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A library is holding a special five-day event honoring successful local writers. One writer will be invited to be a guest speaker for each night from Monday through Friday, and no writer will be asked to participate twice. The writers have each written books in only one of four different genres—science fiction, mystery, historical fiction, and non-fiction. A, J, and X are all science fiction writers. B and Y are both mystery writers. C and Z are both historical fiction writers. L is a non-fiction writer. The following conditions apply without exception:
At least one writer from each genre will be invited to speak on at least one night.
No two authors from the same genre will be invited to speak on the following night.
If C is invited to speak, then X is invited to speak on the following night.
If Y is invited to speak, then neither C nor A are invited to speak.
If X and J are both invited to speak, then neither will speak on either the first or last night.
If L and B are both invited to speak, then neither will speak on either the first or last night.
If L is invited to speak on Friday, then on what days MUST a science fiction writer be invited?
Tuesday and Thursday
Monday and Wednesday
Monday and Thursday
Monday and Tuesday
Only Wednesday
Explanation
If L is the speaker on Friday, then B cannot be a guest speaker at all, since if L and B are both guest speakers then neither can speak on Monday or Friday. If B is not a speaker, then Y must be a speaker, in order for there to be a mystery writer guest speaker. If Y is a guest speaker, then C must not be a guest speaker. Thus, Z must be a guest speaker in order to have a historical fiction writer.
We thus know so far that Y and Z and L are three out of five possible guest speakers (from Monday through Friday). That means the remaining two MUST be science fiction writers. Furthermore, because Y is a guest speaker, A cannot be a guest speaker. Thus, the two science fiction guests are X and J and they both are invited. They must be invited for Tuesday and Thursday, because any other day would force one of them to speak on Monday, which is not possible if both X and J are invited.
Y/Z, X/J, Y/Z, X/J, L
A zoo has four exhibition regions---labelled R, T, V, and W---and each region consists of a vegetarian wing and a carnivore wing. The following conditions apply:
Each exhibition wing houses only mammals or amphibians.
Three of the wings have mammals.
R's vegetarian wing and T's vegetarian wing house amphibians.
If an exhibition region has mammals in one of its wings, then the other wing in that exhibition region has amphibians.
If mammals are housed in V's carnivore wing, then W's vegetarian wing has mammals, too.
If mammals are housed in V's carnivore wing, which one of the following is a complete and accurate list of the wings that CANNOT house mammals?
R's vegetarian wing, T's vegetarian wing, V's vegetarian wing, W's carnivore wing.
R's vegetarian wing, T's vegetarian wing
R's vegetarian wing, T's vegetarian wing, V's vegetarian wing
R's vegetarian wing, T's vegetarian wing, W's carnivore wing
R's vegetarian wing, R's carnivore wing, T's vegetarian wing, V's vegetarian wing, W's carnivore wing
Explanation
R and T's vegetarian wings are already designated locations for amphibians, so they are included in any correct response. Because mammals cannot occupy both wings, V's vegetarian wing cannot house mammals, since V's carnivore wing houses mammals. A rule dictates that if mammals are housed in V's carnivore wing, then W's vegetarian wing must house mammals. Therefore, mammals cannot be housed in V's vegetarian wing and W's carnivore wing, in addition to the wings already noted. Hence, the credited response is: R's vegetarian wing, T's vegetarian wing, V's vegetarian wing, W's carnivore wing.
A barista has seven boxes of tea and coffee of varying types, which she places in a line behind the counter. There are four types of coffee: Colombian, Dark, Espresso, and French. There are three types of tea: Green, Herbal, and Vanilla. The following rules apply:
A box of tea must be fifth
No tea may be placed next to another tea
Herbal may not be next to either Colombian or Espresso
At least two boxes must be between Colombian and Dark
Which of the following cannot be true?
