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LRDI Practice Set 32

The organisms W, X, Y, and Z respond to the antibiotics ferromycin, ganocyclene, and heptocillin in a manner consistent with the following:

  1. Each of the organisms responds to at least one of the antibiotics.
  2. No organism responds to all three antibiotics.
  3. At least two but not all four or the organisms respond to ferromycin.
  4. If W responds to any antibiotic, then X responds to that antibiotic.
  5. If an organism responds to ferromycin, then it responds to ganocyclene.
  6. Y responds to ferromycin.
  1. Each of the following can be true EXCEPT:
  1. W responds to heptocillin.
  2. X responds to ganocyclene.
  3. X responds to heptocillin.
  4. Y responds to heptocillin.
  5. Z responds to ganocyclene.
  1. Which one of the following could be true?
  1. W, X, and Z all respond to ferromycin.
  2. W, X, and Z all respond to ganocyclene.
  3. W and exactly one other organism respond to ganocyclene.
  4. W responds to more of the antibiotics than X does.
  5. More of the organisms respond to ferromycin than to ganocyclene.
  1. Which one of the following could be true?
  1. Exactly one of the organisms responds to ferromycin.
  2. All four of the organisms respond to heptocillin.
  3. At least one of the organisms responds both to ferromycin and to heptocillin.
  4. At least one of the organisms responds neither to ganocyclene nor to heptocillin.
  5. At least one of the organisms responds to ganocyclene but does not respond to ferromycin.
  1. If X does not respond to ferromycin, then which one of the following must be true?
  1. W responds to ganocyclene.
  2. X responds to ganocyclene.
  3. X responds to heptocillin.
  4. Z responds to ferromycin.
  5. Z responds to heptocillin.
  1. If any of the organisms responds to two of the antibiotics, then which one of the following is true about such an organism?
  1. It must respond to ferromycin.
  2. It must respond to ganocyclene.
  3. It must respond to heptocillin.
  4. It cannot respond to ferromycin.
  5. It cannot respond to ganocyclene.
  1. If none of the organisms responds to heptocillin, then which one of the following must be true?
  1. W responds to ferromycin.
  2. X responds to ferromycin.
  3. Z responds to ferromycin.
  4. Exactly three of the organisms respond to ganocyclene.
  5. Exactly four of the organisms respond to ganocyclene.
  1. If three of the organisms respond to exactly the same set of antibiotics as each other, and if Z does not respond to ferromycin, then each of the following must be true EXCEPT:
  1. W responds to ferromycin.
  2. X responds to ganocyclene.
  3. Z responds to ganocyclene.
  4. W responds to exactly the same set of antibiotics as Y.
  5. X responds to exactly the same set of antibiotics as Y.

The Action: The key verb phrase in the opening paragraph here is “respond to”; each organism responds to the three antibiotics in some manner, so we’re dealing with a matching set. Does W get F, or G, or H—or some combination thereof? No doubt that’s what the rules are going to help us to decide, and the same goes of course for the other three organisms. No tricks here—the Key Issue is very straightforward:

1) Which antibiotics does each organism respond to? (All other issues are simply subsets of that. For example, knowing exactly which antibiotics an organism responds to implies which ones it doesn’t, which ones it has in common with the other organisms, which ones it doesn’t have in common, etc. )

The Initial Setup: The simplest way to match up the entities in two groups is to list the definite entities horizontally in columns across your page (here, the four organisms) and place the choices for those entities off to the side, to be filled in as needed. A simple list or grid like so will suffice, and certainly won’t take long to draw or recopy when necessary:

The Rules:

6) Keeping with the Kaplan strategy of beginning with the most concrete information, a quick scan of the rules reveals that Y responds to F, so draw it right in. Having incorporated this, you may have been drawn to the other rules about F:

5) Anywhere we place an F, we’ll also have to place a G, so we may as well place a G under organism Y since we just placed an F there from Rule 6. Off to the side, you’ll want to indicate “If F, then G.” The contrapositive should be readily apparent, and you may have jotted it down or simply taken notice of it here, never to lose sight of it throughout the set: “If no G, then no F.”

3) Rule 3 is about F too, but this one we’ll have to shorthand off to the side. Did you simply make the rule shorter, by writing something to the effect of “2 but not 4 F’s”? If you did, you need to remind yourself to ferret out the implications of the rules: that is, to turn negatives into positives and state the meaning of the rules as clearly as possible. “2 or 3 F’s” is much better. That’s what the rule really means in the context of this set.

There’s no indication that any of the remaining rules should be given priority at this point, so let’s jump back to the beginning. As it turns out, Rules 1 and 2 can be combined on the fly:

1) and 2) Each organism responds to at least one antibiotic, but no organism responds to all three. We can and should perform the same simple arithmetic as above to deduce that each organism will respond to either 1 or 2 antibiotics. “Each gets 1 or 2” is one of many ways to remind us of this.

4) Lastly, Rule 4: Whatever antibiotics W gets, X gets too. Make sure you take a few seconds to work out the implications of this. Whatever goes in the W column must appear also in the X column. But does it work the other way around? No. If W responds to two antibiotics, then X must have the same two. But if W gets only one—for example, G—then X must get G but can also get one more antibiotic, F or H.

