Statement - Conclusions Questions and Answers

Answer: B

Both statements are universal: all poets and all painters lie inside the set of daydreamers. The two sets, poets and painters, are both subsets of daydreamers but nothing connects them to each other. Conclusion I, all painters are poets, does not follow, as the painters circle can lie outside the poets circle. Conclusion II, some daydreamers are not painters, is possible when there are poets who are not painters, but it is not certain, since the painters may be all the daydreamers. A conclusion that is only possible does not follow. So no conclusion emerges, which is the second option.

Answer: B

Only conclusion (II) follows. The second statement says some foods are pains, and that is reversible: if some foods are pains, then some pains are foods, so conclusion (II) holds. Conclusion (I) claims that some pains are bats. All bats are foods, so bats lie inside the set of foods, but the pains that are foods may be a different part of that set, so nothing links pains to bats. A Venn diagram with the pains overlapping only the foods outside the bats satisfies both statements and breaks (I). So option B is correct, and the options that include (I) are wrong.

Answer: C

Conclusions I and III follow. Statement II says some comics are storybooks, and reading it the other way round, some storybooks are comics, which is conclusion I. Since all storybooks are textbooks, the storybooks that are comics are textbooks, so some textbooks are comics, which is conclusion III.

Conclusion II, some textbooks are novels, would need a link between novels and storybooks. Novels are linked only to comics, and only some of them, so it does not follow.

Answer: A

Only conclusion I follows. All cats are dogs, and some bats are cats, so those bats that are cats are also dogs: some dogs are bats. Conclusion I is therefore forced by statements II and III.

Conclusion II says some cats are rats. The only link between rats and the rest is that some rats are bats, and some bats are cats, but the bats that are rats need not be the bats that are cats, so no overlap of cats and rats is guaranteed. Conclusion III, some dogs are rats, depends on the same missing link and does not follow either. That is why ‘Only conclusion I follows’ is right and the options with II or III are wrong.

Answer: D

Only conclusion I follows. 'Most erasers are sharpeners' means at least some erasers are sharpeners, and reversed, some sharpeners are erasers, so I holds. II says all erasers are pencils, but only the converse is given (all pencils are erasers), and some erasers are sharpeners, so II does not follow. III says no pencils are sharpeners, which flatly contradicts the statement 'Some sharpeners are pencils'.

So none, I with III, and I with II are all wrong.

Answer: B

Only conclusions I and II follow. The statements give a chain: all doors are windows, some windows are drawers, all drawers are wood. "Some windows are drawers" is reversible, so "Some drawers are windows" follows (II). Because every drawer is wood, those drawers that are windows are wood, so some windows are wood, and the reverse "Some wood are windows" follows (I). Conclusion III, "Some wood are doors", would need a drawer that is also a door, but the statements only say all doors are windows and some windows are drawers; the doors and the drawers among the windows may not overlap, so III does not follow. Hence only I and II follow.

Answer: A

Only conclusion II follows. The statements are: all dogs are birds, and all birds are goats. Joining them gives all dogs are goats. Since there is at least one dog in the statement, some goats must be dogs, which is conclusion II (the converse of an 'all' statement gives 'some').

Conclusion I, 'all goats are dogs', would need the goats to be no larger a group than the dogs. The statements say the dogs are only a part of the birds, which are themselves a part of the goats, so there can be goats that are not dogs. Conclusion I does not follow. Because II follows and I does not, the answer is 'Only conclusion II follows'.

Answer: A

Only conclusion I follows.

All floors are gates, and no gate is a window, so no floor can be a window. That is exactly conclusion I. Conclusion II says some floors are windows, which directly contradicts it, so II cannot follow.

Because I is certain and II is false, the 'either I or II' and 'neither' options are wrong as well. Only the first option is correct.

Drawing it helps: circle 'floors' inside the circle 'gates' and keep the circle 'windows' fully outside 'gates'. The floor circle is then also outside the window circle, so no floor is a window. A statement that two sets overlap, as in II, cannot be drawn without breaking this picture.

Answer: C

Conclusions I and II follow.

All papers are pens and some pens are markers; all markers are whiteners. Since some pens are markers and all markers are whiteners, those pens are whiteners, so some whiteners are pens (I). 'Some pens are markers' can be turned round to 'some markers are pens' (II). Nothing joins papers to whiteners directly, because the pens that are markers need not be the pens that are papers, so III does not follow.

Hence only I and II follow.

A diagram makes the conclusions clear: papers inside pens, markers overlapping pens, and markers entirely inside whiteners. The overlap of pens and markers lies inside the whiteners, so some whiteners are pens. Papers are inside pens, but no link joins papers to markers, so papers and whiteners need not meet.

Answer: A

Only conclusion III follows. Statements A and B chain together as ducks ⊂ cats ⊂ lions, so every duck is a lion, which is exactly conclusion III. Conclusion I says no lion is a cat, but statement B makes every cat a lion, so there are lions that are cats (the cats themselves), and I is false. Conclusion II says no cat is a duck, but statement A makes every duck a cat, so some cats are ducks, and II is false. Statement C, that some lions are jungles, links to nothing else and decides none of the three conclusions. Only III is left, which is the first option.