Card 0 of 2136
A gym teacher wants his 6 students to line up in height order, from shortest to tallest. Corrin and Theresa are girls. Ben, Jonathan, Will, and Dan are the boys.
- Will is not the tallest.
- No girl is taller than Jonathan
- Dan is shorter than Corrin, but taller than Theresa.
- Ben is the tallest
If Will was the shortest in line, what must the order be?
If Will is locked into the first position, all other positions are set and cannot be changed, according to the rest of the rules.
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A gym teacher wants his 6 students to line up in height order, from shortest to tallest. Corrin and Theresa are girls. Ben, Jonathan, Will, and Dan are the boys.
- Will is not the tallest or the shortest.
- No girl is taller than Jonathan.
- Dan is shorter than Corrin, but taller than Theresa.
- Ben is the tallest.
Who are the only people that can be 5th in line?
Ben has to be 6th always. Theresa has to always be first. Corrin must always be earlier in line than Jonathan, so she can not be 5th. Will is interchangeable between the 2nd-5th spots, so he and Jonathan are the only ones that can be 5th.
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A gym teacher wants his 6 students to line up in height order, from shortest to tallest. Corrin and Theresa are girls. Ben, Jonathan, Will, and Dan are the boys.
- Will is not the tallest or the shortest.
- No girl is taller than Jonathan
- Dan is shorter than Corrin, but taller than Theresa.
- Ben is the tallest
Who must be first in line?
Theresa must precede everyone. She has to be shorter than Dan and Corrin and Jonathan. Will cannot be shortest. Ben has to be the tallest. Thus, only Theresa can be 1st.
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A gym teacher wants his 6 students to line up in height order, from shortest to tallest. Corrin and Theresa are girls. Ben, Jonathan, Will, and Dan are the boys.
- Will is not the tallest or the shortest.
- No girl is taller than Jonathan
- Dan is shorter than Corrin, but taller than Theresa.
- Ben is the tallest
What positions can Corrin fill?
Corrin must follow Theresa and Dan, thus she cannot be 1st or second. She must also come before Jonathan and Ben, so she cannot be 5th or 6th. Thus, Corrin can only be 3rd or 4th.
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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.
Which of the following is an acceptable list of guest speakers for the library's special event from Monday to Friday?
This question is actually a combination of sequencing and grouping. The test-taker must determine both which variables will be involved in the sequence and the order in which the variables are placed in sequence. Answering this particular question is simply a matter of checking the rules in the question stem. Each incorrect answer breaks one or more rules.
L, J, C, X, Y is incorrect because C may not be invited if Y is invited. Z must be invited instead.
A, C, B, J, Z is incorrect because L is not invited. L is the only non-fiction writer and thus MUST be one of the five invited speakers.
X, L, C, B, Z is incorrect because X must follow C.
A, X, Y, J, L is incorrect because A and X are both science-fiction writers, and they are not allowed to speak on consecutive nights.
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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 of 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.
Which two writers cannot BOTH be invited to speak?
Since X always follows C and J is participating, we have the pair of X and J. X and J are both science fiction, so there must be at least one space between them. Neither can speak in either the first or last slot. C must come directly before X. Thus, we have either CX_J_ or _JCX_.
We know that L must be part of any correct diagram, and we still need a mystery writer, either B or Y. Y cannot fit because Y and C can't both be part of the diagram. B cannot fit because There is no way to fit L and B without either one or both speaking first or last.
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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 of science-fiction, mystery, historical fiction, and non-fiction will all 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 C and A are both invited to speak, which two writers CANNOT speak on consecutive nights?
If C is invited to speak, then we know that C and X will be speaking on consecutive nights. Since C and A are invited to speak, then we know that Y is NOT invited to speak, which means that B IS invited (because at least one of the two mystery writers must speak. L always speaks.
Thus, we know our diagram will be some sequence of CX, A, B, and L. Since L and B are both invited, neither may speak first or last. Thus, a possible diagram may be something like C, X, L, B, A. L and B will always be surrounded on either side by the groups CX and A. Thus, there is no combination in which the A and CX blocks touch, and no consecutive grouping of those letters may take place.
