From among ten stones, a jeweler will select six, one for each of six rings. Of the stones, three -- F, G, and H -- are rubies; three -- J, K, and M -- are sapphires; and four -- W, X, Y, and Z -- are topazes. The selection of stones must meet the following restrictions:At least two of the topazes are selected.If exactly two of the sapphires are selected, exactly one of the rubies is selected.If W is selected, neither H nor Z is selected.If M is selected, W is also selected.Which one of the following could be the selection of stones?
Answer(s): D
Even if you were blown away by this game's rules, this is a point worth getting, and worth getting quickly. Rule 1's requirement of 2 topazes minimum is violated by option [F, G, J, K, M, W]. Rule 2's 2 sapphires: 1 ruby ratio is violated by option [F, G, J, K, W, X]., which gives us 2 : 2 : 2. Rule 3 is violated by option [G, H, K, W, X, Z], which gives us W, H, and Z all at once. And Rule 4 is violated by option [F, G, H, M, X, Y], which gives us M without W. Option [G, H, J, X, Y, Z] must be correct sight unseen, and perhaps finding it, and then analyzing it, can provide us with some needed insight into the game and the heart to keep going with it.
From among ten stones, a jeweler will select six, one for each of six rings. Of the stones, three -- F, G, and H -- are rubies; three -- J, K, and M -- are sapphires; and four -- W, X, Y, and Z -- are topazes. The selection of stones must meet the following restrictions:At least two of the topazes are selected.If exactly two of the sapphires are selected, exactly one of the rubies is selected.If W is selected, neither H nor Z is selected.If M is selected, W is also selected.Which one of the following must be true?
Answer(s): E
Those who worked out the number options we laid out above had no trouble with this one. No matter how you slice it, at least one stone type -- and possibly two -- are represented by exactly 3 stones. And even if you didn't work out every possibility, simply seeing that 2 : 2 : 2 was an impossible ratio(because of Rule 2) might have led you to suspect that option [Of at least one ... three stones are selected.] was a true statement.Options [G is selected.], [J is selected.] and [X is selected.] are far from necessarily true--there are lots of possibilities in which G, J, and X respectively are not present. And the possibility of choosing, say, 3 sapphires + 3 topazes means that option [Of at least one ... one stone are selected] need not be true either.
From among ten stones, a jeweler will select six, one for each of six rings. Of the stones, three -- F, G, and H -- are rubies; three -- J, K, and M -- are sapphires; and four -- W, X, Y, and Z -- are topazes. The selection of stones must meet the following restrictions:At least two of the topazes are selected.If exactly two of the sapphires are selected, exactly one of the rubies is selected.If W is selected, neither H nor Z is selected.If M is selected, W is also selected.If Z is selected, which one of the following could be true?
Write out your roster, circle Z on it, and realize that that's a trigger for rejecting W (Rule 3's contrapositive) and thus for rejecting M (Rule 4's contrapositive). That's all we need. With sapphire M gone, clearly options [All three of the sapphires are selected.], [Both J and M are selected.], and [Both K and M are selected.] are impossible. And if option [None of the rubies is selected.] were true -- no rubies -- our remaining 2 sapphires and maximum of 3 topazes would leave us short of our desired total of 6. So [None of the sapphires is selected.] is possible by default. Indeed, all three rubies plus topazes X, Y, Z would constitute an acceptable set of 6.
From among ten stones, a jeweler will select six, one for each of six rings. Of the stones, three -- F, G, and H -- are rubies; three -- J, K, and M -- are sapphires; and four -- W, X, Y, and Z -- are topazes. The selection of stones must meet the following restrictions:At least two of the topazes are selected.If exactly two of the sapphires are selected, exactly one of the rubies is selected.If W is selected, neither H nor Z is selected.If M is selected, W is also selected.If exactly two rubies are selected, which one of the following must be true?
This is sheer arithmetic. If we choose exactly 2 rubies, we cannot choose 2 topazes -- remember, 2: 2 : 2 is forbidden -- so we need exactly 3 topazes (and have proved thatE.is impossible, incidentally).And 2 rubies + 3 topazes only = 5 stones, so there will be exactly 1 sapphire chosen, choice [Exactly one sapphire...] What that sapphire is, is unclear; it could be J, as option [J is selected.] suggests, but need not. And options [H is selected.]. and [Z is selected.] are much more certain as to the identity of particular stones than we can possibly be, under this question's circumstances.
From among ten stones, a jeweler will select six, one for each of six rings. Of the stones, three--F, G, and H-- are rubies; three--J, K, and M--are sapphires; and four--W, X, Y, and Z--are topazes. The selection of stones must meet the following restrictions:At least two of the topazes are selected.If exactly two of the sapphires are selected, exactly one of the rubies is selected.If W is selected, neither H nor Z is selected.If M is selected, W is also selected.Which one of the following must be true?
We have deduced that at least two topazes must be chosen at all times. And which two? Hard to say; but since we can never choose W and Z together (Rule 3), we will always need to choose at least one of the remaining topazes. That's all that option [The selection of stones includes either X or Y, or both.] is saying. Our work in Step 4, above, demonstrates that neither option [The selection of stones includes at least one ruby.]. nor option [The selection of stones includes at most two rubies.], need be true. Contrary to these both options, we could choose no rubies at all (if we used 3 sapphires and 3 topazes). The remaining choices may require a little trial and error, but the selection of, for instance, "G,J,K,M,W,Y" proves that neither option [The selection of stones includes either F or Z, or both.] nor option [The selection of stones includes either X or Z, or both.] need be true.
Post your Comments and Discuss Test Prep LSAT Test exam prep with other Community members:
Our website is free, but we have to fight against AI bots and content theft. We're sorry for the inconvenience caused by these security measures. You can access the rest of the LSAT Test content, but please register or login to continue.