Key Deductions: We’ve already begun our deductive work by piecing together the number information above. We saw that each organism will respond to either 1 or 2 antibiotics, and also that exactly 2 or 3 organisms will respond to F. We also went right ahead and put FG into our Y column, and now, factoring in Rule 2, we can safely conclude that organism Y, responding to F and G, is done and fully accounted for. What else? We can combine Rules 2 and 5 to deduce that no organism responds to both F and H. F requires G, and adding H as well would violate Rule 2. And here’s one more thing you may have noticed, (but if you didn’t, is not a huge drawback): What happens if W responds to F? Then so does X (Rule 4). And we know that Y responds to F (Rule 6), so Z cannot because then all four would be responding to F, in violation of Rule 3. Stated simply: If W responds to F, then Z doesn’t respond to F. If you saw this, great, if not, no biggie; you probably had the opportunity to work through this at some point during the questions. We won’t even bother including it in our master sketch. And speaking of which:

The Final Visualization: Here is all the information we have at our disposal to dispose of the seven questions hanging in the balance:

The Questions:

1. (D)

May as well begin by checking our key deductions, looking for the odd man out here. And our previous work with Y takes us where we need to go. We saw that since Y gets F (Rule 6), and therefore gets G (Rule 5), it cannot get H also because that would violate Rule 2. (D) is the impossibility here; all the rest work just fine.

2. (B)

We’ve most likely deduced enough up front to knock these choices out quickly, so take ‘em one at a time. We’re looking for something that’s possible:

(A) Since Y already has F, linking W, X, and Z with F would result in four F’s—a direct violation of Rule 3.

(B) No problem here: Nothing prohibits four G’s across the board. We need to get one more F in there to take care of Rule 3, but other than that, smooth sailing.

(C) If W responds to G, then so does X (Rule 4), and we already know that Y responds to G. So (C) is impossible: If W responds to G, then at least two more that we know of must respond to G as well.

(D) directly contradicts Rule 4: Whatever W gets, X gets, so there’s no way W can respond to more antibiotics than X.

(E) Same thought as (D), only stemming from Rule 5: Whatever gets F, gets G; so there can’t be more organisms with F than G.

3. (E)

Same drill as 19. We’re simply looking for what could be true, so our job is to test the choices until something possible appears. Unfortunately, we have to wait until the bottom of the list in choice (E): Rule 5 states that wherever there’s F, there’s G. This doesn’t work the other way around. While Y has both F and G, it’s perfectly possible for at least one of the other organisms to have G without F. In fact, consulting the partial arrangement worked out for correct choice (B) in Q. 2 confirms this: it’s possible that G is linked to all four while only two organisms respond to F. (E) could be true. As for the others:

(A) directly contradicts Rule 3—we need 2 or 3 F’s here.

(B) As we saw earlier, Y cannot respond to H because it already responds to F and G and no organism is allowed to respond to all three.

(C) Here’s another deduction we worked out above: Since whatever responds to F must also respond to G (Rule 5), no organism that responds to F may respond to H because that would lead to a prohibited threesome.

(D) is the trickiest of the bunch because it’s stated in the negative. Is it possible for any organisms to be without G and H? Well, Rule 1 reminds us that each organism must match up with at least one antibiotic, and if G and H are out, then F is the only one left. But a solo F is against the rules—Rule 5 in particular, which states that wherever F appears, G appears.

4. (D)

Our first hypothetical of the set appears here in 21: No F for X. The contrapositive of Rule 4 tells us that whatever X doesn’t get, W doesn’t get, so no F for X also means no F for W. We still need another F to satisfy Rule 3, so Z must respond to F, as well as to G thanks to Rule 5. Do we have our answer yet? Yup—(D) must be true, and gets the point for 21. (A), (B), and (C) can, but need not, be true, while (E) is flat-out impossible: If Z responds to H, then Z’s got the trifecta, all three antibiotics—and we know of course that that’s not allowed.

5. (B)

There are many ways to go about this one. One quick way is to simply plot out the possibilities and check them against the choices. The only pairs of antibiotics an organism can respond to are FG and GH. The only other pair that can be formed from the three antibiotics is FH, and we’ve seen a number of times why this pair doesn’t work (where F goes, G goes, therefore no H—all that Rule 2 and Rule 5 business). So lets call FG option 1, and GH option 2. Checking the choices:

(A) Not in option 2 it doesn’t.

(B) Yup. Either way, G’s called into service. That’s our answer, and naturally we’d move on immediately. But for the record:

(C) No H in option 1.

(D) Sure it can—right there in option 1.

(E) Au-contraire! Such an organism must respond to G.

6. (E)

H is off the market for the sake of this question, which means that this scenario is going to be dominated by F’s and G’s. But wait a minute: Wherever F is, G is. And wherever F isn’t, G’s going to have to be there, too, since H is temporarily out of the picture. Bottom line: G’s ubiquitous; omnipresent so to speak. Or, another way to put it is choice (E). (D) is obviously wrong if (E) is right; there must be four G’s, not three. (A) and (B) bite the dust if we give an FG pair to Z and solo G’s to W and X. However, we can also place FG pairs under W and X, with a solo G in Z’s slot, contrary to the assertion in (C).

7. (C)

The second if-clause is more concrete than the first, so it’s wise to begin there. If Z doesn’t get F, then Z gets G or H or both. So far so good. But that plays into the more abstract hypothetical which tells us that three of the four organisms respond to the same set of antibiotics. Since Y responds F, and Z doesn’t, and we still need at least two F’s listed, Z must be the odd organism out: W, X, and Y must therefore be the three identical ones. Each of those responds to both F and G, while Z responds to G or H or both, as noted above. That tells us almost everything we could possibly know about the situation, and all the choices match this scenario except for (C): it’s possible that Z responds to only H.

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