A committee ranks five towns—Pune, Qulloo, Rampur, Saharanpur, Tilak Nagar—from first (best) to fifth (worst) on each of three criteria: climate, location, friendliness.
- For each of the three criteria, none of the five towns receives the same ranking as any other town does.
- In climate, Tilak Nagar is ranked third, and Saharanpur fourth.
- In location, Qulloo is ranked second, Rampur third, Pune fourth.
- In friendliness, Tilak Nagar’s ranking is better than Pune’s, Qulloo is ranked fourth and Saharanpur fifth.
- Rampur receives a better ranking in climate than in friendliness.
- Qulloo’s three ranking are all different from each other.
- Which of the following is a complete and accurate list of the rankings any one of which could be the ranking on climate given to Rampur?
- first, second
- first, fifth
- second, fifth
- first, second, fifth
- Which of the following is a town that CANNOT be ranked fifth on any one of the three criteria?
- Tilak Nagar
- Which of the following could be true?
- Pune is ranked first in both climate and friendliness.
- Qulloo is ranked second in both climate and location.
- Rampur is ranked first in climate and third in both location and friendliness.
- Saharanpur is ranked fifth in friendliness and fourth in both climate and location.
- Tilak Nagar is ranked third in both climate and friendliness.
- If Qulloo is ranked first in climate, then it must be true that
- Pune is ranked second in climate
- Pune is ranked third in friendliness
- Rampur is ranked second in friendliness
- Rampur is ranked third in friendliness
- Tilak Nagar is ranked fifth in location
- If Pune is ranked second in climate, then which one of the following can be true?
- Pune is ranked second in friendliness.
- Qulloo is ranked first in climate.
- Rampur is ranked first in friendliness.
- Rampur is ranked fifth in climate.
- Tilak Nagar is ranked third in friendliness.
- If Tilak Nagar is ranked first in location and Rampur is ranked second in friendliness, then it is possible to deduce with certainty all three rankings for exactly how many of the towns?
- Which one of the following statements CANNOT be true?
- Pune is ranked first in climate.
- Qulloo is ranked fifth in climate.
- Rampur is ranked third in friendliness.
- Saharanpur is ranked first in location.
- Tilak Nagar is ranked second in friendliness.
The Action: Something of a rarity—a triple sequencing set. But that doesn’t necessarily make it problematic. Check how much data we’re given. We’re ranking five towns—Pune, Qulloo, Rampur, Saharanpur, and Tilak Nagar (abbreviated as P, Q, R, S, T)—from 1 to 5, best to worst, in three different categories—climate, location, and friendliness. Our job will be to put the towns in order based on the rankings they receive in each of the three categories. The Key Issues are:
1) How are the towns ranked in each category?
2) How are the towns ranked in each category based on their rankings in the other categories?
3) What town is ranked higher and lower than which other towns in each category?
The Initial Setup: As with our previous ranking set—Set 1—working vertically seems to make the most sense. It’s very intuitive and easy to handle:
Remember that each town has a rank in each category.
1) The first rule is simply a loophole closer. There are no ties is what it’s saying.
2) In the climate category, enter T 3rd and S 4th. Simple.
3) Here three of the five location rankings are given to us: Q 2nd, R 3rd, P 4th.
4) As in question stems with more than one piece of information, start with the concrete and then go to the abstract. Under friendliness, rank Q 4th and S 5th. We’re also told that T is better than P in this category. Nearby, jot down a physical reminder that T is ranked higher than P in friendliness (see figure, below).
5) R is ranked higher in climate than friendliness. Just make a note of this rule or circle it for now. We’ll come back to it under Key Deductions.
6) Q’s rankings are already set for location and friendliness, so we can deduce quite a lot from this requirement that Q’s rankings all be different. Since Q takes 2nd in one category and 4th in another, Q’s climate ranking—the one remaining—cannot be 2nd or 4th. And the 3rd slot under climate is already taken. Therefore, Q must be ranked 1st or 5th in climate. Make a note of that.