Coffee is both first and last
Coffee is both first and sixth
Two boxes of coffee are next to each other
Tea is both first and last
Coffee is third and fourth
Explanation
If coffee were first and last, then two boxes of tea would need to be next to each other. Since one box would need to be fifth and since we could not put tea first or seventh, there is no way to separate all the boxes of tea.
A new grocery store is deciding which brands of candy bars to sell in its opening stock. The store will select exactly five of the following eight brands to stock: Brighter, Charm, Delico, Flare, Handy, Joyful, Little, and Prospine. The selection of brands must follow these conditions:
If both Charm and Flare are selected, Delico is also selected.
If Handy is selected, neither Brighter nor Flare is selected.
If Little is selected, Joyful is not selected.
Of the brands Brighter, Joyful, and Prospine, exactly two are selected.
If both Flare and Joyful are selected, which of the following is a pair of brands both of which could also be selected?
Charm and Prospine
Charm and Little
Brighter and Handy
Delico and Handy
Flare and Little
Explanation
Since you know Flare is selected, based off the second global rule, you know that Handy is not selected (by the contrapositive, if Flare is selected, Handy is not selected). This allows you to eliminate the two answer choices that include Handy.
Also, since you know Joyful is selected, based off the third global rule, you know that Little is not selected. This allows you to eliminate the two answer choices that include Little.
You are left with the correct answer: Charm and Prospine. You can verify this by filling the two spots with Charm and Prospine, which leads to the final spot being filled by Delico (via the first global rule).
A social psychologist is conducting a study involving six individuals who are from three regions in the country. Fred, Greg, and Helen are from the northeast. Kate, Lyle, and Norm are from the west. And Ted, Vickie, and Zach are from the south.
Due to certain demographic and other requirements for the study, the selection of these individuals for the study must meet the following conditions:
Fred and Helen are not both selected.
Norm and Ted are not both selected.
If Helen is selected, Kate must also be selected.
If Kate is selected, Norm must also be selected.
Each of the following is a pair of individuals that could be selected together EXCEPT:
Kate and Ted
Fred and Greg
Helen and Kate
Lyle and Norm
Ted and Vickie
Explanation
Kate and Ted cannot both be selected because:
-
If Kate is selected, then Norm must be selected.
-
If Norm is selected, then Ted cannot be selected because Norm and Ted cannot both be selected together, according to one of the conditions.
Therefore, Kate and Ted cannot be selected together, for it leads to a violation of the condition that Norm and Ted cannot both be selected together.
A chef is arranging spices on a shelf. Four of the spices are in large jars: garlic, oregano, pepper, and salt. Three of the spices are in small jars: basil, cumin, and mint. The following conditions apply:
A large jar must be first or fourth
Pepper must come after cumin but before basil
The jar of salt must be the first large jar in the line
Basil cannot be immediately before or after garlic
When pepper is third, which of the following could be true?
oregano is fifth
mint is second
garlic is second
cumin is fifth
oregano is second
Explanation
When pepper is third, salt and cumin are the only spices to come before it. As a result, oregano, garlic, and mint cannot be second. Further, cumin must come before pepper and, therefore, cannot be fifth. Oregano could be fifth.
Three circus performers—Flo, Genie, and Kyle—will perform the following six circus acts: acrobatics; ball juggling; clowning; dunking; elephant demonstrations; fire twirling. Each act is performed only once in any given show, and only one act is performed at a time. The following conditions dictate the sequencing of these acts:
- Flo performs exactly one act before Genie performs any of her acts
- Flo does not perform first and he does not perform last
- Genie does not do acrobatics and ball juggling
- Kyle does not do acrobatics and elephant demonstrations
- Ball juggling is performed immediately after the elephant demonstrations
If Kyle performs last, then which of the following must be true?
Genie performs some time after Kyle and Flo.
Genie performs second.
Genie performs immediately after Kyle.
Genie does elephant demonstrations immediately before Kyle performs.
Flo does ball juggling.