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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 of science-fiction, mystery, historical fiction, and non-fiction will all 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 A is invited to speak on Thursday, how many different writers could possibly be the invited speaker for Wednesday?
If A is invited, then we know that Y is NOT invited. If Y is NOT invited, we know that B MUST be invited, because he is the only remaining mystery writer. L is always invited.
Since B and L are both invited, they cannot speak on the first or last day. They must thus occupy two of either Tuesday, Wednesday, or Thursday. Since A is scheduled to speak on Thursday, they must both speak on either Tuesday or Wednesday and either L or B can speak on Wedneday.
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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 of science-fiction, mystery, historical fiction, and non-fiction will all 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 it is no longer necessary to invite at least one writer from every genre, which of the following is FALSE?
Writers of the same genre may not speak on consecutive nights. With only five slots to fill, two of the three science fiction writers must speak on Monday and Friday (e.g. A_J_X). If both X and J are invited (and they are, if we are inviting all of the science fiction authors), then at least one will be forced to speak on Monday or Friday, which is not allowed.
The modification of the rules is actually just a bit of a red herring, since all of the answer choices except for the one regarding science fiction writers is true regardless.
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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?
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
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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.
Which of the following groups of three writers is NEVER invited together?
It is impossible for there to be a valid schedule of guests that includes all of X, J, and B. This is because a week that includes X, J, and B also includes L, since L is always included. The pairs of X and J and L and B can never be invited in the same week, because none of the four are allowed to speak on Monday or Friday when paired that way. This means there are four writers who must fit into three days. Impossible.
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The Silvermine Railway's F train takes a loop through the region in which it operates. It stops at five passenger stops-- Aberdeen, Basilica, Habermark, Ramrock, and Terroire, although not necessarily in that order. The F train begins and ends each loop at the railyard, which is not considered a passenger stop. The order of the stops on the route must conform to the following conditions without exception:
The F train stops at each of the five passenger stops exactly once per loop and does exactly two complete loops per day. The railyard is where the train begins and ends each loop. After leaving the railyard at the beginning of the day, the train will stop at each of the five passenger stops before completing its loop by returning to the railyard. The train will then proceed to stop at each of the five passenger stops once again (in the same order it did the first time around) before once again stopping at the railyard and thus completing its second and final loop of the day.
The F train will never stop at Habermark and Basilica consecutively.
The F train will stop at at least two other passenger stops two times before stopping at Aberdeen for the second time.
If Terroire is the third stop, then Habermark is the second stop.
If Aberdeen is the fourth stop, then Habermark is not the fifth stop.
Aberdeen is earlier on the route than at least one of Habermark and Ramrock.
Which of the following lists of five stops is a possible order of stops that the F train made at passenger stops in a single day?
The key insight necessary in order to answer this question is to realize that the question is asking about the stops the F train makes in an ENTIRE day (i.e. two complete loops of its route) rather than just a single route. Thus, you are not simply identifying a legal order of stops in a route, e.g. 1, 2, 3, 4, 5, but are also identifying possible orders BETWEEN the two routes, e.g. 3, 4, 5, 1, 2, 3. The question also specifies passenger stops, so the railyard is not really a consideration here.
\[Habermark, Basilica, Terroire, Aberdeen, Ramrock\]
Habermark and Basilica can never be consecutive stops.
\[Aberdeen, Basilica, Terroire, Ramrock, Habermark\]
There are at least two stops that the train stops at twice before stopping at Aberdeen for the second time. This is simply another way of saying that there are two stops that come before Aberdeen on a single loop of the route. This is a very useful insight for this game. If we rearrange the order of the stops so that Aberdeen is third, we get Ramrock, Habermark, Aberdeen, Basilica, Terroire. Aberdeen is earlier on the route than at least one of Ramrock or Habermark, but, with Aberdeen as third, both Ramrock and Habermark come before Aberdeen. Pushing Aberdeen to fourth or fifth does nothing to change this. Thus, this is an impossible list.
