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Jeremy is taller than Jean. John is shorter than Jeremy. John is shorter than Jean. If the first two sentences are true, the third is __________.
Let's use symbols from math to help us understand this:
(1) Jeremy is taller than Jean: Jeremy > Jean
(2) John is shorter than Jeremy: John < Jeremy
This could be rewritten: Jeremy > John
Thus, we know that Jeremy is taller than Jean and John; however, we do not know anything about the relationship between John and Jean.
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Thomas is smarter than Luca. Luca is smarter than John. John is smarter than Thomas. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this.
(1) Thomas is smarter than Luca: Thomas > Luca
(2) Luca is smarter than John: Luca > John
We could string these together as well:
Thomas > Luca > John
John is not smarter than Thomas; therefore, this is false.
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Baruch is weirder than Frederick. Frederick is weirder than Arthur. Baruch is weirder than Arthur. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this.
(1) Baruch is weirder than Frederick: Baruch > Frederick
(2) Frederick is weirder than Arthur: Frederick > Arthur
These can all be combined to give us:
Baruch > Frederick > Arthur
It is indeed the case that (3) Baruch > Arthur.
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Godfrey is more unknown than Henry. Henry is better known than Giles. Giles is more unknown than Godfrey. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this. "Greater than" (>) will mean "more known," and "less than" (<) will mean "more unknown."
(1) Godfrey is more unknown than Henry: Godfrey < Henry
This could be rewritten: Henry > Godfrey
(2) Henry is better known than Giles: Henry > Giles
Thus, we know that Henry is more known than both Giles and Godfrey; however, this does not tell us anything about the relationship between Giles and Godfrey. Therefore (3) is uncertain.
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Teddy has more fun than Jack. Franklin has less fun than Jack. Teddy has more fun than Franklin. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this. "Greater than" (>) will mean "has more fun," and "less than" (<) will mean "has less fun."
(1) Teddy has more fun than Jack: Teddy > Jack
(2) Franklin has less fun than Jack: Franklin < Jack
This could also be written: Jack > Franklin
Therefore, we could string all of these together into:
Teddy > Jack > Franklin
Therefore, (3) Teddy > Franklin does hold.
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Andrew is taller than Abraham. Abraham is shorter than Charles. Charles is taller than Andrew. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “taller,” and “less than” (<) will mean “shorter.”
(1) Andrew is taller than Abraham: Andrew > Abraham
(2) Abraham is shorter than Charles: Abraham < Charles
This could be rewritten: Charles > Abraham
Another way of looking at these two would be:
(1) Abraham < Andrew
(2) Abraham < Charles
This tells us that Abraham is shorter than Andrew and Charles. It tells us nothing about the relationship between Charles and Andrew.
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Physics is more difficult than chemistry. Chemistry is easier than philosophy. Philosophy is easier than physics. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “more difficult,” and “less than” (<) will mean “easier.”
(1) Physics is more difficult than chemistry: Physics > chemistry
This could be rewritten: Chemistry < physics
(2) Chemistry is easier than philosophy: Chemistry < philosophy
Therefore, this tells us that chemistry is easier than the other two subjects. However, it does not tell us anything about the relationship between philosophy and physics.
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It is easier to drive in snow than it is in ice. It is harder to drive in snow than in rain. It is easier to drive in rain than in ice. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “harder to drive in,” and “less than” (<) will mean “easier to drive in.”
(1) It is easier to drive in snow than it is in ice: snow < ice
(2) It is harder to drive in snow than in rain: snow > rain
This could be rewritten: rain < snow.
All of these could be combined to give us: rain < snow < ice.
This means that rain is indead easier to drive in that ice.
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Robert runs more quickly than Nicole. Nicole runs more quickly than Fred. Fred runs more slowly than Robert. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “runs more quickly,” and “less than” (<) will mean “runs more slowly.”
(1) Robert runs more quickly than Nicole: Robert > Nicole
(2) Nicole runs more quickly than Fred: Nicole > Fred
This could give us a combined statement:
Robert > Nicole > Fred
Now, (3) could be rewritten: Fred < Robert. This is the same thing as Robert > Fred, which we do see above as being true.
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Nuclear power is more efficient than coal power. Coal power is less efficient than gas power. Gas power is more efficient than nuclear power. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “more efficient than,” and “less than” (<) will mean “less efficient than.”
(1) Nuclear power is more efficient than coal power: nuclear > coal
This could be rewritten as: coal < nuclear
(2) Coal power is less efficient than gas power: coal < gas
Thus, we are told that coal is less efficient than both nuclear and gas; however, we are told nothing about the relationship between nuclear and gas power.
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There are more cabs than trucks on the roads in New York City. There are more motorcycles than there are trucks on the roads in New York City. There are more cabs than motorcycles on the roads in New York City. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “more on the road,” and “less than” (<) will mean “less on the road.”
