A music store carries exactly ten types of CDs -- both new and used of each of jazz, opera, pop, rap, and soul. The store is having a sale on some of these types of CDs. The following conditions must apply:Used pop is on sale; new opera is not.If both types of pop are on sale, then all soul is.If both types of jazz are on sale, then no rap is.If neither type of jazz is on sale, then new pop is.If either type of rap is on sale, then no soul is.Which one of the following CANNOT be true?
Answer(s): D
For most of us, this one is well worth skipping; unless you have an extraordinary command of the play of the rules, the prospect of trying out each of the choices -- laboriously and accurately -- may be a depressing one.And following this question come three with concrete information, which are much more tempting. Trial & error is what's called for. Since the right answer CANNOT be true, then all of the other choices can or must be.You must proceed into the choices confident that four of them will be workable.
A music store carries exactly ten types of CDs -- both new and used of each of jazz, opera, pop, rap, and soul. The store is having a sale on some of these types of CDs. The following conditions must apply:Used pop is on sale; new opera is not.If both types of pop are on sale, then all soul is.If both types of jazz are on sale, then no rap is.If neither type of jazz is on sale, then new pop is.If either type of rap is on sale, then no soul is.If neither type of jazz is on sale, then each of the following must be true EXCEPT:
Answer(s): A
Crossing out J and j, as the question stem demands, means that P must be circled (Rule 4). Having circled P, Rule 2 demands that both S and s be circled; and, in turn, Rule 5's contrapositive demands that both rap CD's be crossed out. Everything's determined except the fate of our lonely floater, used opera, which stars in correct choice [Used opera is on sale.] We didn't break the flow of the logic to check [New rap is not on sale.] through [Used soul is on sale.] as we went, but indeed all four turn out to be true.
A music store carries exactly ten types of CDs -- both new and used of each of jazz, opera, pop, rap, and soul. The store is having a sale on some of these types of CDs. The following conditions must apply:Used pop is on sale; new opera is not.If both types of pop are on sale, then all soul is.If both types of jazz are on sale, then no rap is.If neither type of jazz is on sale, then new pop is.If either type of rap is on sale, then no soul is.If new soul is the only type of new CD on sale, then which one of the following CANNOT be true?
The "if" demands that we do two things: not just circle S on the sketch, but also cross out J, O, P, and R. That four letter word "only" has such power! Now: With S circled, Rule 5's contrapositive kicks in and forces us to cross out r as well (which means that C.is a true statement, though probably you wouldn't stop to notice that).Meanwhile, Rule 4's contrapositive requires that we circle at least one of the jazz CDs, and J is crossed out, so j must be circled.
A music store carries exactly ten types of CDs -- both new and used of each of jazz, opera, pop, rap, and soul. The store is having a sale on some of these types of CDs. The following conditions must apply:Used pop is on sale; new opera is not.If both types of pop are on sale, then all soul is.If both types of jazz are on sale, then no rap is.If neither type of jazz is on sale, then new pop is.If either type of rap is on sale, then no soul is.If exactly four of the five types of used CDs are the only CDs on sale, then which one of the following could be true?
Answer(s): C
The only CDs on sale are exactly four of the five used ones. So your sketch needs first to have all the new CDs(i.e. the CAPITALIZED LETTERS) crossed out; and then you have to deal with the 4/1 split. One of those 4 on- sale CDs is used pop (Rule 1). What about the others? More importantly, which is the one and only used CD not on sale?Jazz may come to mind first because its rule (Rule 4) is the only one that begins in the negative. Suppose used jazz, j, is the one and only crossed-out used CD. What happens then? Rule 4 kicks in and says that new pop is on sale. But that can't happen: In this question, none of the new CDs is on sale. So our original premise is wrong. Used jazz must be on sale, so options [Used jazz is not on sale.] and [Neither type of jazz is on sale.] are false statements; toss them out. Meanwhile, your eye might alight on E., and you can toss E. in no time. If all the rap and soul (R, r, S, s) are crossed out, then we cannot fulfill the requirement that 4 out of 5 used CDs be on sale.We're down to options [Used opera is not on sale.] and [Used rap is not on sale.]. Suppose option [Used opera is not on sale.] is the statement that "could be true"; suppose used opera is not on sale. Can the four on-sale CDs be "p, j, r, s"? No way! Putting both a rap and a soul CD on sale simultaneously is a blatant violation of Rule 5. And indeed, if "p, j, o, s" are all on sale and everything else is not, no rules are violated.
During a single week, from Monday through Friday, tours will be conducted of a company's three divisions -- Operations, Production, Sales. Exactly five tours will be conducted that week, one each day. The schedule of tours for the week must conform to the following restrictions:Each division is toured at least once.The Operations division is not toured on Monday.The Production division is not toured on Wednesday.The Sales division is toured on two consecutive days, and on no other days. If the Operations division is toured on Thursday, then the Production division is toured on Friday.Which one of the following CANNOT be true of the week's tour schedule?
If the right answer CANNOT be true, it follows that the 4 wrong answers can. This is a likely one to skip, since you will surely see some concrete examples of what can and cannot be true in the remaining questions.However, let's assume that you decided to attack this one right off.
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