\[Terroire, Basilica, Ramrock, Habermark, Aberdeen\]
This is wrong for essentially the same reason as \[Aberdeen, Basilica, Terroire, Ramrock, Habermark\]. Rearranging this so that Aberdeen is third puts Ramrock and Habermark in an impossible position. These are both really exercises testing the understanding of there being two routes in a day versus one.
\[Habermark, Terroire, Aberdeen, Ramrock, Basilica\]
Habermark and Basilica are consecutive stops. Even if Habermark is actually the first stop and the order of the stops in the route is as listed, Habermark will be the next stop after Basilica when it starts the second loop. The conditions say that the train doesn't stop at the railyard-- it merely passes it-- and also specifies that the railyard is not considered a passenger stop. The question asks for passenger stops specifically.
Thus, \[Aberdeen, Basilica, Ramrock, Habermark, Terroire\] is the correct answer. It reflects the valid route of Habermark, Terroire, Aberdeen, Basilica, Ramrock.
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A gym teacher wants his 6 students to line up in height order, from shortest to tallest. Corrin and Theresa are girls. Ben, Jonathan, Will, and Dan are the boys.
- Will is not the tallest or the shortest.
- No girl is taller than Jonathan
- Dan is shorter than Corrin, but taller than Theresa.
- Ben is the tallest
Which of the following must be true about acceptable height orders?
Theresa will always be at the front of the line, and Ben at the back. Theresa must be in front of Dan, Corrin, and Jonathan, and Will cannot be 1st.
Additionally, because of Will's interchangeability, there is no certainty that Dan will be between certain people or that Will is always between certain people. These answers are possibilities, but not certainties.
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The Silvermine Railway's F train takes a loop through the region in which it operates. It stops at five passenger stops-- Aberdeen, Basilica, Habermark, Ramrock, and Terroire, although not necessarily in that order. The F train begins and ends each loop at the railyard, which is not considered a passenger stop. The order of the stops on the route must conform to the following conditions without exception:
The F train stops at each of the five passenger stops exactly once per loop and does exactly two complete loops per day. The railyard is where the train begins and ends each loop. After leaving the railyard at the beginning of the day, the train will stop at each of the five passenger stops before completing its loop by returning to the railyard. The train will then proceed to stop at each of the five passenger stops once again (in the same order it did the first time around) before once again stopping at the railyard and thus completing its second and final loop of the day.
The F train will never stop at Habermark and Basilica consecutively.
The F train will stop at at least two other passenger stops two times before stopping at Aberdeen for the second time.
If Terroire is the third stop, then Habermark is the second stop.
If Aberdeen is the fourth stop, then Habermark is not the fifth stop.
Aberdeen is earlier on the route than at least one of Habermark and Ramrock.
If Terroire is the fifth passenger stop, which of the following must be true?
If Terroire is the fifth stop, then Ramrock and Basilica must be consecutive stops.
If Terroire is the fifth stop, then Aberdeen cannot be the fourth stop, because one of Ramrock or Habermark must come after Aberdeen. Aberdeen can never be earlier than the third stop. Thus, Aberdeen must be in the third stop.
_ _ A _ T
The fourth stop must be one of Habermark or Ramrock, because, again, at least one must come after Aberdeen.
_ _ A H/R T
That means that Basilica is one of the first two stops. However, because Basilica and Habermark are never consecutive stops, then Ramrock must be one of the first two stops as well, and Habermark is the fourth stop.
B/R B/R A H T
There is no more information to determine whether Basilica or Ramrock comes first, but it doesn't matter as they will be consecutive stops regardless. With this diagram, the other answers are obviously false. Habermark is always the fourth stop. Aberdeen is always the third stop. It is possible to make Basilica and Aberdeen consecutive instead of Ramrock and Aberdeen. It is possible for there to be two stops between Habermark and Basilica, by making Basilica be the first stop.
