one that correctly represents the contribution of each criterion across the five itineraries.