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 J and M are the only sapphires selected, which one of the following could be true?
Answer(s): B
Interestingly--if frustratingly--this last question proves to be one of the most concrete, and hence one of the easiest. We hope that you didn't get bogged down on some of the earlier ones and miss out onthis one. In your roster, select J and M, and cross out K, in line with the question stem's if. Rule 4 requires that you select W, and Rule 3 requires that you cross out H and Z. At the same time, Rule 2 (we use it at last!) kicks in--there will be exactly 1 ruby chosen, and hence 3 sapphires. And with Z gone, those 3sapphires are W, X, and Y. So: J, M, W, X, and Y are definitely chosen, and the final stone will be a ruby, either F or G.Option [F and X are both selected.] is therefore the only possibility among the choices. Option [F and G are both selected.] would stick us with a total of 7 stones. And each of the remaining choices mentions a stone that we have definitively rejected: H in option [G and H are both selected.], K in option [G and K are both selected], and Z in option [Y and Z are both selected].
There are exactly ten stores and no other buildings on Oak Street. On the north side of the street, from west to east, are stores 1, 3, 5, 7, and 9; on the south side of the street, also from west to east, are stores 2, 4, 6, 8,and 10. The stores on the north side are located directly across the street from those on the south side, facing each other in pairs, as follows: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10. Each store is decorated with lights in exactly one of the following colors: green, red, and yellow. The stores have been decorated with lights according to the following conditions:No store is decorated with lights of the same color as those of any store adjacent to it. No store is decorated with lights of the same color as those of the store directly across the street from it. Yellow lights decorate exactly one store on each side of the street.Red lights decorate store 4.Yellow lights decorate store 5.Which one of the following could be an accurate list of the colors of the lights that decorate stores 2, 4, 6, 8, and 10, respectively?
The right answer is an acceptable matching for the five south side streets, and we've got most of that worked out. Stores 4 and 6 are red and green respectively, so options [green, red, yellow, red, green] and [yellow, green, red, green, red] can be crossed out. There is one and only one yellow light, so option [green, red, green, red, green] with no yellows and option [yellow, red, green, red, yellow] with two are both eliminated.
There are exactly ten stores and no other buildings on Oak Street. On the north side of the street, from west to east, are stores 1, 3, 5, 7, and 9; on the south side of the street, also from west to east, are stores 2, 4, 6, 8, and 10. The stores on the north side are located directly across the street from those on the south side, facing each other in pairs, as follows: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10. Each store is decorated with lights in exactly one of the following colors: green, red, and yellow. The stores have been decorated with lights according to the following conditions:No store is decorated with lights of the same color as those of any store adjacent to it. No store is decorated with lights of the same color as those of the store directly across the street from it. Yellow lights decorate exactly one store on each side of the street.Red lights decorate store 4.Yellow lights decorate store 5.If green lights decorate store 7, then each of the following statements could be false EXCEPT:
Answer(s): D
A mini-sketch for this question should recopy what we know and add "G" to store 7. Store 9, which we knew was "G/R," is now definitively "R." And that's it; we cannot confirm anything more on the south side. But that's enough: store 9 has to be red, so option [Red lights decorate store 9.] cannot be false.Of options [Green lights decorate store 2.] and [Yellow lights decorate store 2.], exactly one is true -- store 2 is green or yellow -- but we don't know which. Store 8could be red or yellow, so [Red lights decorate store 8.] can be false. And store 10 remains uncertain, so option [Green lights decorate store 10.] can be false too.
There are exactly ten stores and no other buildings on Oak Street. On the north side of the street, from west to east, are stores 1, 3, 5, 7, and 9; on the south side of the street, also from west to east, are stores 2, 4, 6, 8, and 10. The stores on the north side are located directly across the street from those on the south side, facing each other in pairs, as follows: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10. Each store is decorated with lights in exactly one of the following colors: green, red, and yellow. The stores have been decorated with lights according to the following conditions:No store is decorated with lights of the same color as those of any store adjacent to it. No store is decorated with lights of the same color as those of the store directly across the street from it. Yellow lights decorate exactly one store on each side of the street.Red lights decorate store 4.Yellow lights decorate store 5.Which one of the following statements must be true?
This one is a slam-dunk. We have deduced that store 1 has red lights.
There are exactly ten stores and no other buildings on Oak Street. On the north side of the street, from west to east, are stores 1, 3, 5, 7, and 9; on the south side of the street, also from west to east, are stores 2, 4, 6, 8, and 10. The stores on the north side are located directly across the street from those on the south side, facing each other in pairs, as follows: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10. Each store is decorated with lights in exactly one of the following colors: green, red, and yellow. The stores have been decorated with lights according to the following conditions:No store is decorated with lights of the same color as those of any store adjacent to it. No store is decorated with lights of the same color as those of the store directly across the street from it. Yellow lights decorate exactly one store on each side of the street.Red lights decorate store 4.Yellow lights decorate store 5.If green lights decorate five stores on the street, then which one of the following statements must be true?
Answer(s): E
The trick here is to figure out which of the ten stores are the five that will have green lights. On the north side, with store 3 always green, we will have to have a green light in store 7 or 9. (Remember, adjacent greens are prohibited.) It may be smart to draw out both possibilities. And happily the south side is determinable. On the south side, we need three more greens, and clearly they'll have to be stores 2, 6, and10. And with store 4 always red, the requisite (Rule 3) yellow will go to store 8. So here are the two options:NEW QUESTIONS
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