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The Silvermine Railway's F train takes a loop through the region in which it operates. It stops at five passenger stops-- Aberdeen, Basilica, Habermark, Ramrock, and Terroire, although not necessarily in that order. The F train begins and ends each loop at the railyard, which is not considered a passenger stop. The order of the stops on the route must conform to the following conditions without exception:
The F train stops at each of the five passenger stops exactly once per loop and does exactly two complete loops per day. The railyard is where the train begins and ends each loop. After leaving the railyard at the beginning of the day, the train will stop at each of the five passenger stops before completing its loop by returning to the railyard. The train will then proceed to stop at each of the five passenger stops once again (in the same order it did the first time around) before once again stopping at the railyard and thus completing its second and final loop of the day.
The F train will never stop at Habermark and Basilica consecutively.
The F train will stop at at least two other passenger stops two times before stopping at Aberdeen for the second time.
If Terroire is the third stop, then Habermark is the second stop.
If Aberdeen is the fourth stop, then Habermark is not the fifth stop.
Aberdeen is earlier on the route than at least one of Habermark and Ramrock.
What is the maximum possible number of passenger stops between Habermark and Basilica in a single day?
The maximum number of stops is 2. The largest distance around a circle is from a single point back to itself. In this case, the maximum possible number of stops is four. (Count how many numbers there are between the 1s: 1 2 3 4 5 1). The maximum possible number of stops between two different points is three; this is the case if the two are adjacent to each other (Count how many numbers there are between 1 and 2: 2 3 4 5 1).
Habermark and Basilica, however, cannot be adjacent. There must be at least one stop between them. This means that the maximum possible number of stops between them is two. (Count how many numbers there are between 1 and 3: 3 4 5 1 2 3).
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The Silvermine Railway's F train takes a loop through the region in which it operates. It stops at five passenger stops-- Aberdeen, Basilica, Habermark, Ramrock, and Terroire, although not necessarily in that order. The F train begins and ends each loop at the railyard, which is not considered a passenger stop. The order of the stops on the route must conform to the following conditions without exception:
The F train stops at each of the five passenger stops exactly once per loop and does exactly two complete loops per day. The railyard is where the train begins and ends each loop. After leaving the railyard at the beginning of the day, the train will stop at each of the five passenger stops before completing its loop by returning to the railyard. The train will then proceed to stop at each of the five passenger stops once again (in the same order it did the first time around) before once again stopping at the railyard and thus completing its second and final loop of the day.
The F train will never stop at Habermark and Basilica consecutively.
The F train will stop at at least two other passenger stops two times before stopping at Aberdeen for the second time.
If Terroire is the third stop, then Habermark is the second stop.
If Aberdeen is the fourth stop, then Habermark is not the fifth stop.
Aberdeen is earlier on the route than at least one of Habermark and Ramrock.
If the stops were numbered from 1 to 5 from earliest to latest, which stop has the least possibilities regarding which of the passenger stops it represents?
The 3rd stop is the most constrained by the conditions. Aberdeen MUST be in either the third or fourth position. If it is in the third position, then obviously nothing else can be in the third position. If it is in the fourth position, then the diagram for the game looks like the following:
B/H T H/B A R.
T and R cannot occupy the third position. Only A, B, and H can possibly occupy the third position. T cannot be in the third position, because then B and H would be forced into the first two stops. They are not allowed to be consecutive stops. R cannot occupy the third position, because A would have to go into to the fourth position and H would have to go into the fifth position. H cannot be in the fifth position if A is in the fourth position.
The first, second, and fifth positions are restricted only in that A cannot occupy these positions.
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The Silvermine Railway's F train takes a loop through the region in which it operates. It stops at five passenger stops-- Aberdeen, Basilica, Habermark, Ramrock, and Terroire, although not necessarily in that order. The F train begins and ends each loop at the railyard, which is not considered a passenger stop. The order of the stops on the route must conform to the following conditions without exception:
The F train stops at each of the five passenger stops exactly once per loop and does exactly two complete loops per day. The railyard is where the train begins and ends each loop. After leaving the railyard at the beginning of the day, the train will stop at each of the five passenger stops before completing its loop by returning to the railyard. The train will then proceed to stop at each of the five passenger stops once again (in the same order it did the first time around) before once again stopping at the railyard and thus completing its second and final loop of the day.
The F train will never stop at Habermark and Basilica consecutively.