Explanation
This question calls for an answer that reflects what must happen, not what could happen. We know that Kyle must go first, so Kyle occupies slots 1 and 6. We know that Flo must go before Genie performs her first act. So Genie cannot occupy slot 2. That means Genie must perform after some time after Kyle and Flo, which is the credited response.
A human resources manager must schedule a round of interviews during a particular day. Six different time slots are available in the afternoon and are numbered one through six in sequential order. Six candidates - Joe, Jim, Mary, Bob, Jess, and Sue - must be scheduled during the afternoon. Only one candidate can occupy each interview slot. The assignment of interview slots is subject to the following restrictions:
- Either Mary or Bob must occupy the second time slot.
- Joe must occupy the sixth time slot.
- Mary and Bob cannot occupy consecutive time slots.
- Jim and Mary must occupy consecutive time slots.
- Sue must be interviewed before Jess.
If Jim is assigned to the fourth slot, which of the following must be true?
Mary must occupy the fifth slot.
Mary must occupy the third slot.
Sue must occupy the third slot.
Jess must occupy the first slot.
Bob must occupy the third slot.
Explanation
The only restriction that involves Jim is that he and Mary must occupy consecutive slots. Therefore, if Jim occupies the fourth slot, Mary must occupy the third or fifth slot. Since Mary can't be in the second slot, Bob must be assigned to this slot. Lastly, Mary and Bob cannot occupy consecutive slots. So if Bob is in the second slot, Mary cannot be in the third slot. Mary must be in the fifth time slot. Now the 2nd, 4th, 5th, and 6th slots are all accounted for. Finally, since Sue must be interviewed before Jess, Sue must be 1st and Jess must be 3rd.
A new grocery store is deciding which brands of candy bars to sell in its opening stock. The store will select exactly five of the following eight brands to stock: Brighter, Charm, Delico, Flare, Handy, Joyful, Little, and Prospine. The selection of brands must follow these conditions:
If both Charm and Flare are selected, Delico is also selected.
If Handy is selected, neither Brighter nor Flare is selected.
If Little is selected, Joyful is not selected.
Of the brands Brighter, Joyful, and Prospine, exactly two are selected.
If both Flare and Joyful are selected, which of the following is a pair of brands both of which could also be selected?
Charm and Prospine
Charm and Little
Brighter and Handy
Delico and Handy
Flare and Little
Explanation
Since you know Flare is selected, based off the second global rule, you know that Handy is not selected (by the contrapositive, if Flare is selected, Handy is not selected). This allows you to eliminate the two answer choices that include Handy.
Also, since you know Joyful is selected, based off the third global rule, you know that Little is not selected. This allows you to eliminate the two answer choices that include Little.
You are left with the correct answer: Charm and Prospine. You can verify this by filling the two spots with Charm and Prospine, which leads to the final spot being filled by Delico (via the first global rule).
Three circus performers—Flo, Genie, and Kyle—will perform the following six circus acts: acrobatics; ball juggling; clowning; dunking; elephant demonstrations; fire twirling. Each act is performed only once in any given show, and only one act is performed at a time. The following conditions dictate the sequencing of these acts:
- Flo performs exactly one act before Genie performs any of her acts
- Flo does not perform first and he does not perform last
- Genie does not do acrobatics and ball juggling
- Kyle does not do acrobatics and elephant demonstrations
- Ball juggling is performed immediately after the elephant demonstrations
Which one of the following could be true?
Fire twirling is the first act performed.
Acrobatics is the first act performed.
Ball juggling is the second act performed.
Elephant demonstrations is the first act performed.
Elephant demonstrations is the last act performed.
Explanation
Flo does acrobatics, so it cannot come first.
For ball juggling to go second, elephant demonstrations would have to first. But elephant demonstrations can't go first because Kyle must go first and he doesn't do elephant demonstrations.
Finally, elephant demonstrations can't go last because ball juggling must follow.
Consequently, the only option left is fire twirling going first---and that is the credited response.