Here’s what we’ve got so far:
Seven out of 15 slots filled. But we can do more:
Key Deductions: Back to Rule 5 which said that R is ranked higher in climate than in friendliness. Since T and S are 3rd and 4th in climate, respectively, R must be ranked either 1st or 2nd in climate. (Look at it this way: If R were 5th in climate, there would be no way for its climate ranking to be better than its friendliness ranking.) Make a note of that, too. Meanwhile, note that R will have to be ranked either 2nd or 3rd in friendliness (since the 3rd and 4th slots are taken, and a ranking of #1 for R would violate Rule 5).
And yet we can go further. Under location, note that slots 1 and 5 are available to S and T in either order. Jot that down in the sketch.
Finally, we’re rewarded if we combine Rules 4 and 5. If T’s friendliness ranking is to be higher than P’s, and if R can only be ranked 2nd or 3rd in friendliness, then there are no two ways about it: T will have to be ranked 1st in friendliness. (Nothing else is left!) It all looks like this:
The Final Visualization: An extremely helpful sketch:
Note that the most ambiguity exists under climate, where P, Q, and R are yet to be placed—yet we know the limitations.
We’ve already done the work on this one. The only climate rankings available for R are 1st and 2nd, choice (B).
R must be either 1st or 2nd in climate, 3rd in location, and either 2nd or 3rd in friendliness. So R can’t be ranked 5th in any of the three criteria, answer choice (C). All of the others are open to at least one 5th place ranking in at least one category.
Here we simply need to test each choice.
(A) T must be ranked 1st in friendliness, so P can’t be 1st there.
(B) violates Rule 6—Q can’t have identical rankings in any two categories.
(C) R can be ranked 1st in climate with P 2nd and Q 5th, and we know that R is for sure ranked 3rd in location (Rule 3). Meanwhile, R can be ranked 3rd in friendliness with T 1st and P 2nd. (C) is possible and the correct answer. On Test Day, you’d stop and go on to the next question, but for the record:
(D) S can’t be ranked 4th in location, because P was assigned that spot by Rule 3.
(E) We deduced above that T must be ranked 1st in friendliness, not 3rd.
We’ve seen that R must be ranked either 1st or 2nd in climate, so if as the stem demands, Q is ranked 1st in climate, then R is 2nd. But scanning the choices, we see that’s not a choice, so keep going. Since R is 2nd in climate, Rule 5 demands that R be ranked 3rd in friendliness, and that’s choice (D). The long road would be to eliminate the wrong choices:
(A) With Q 1st, R, not P, must be ranked 2nd in climate.
(B) P can’t be ranked 3rd in friendliness, since we deduced that R is.
(C) If R is ranked 3rd in friendliness, then it’s not ranked 2nd there.
(E) T could be ranked 5th in location, but it needn’t be. T could be ranked 1st with S 5th.
The stem info (that P is 2nd in climate) completes the climate rankings: R must take 1st and Q is left in 5th, all of which eliminates choices (B) and (D) as statements that can be true. With R 1st in climate, R can be ranked either 2nd or 3rd in friendliness (Rule 5), which means that P can either be ranked 2nd or 3rd in friendliness as well. Choice (A) is possible, and thus the correct answer. T is still ranked 1st in friendliness, so (C) and (E) are out.
Here’s a question where—because you’re given two concrete pieces of information—you might want to create a unique sketch, with T 1st in location (leaving S 5th in that category), and R 2nd in friendliness (leaving P 3rd in that category). A new sketch quickly reveals that both of those categories are complete.
What’s up with climate? Since R is 2nd in friendliness, R must be ranked 1st in climate lest we violate Rule 5. Q, we had deduced, is always either 1st or 5th in climate, so now Q is 5th. That leaves P ranked 2nd. Every town’s ranking is determined for each of the three criteria—choice (E).
Several times so far, we’ve used the deduction we made upfront that T must be ranked 1st in friendliness. It’s useful again now: (E), which attempts to place T 2nd, can’t be true, and is the answer.
All four of the other choices are things we’ve seen throughout the set; all of them could be true.Online CAT LRDI Course @ INR 2499 only
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