Raman receives one credit score for each of the following six courses: economics, geology, history, Italian, physics, and Russian. From highest to lowest, the possible credit scores are A, B, C, D, and E. E is the only failing credit score. Two letter credit scores are consecutive if and only if they are adjacent in the alphabet.
- Raman’s credit scores in geology and physics are consecutive.
- His credit scores in Italian and Russian are consecutive.
- He receives a higher credit score in economics than in history.
- He receives a higher credit score in geology than in physics.
- If Raman receives the same credit score in economics and Italian, and if he fails Russian, which one of the following must be true?
- Raman’s geology credit score is a B.
- Raman’s history credit score is a D.
- Raman’s history credit score is an E.
- Raman’s physics credit score is a B.
- Raman’s physics credit score is a C.
- If Raman passes all his courses and receives a higher credit score in geology than in either language, which one of the following must be true?
- He receives exactly one A.
- He receives exactly one B.
- He receives exactly two Bs.
- He receives at least one B and at least one C.
- He receives at least one C and at least one D.
- If Raman receives a higher credit score in physics than in economics and receives a higher credit score in economics than in either language, which one of the following allows all six of his credit scores to be determined?
- His credit score in history is D.
- His credit score in Italian is D.
- His credit scores in history and Italian are identical.
- His credit scores in history and Russian are identical.
- His credit score in history is higher than his credit score in Russian.
- If Raman receives a higher credit score in physics than in economics and receives a higher credit score in history than in Italian, exactly how many of his credit scores can be determined?
- Assume that Raman’s credit score in physics is higher than his credit score in Italian and consecutive with it and that his credit scores in Russian and physics differ. Which one of the following must be true?
- Raman receives both an A and a B.
- Raman receives both an A and a C.
- Raman receives both a B and a D.
- Raman receives both a B and an E.
- Raman receives both a D and an E.
- Assume that Raman receives a lower credit score in economics than in physics. He must have failed at least one course if which one of the following is also true?
- He receives a lower credit score in Italian than in economics.
- He receives a lower credit score in Italian than in physics.
- He receives a lower credit score in physics than in Italian.
- He receives a lower credit score in Russian than in economics.
- He receives a lower credit score in Russian than in history.
We are to rank six courses—economics, geology, history, Italian, physics, and Russian—according to credit scores: A (highest), B, C, D, and E (the only failing credit score). Raman receives one letter credit score for each course, a “loophole-closing” rule. The set spells out that credit scores are “consecutive” if they’re next to each other in the alphabet (although notice that this term is nothing mysterious—it’s exactly what “consecutive” means in everyday life). The Key Issues will be:
1) What course receives what credit score?
2) What courses can, must, or cannot receive the same credit score as what other courses?
3) What courses can, must, or cannot receive credit scores that are consecutive with what other courses?
The number limitations are a challenge here: Five credit scores for six courses means that there aren’t enough credit scores to go around; hence, at least one credit score will have to be awarded to at least two courses. But it’s also worth noting that there could be certain credit scores that Raman doesn’t receive for any course. In other words, you need to realize upfront that some of the 5 credit scores need not be used.
The Initial Setup:
A natural way to visualize this set is vertically: A through E, with A on top. It’s intuitive to work vertically here, isn’t it? Remember to list the courses off to the side:
1) The key here is to recognize that we don’t know which course receives the higher credit score. Symbolize this by writing G immediately above P, and P immediately above G next to it, as a reminder that it can go either way
2) As with Rule 1, we don’t know which course receives the higher credit score, so write R above I, and I above R next to it.
3) That Raman’s credit score in economics is higher than his credit score in history doesn’t mean that they’re necessarily consecutive (though they could be). Shorthand this by drawing an E, a couple of dots underneath it, and then an H.
4) Did you recognize these as the same two entities from Rule 1? Combining Rules 1 and 4, we see that G will always be exactly one credit score above P. Go back and scratch out the other possibility (P over G).
Key Deductions: The major one is the realization that G and P occupy two consecutive credit scores in that order. It’s also worth noting that we have no “floaters” in this set—every entity is mentioned in at least one rule. And you might also notice that the minimum number of credit scores that need to be used is two (for instance, Raman could receive As in physics, econ, and Russian, and Bs in geology, history, and Italian), but that it’s eminently possible that all five credit scores are used. Very slippery set, this.
