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

Each of the five itineraries, A through E, has a combined score built from two pieces stacked in a bar: the bottom piece from the probability of not reaching on time, weighted at eighty percent, and the top piece from the travel time, weighted at twenty percent after scaling against the longest travel time in the group.

1. Itinerary A (train, taxi, bus, train): the weakest reliability of the five and the longest travel time, giving it both the largest bottom segment and the tallest overall bar.
2. Itinerary B (taxi, train, flight, train): a moderate failure chance with a notably short travel time thanks to the flight leg, giving it a smaller top segment than most of the others.
3. Itinerary C (all train): the lowest failure chance of the five, giving it clearly the smallest bottom segment, with a travel time that is only moderately long, together producing the shortest bar of the group.
4. Itinerary D (train, taxi, train, train): a failure chance close to itinerary C's but with a longer travel time, keeping its bar a little taller than C's.
5. Itinerary E (train, bus, flight, train): a failure chance between B and D, with a travel time shortened by its own flight leg.

Since the eighty percent weight on failure always outweighs the twenty percent weight on time, every bar's bottom segment is bigger than its top segment, and the tallest bar overall belongs to A while the shortest belongs to C.

Let's summarize:

• Bar height ranks in the order A, B, E, D, C from tallest to shortest.
• The bottom, failure related, portion always outweighs the top, time related, portion in every bar.
• Only one of the four diagrams shows this exact pattern correctly across all five bars.

So the diagram that best represents the contribution of each criterion is the fourth one listed.