(1) There are more cabs than trucks on the roads in New York City: cabs > trucks
This could be rewritten as: trucks < cabs
(2) There are more motorcycles than there are trucks on the roads in New York City: motorcycles > trucks
This could be rewritten as: trucks < motocycles
Thus, we are actually only being told something about trucks—there are fewer of them than both cabs and motorcycles (in New York City). Thus, we cannot say anything about the relationship between the number of cabs and the number of motorcycles.
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Gremlins are more frightening than ogres. Skeletons are less frightening than ogres. Gremlins are more frightening than skeletons. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “more frightening,” and “less than” (<) will mean “less frightening.”
(1) Gremlins are more frightening than ogres: gremlins > ogres
(2) Skeletons are less frightening than ogres: skeletons < ogres
This could be rewritten as: ogres > skeletons
All together, we can say:
gremlins > ogres > skeletons
Therefore, it is indeed the case that gremlins are more frightening than skeletons.
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George has a greater salary than John. Filbert has a lower salary than George. John’s salary is less than Filbert's. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “has a greater salary than,” and “less than” (<) will mean “has a lower salary than.”
(1) George has a greater salary than John: George > John
(2) Filbert has a lower salary than George: Filbert < George
This could be rewritten as: George > Filbert
This means that we are being told that George has a greater salary than both John and Filbert; however, it tells us nothing about the relation between these latter two men.
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Paul is smarter than Peter. Peter is smarter than Andrew. Andrew is smarter than Paul. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “is smarter than.”
(1) Paul is smarter than Peter: Paul > Peter
(2) Peter is smarter than Andrew: Peter > Andrew
These could be combined to give us:
Paul > Peter > Andrew
Therefore, it is false to say that Andrew is smarter than Paul.
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Emmanuel is more boring than David. Emmanuel is less boring than John. David is more boring than John. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “is more boring than,” and “less than” (<) will mean “is less boring than.”
(1) Emmanuel is more boring than David: Emmanuel > David
(2) Emmanuel is less boring than John: Emmanuel < John
This could be rewritten: John > Emmanuel
We could thus combine these as: John > Emmanuel > David
Thus it is false to say that David is more boring than John.
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Children are more immature than adults. Adults are more mature than teenagers. Teenagers are more mature than children. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “more mature,” and “less than” (<) will mean “more immature.”
(1) Children are more immature than adults: children < adults
This could be rewritten: adults > children
(2) Adults are more mature than teenagers: adults > teenagers
Therefore, all that we are being told is that adults are more mature than both teenagers and children. Nothing can be inferred regarding the relative status of teenagers and children.
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Thomas is braver than Henry. Thomas is more cowardly than Athanasius. Athanasius is braver than Henry. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “braver,” and “less than” (<) will mean “more cowardly (less brave).”
(1) Thomas is braver than Henry: Thomas > Henry
(2) Thomas is more cowardly than Athanasius: Thomas < Athanasius
Note, this could be rewritten: Athansius > Thomas
Thus, we could put together the two statements and get:
Athanasius > Thomas > Henry
Therefore, it is true to say that Athanasius is braver than Henry.
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The tuba has a more beautiful tone than the trumpet. The flute has a less beautiful tone than the trumpet. The tuba has a less beautiful tone than the flute. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “has a more beautiful tone,” and “less than” (<) will mean “has a less beautiful tone.”
(1) The tuba has a more beautiful tone than the trumpet: tuba > trumpet
(2) The flute has a less beautiful tone than the trumpet: flute < trumpet
This could be rewritten: trumpet > flute
Therefore, we could combine these to get:
tuba > trumpet > flute
Therefore, it is not true to say that the tuba has a less beautiful tone than the flute.
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Oatmeal wakes Sara better than chocolate does. Peanut butter makes Sara drowsier than does chocolate. Oatmeal wakes Sara better than does peanut butter. If the first two sentences are true, the third is __________.
Let’s use symbols from math to help us understand this and treat "wakes" as the opposite of "makes drowsier (i.e. less awake)." “Greater than” (>) will mean “wakes,” and “less than” (<) will mean “makes drowsier.”
(1) Oatmeal wakes Sara better than chocolate does: oatmeal > chocolate
(2) Peanut butter makes Sara drowsier than does chocolate: peanut butter < chocolate
This could be rewritten: chocolate > peanut butter
Note that we could combine all of these into:
oatmeal > chocolate > peanut butter
Thus, oatmeal does indeed wake Sara better than peanut butter.
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Scott is more beneficent than Michael. Michael is more miserly than Peter. Scott is more beneficent than Peter. If the first two sentences are true, the third is __________.
Some vocabulary is necessary first. "Beneficient" means "giving or generous." (Think of "benefit," which is related to this word). To be "miserly" is to be "stingy," not wishing to give out money or gifts.
Now, let's use symbols from math to help us understand this. “Greater than” (>) will mean “more beneficent,” and “less than” (<) will mean “more miserly (i.e. less beneficent).”
(1) Scott is more beneficent than Michael: Scott > Michael
Note that this could be rewritten: Michael < Scott
(2) Michael is more miserly than Peter: Michael < Peter
Therefore, all that we are being told is that Michael is less beneficent than both of the other men. There is no necessary relationship described about Scott and Peter.
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