The Final Visualization: Here’s what we have as we go on to the questions:
The only failing credit score is E, so that’s what Raman got in Russian. Rule 2 means that he got a D in Italian. The stem tells us that Raman receives a D in economics as well, and economics should remind you of Rule 3. Since Raman’s econ credit score is higher than his history credit score, Raman has to receive an E in history (there’s nothing lower). Choice (C) is what must be true.
(B) is false, while (A), (D), and (E) are all possible only.
Raman fails nothing, so E is out of the picture. Hence (follow this now), the lowest credit score that Raman can receive in geology is B, since the two languages have to go below it. Geology could receive an A, too. So we have an A or B in geology, and Italian and Russian occupying lower, consecutive credit score levels. Now scan your rules and remember Rule 1: physics will receive a B or a C, depending on the geology credit score. The upshot is that that block of four courses—geology, physics, and the two languages—has to cover at least three credit scores, whether it be ABC or BCD, and that makes answer choice (D) true: No matter what, Raman has to receive a minimum of one B and one C. For this question, you may have found it easier (and quicker) to try out each choice. Here’s why the other choices don’t measure up:
(A) and (C) Geology B; physics, Italian, and econ C; Russian and history D. Possible, and thus neither of these choices has to be true.
(B) Keep the scenario above but move economics up to a B. Choice (B) needn’t be true either.
(E) An A in geology, Bs in physics, Italian, and economics, and Cs for Russian and history eliminates (E).
Remember how we jotted down Rule 3 (see above)? Sketch the same kind of thing as you read along in this stem, and you get:
Then add geology above physics (Rule 1 should be second nature by now) and you will recognize that all 5 credit scores will have to be used here: Geology A; physics B; econ C; Italian and Russian D and E in either order. That language ambiguity, and the placement of history, are all that remain for a total ranking, which is what the question is looking for. To solve the problem, you can check out the impact of each choice in turn, or just recognize that since history is always below econ, setting history above one of the languages does the job. Either way, you get to choice (E): it mandates a D in history and an E in Russian (and hence a D in Italian). All six credit scores are set, and choice (E) is our answer.
(A) We still don’t know his definite credit scores for Italian and Russian.
(B) Russian is set, but his history credit score is still undetermined.
(C) and (D) are wrong for the same reason. If Raman gets the same credit score in history and a language, that credit score will be D or E (see above). But what about the other language? Too much ambiguity is left.
This stem is similar to Q. 3’s and leads (after using the related rules) to the ranking: geology, physics, economics, history, Italian. Hence all 5 credit scores are needed—from geology A to Italian E. The only course left is Russian. If Raman received an E in Italian, he must have received a D in Russian (Rule 2). The credit scores for all 6 courses are determined, answer choice (E).
Once this stem is unpacked, it leads to the ranking: geology, physics, Italian, Russian; four classes with different and consecutive credit scores. This leads to only two possibilities: ABCD and BCDE. We don’t have to worry about economics and history, because we are looking for what must be true, and as long as economics is higher than history, those courses can be thrown in nearly anywhere. Which two credit scores must Raman receive; in other words, what two credit scores are in both possibilities? B, C, and D appear in both possibilities above, and B and D are the ones that the testmakers chose in choice (C).
Working with the stem and rules leads to: geology, physics, economics, history. These four courses receive different credit scores, but so far we need not have an E credit score awarded, but the question is asking for one; recognize that anything below history would have to get that desired E. Scan the choices. Choice (E) accomplishes what we want quite nicely: E is the only credit score for Russian, if Russian falls below history.
(A) and (B) In either case, an E is not mandated. Note for instance, geology A; physics B; econ and Russian C; Italian and history D.
(C) Moving the Italian/Russian pair up certainly can’t help: If Italian and geology receive As and Russian and physics receive Bs, Raman still needn’t receive a failing credit score.
(D) This is a possibility: Geology A; physics B; Italian and econ C; Russian and history D. (D) doesn’t do it.
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