The F train will stop at at least two other passenger stops two times before stopping at Aberdeen for the second time.
If Terroire is the third stop, then Habermark is the second stop.
If Aberdeen is the fourth stop, then Habermark is not the fifth stop.
Aberdeen is earlier on the route than at least one of Habermark and Ramrock.
If the ninth passenger stop of the day is made at Aberdeen, then for which of the following can you determine the exact positions on the route?
The correct answer is Terroire and Ramrock.
This is actually very similar to another question in this set. If the ninth stop is Aberdeen, then that means that on the route that the F train is taking, Aberdeen is the fourth stop. When Aberdeen is the fourth stop, then the diagram is always B/H T B/H A R. Only the positions of Basilica and Habermark are uncertain, and those are uncertain only in that we don't know which is first and which is third.
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The Silvermine Railway's F train takes a loop through the region in which it operates. It stops at five passenger stops-- Aberdeen, Basilica, Habermark, Ramrock, and Terroire, although not necessarily in that order. The F train begins and ends each loop at the railyard, which is not considered a passenger stop. The order of the stops on the route must conform to the following conditions without exception:
The F train stops at each of the five passenger stops exactly once per loop and does exactly two complete loops per day. The railyard is where the train begins and ends each loop. After leaving the railyard at the beginning of the day, the train will stop at each of the five passenger stops before completing its loop by returning to the railyard. The train will then proceed to stop at each of the five passenger stops once again (in the same order it did the first time around) before once again stopping at the railyard and thus completing its second and final loop of the day.
The F train will never stop at Habermark and Basilica consecutively.
The F train will stop at at least two other passenger stops two times before stopping at Aberdeen for the second time.
If Terroire is the third stop, then Habermark is the second stop.
If Aberdeen is the fourth stop, then Habermark is not the fifth stop.
Aberdeen is earlier on the route than at least one of Habermark and Ramrock.
Which of the following could be added to the existing conditions and cause absolutely no changes whatsoever to the possible set of routes?
\[If Terroire is the third stop, then Ramrock is the fifth stop.\]
This causes no changes, because Terroire is never the third stop. You can predicate anything on Terroire being the third stop, because it will never happen.
\[Aberdeen is always the fourth stop.\]
Aberdeen is sometimes the third stop. This removes that possiblity from the set of possible routes.
\[Basilica must come before Habermark.\]
Basilica can come after Habermark on several valid routes, such as H T B A R.
\[Habermark must come before Ramrock.\]
This removes the possibility of routes like R B A T H.
\[Only one of Basilica or Habermark comes before Aberdeen.\]
This removes the possibility of routes like B T H A R or H T B A R, as shown above.
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A gym teacher wants his 6 students to line up in height order, from shortest to tallest. Corrin and Theresa are girls. Ben, Jonathan, Will, and Dan are the boys.
- Will is not the tallest or the shortest.
- No girl is taller than Jonathan
- Dan is shorter than Corrin, but taller than Theresa.
- Ben is the tallest
Which of the following is an acceptable ranking?
Using the question's rules, you can figure out each student's general positions. Ben always has to be #6, as the tallest. Theresa must always be before Dan, and Dan must always precede Corrin. Thus, Corrin can never come before Theresa. Jonathan must be either 4th or 5th, because the girls have to precede him, and Dan has to come in the middle of that, taking up 3 spots. Will cannot be the shortest, or the tallest (as Ben is), so he can go anywhere that isn't the 1 or 6 spot.
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A gym teacher wants his 6 students to line up in height order, from shortest to tallest. Corrin and Theresa are girls. Ben, Jonathan, Will, and Dan are the boys.
- Will is not the tallest or the shortest.
- No girl is taller than Jonathan
- Dan is shorter than Corrin, but taller than Theresa.
- Ben is the tallest
If Will is shorter than Dan, what must be true?
Will can not be the shortest or tallest. If he is shorter than Dan, than he is also shorter than Corrin. This also means he must be shorter than Jonathan, who is taller than the girls. Thus, Will can only be the 5th tallest, in between Theresa (the shortest), and Dan in 4th tallest.
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