31. If the first two statements are true, the third statement is :
I. A toothpick is useful.
II. Useful things are valuable.
III. A toothpick is valuable.


Option “A” is correct.
To the extent that a toothpick is useful, it has value.

32. If the first two statements are true, the third statement is :
I. Tom puts on his socks before he puts on his shoes.
II. He puts on his shirt before he puts on his jacket.
III. Tom puts on his shoes before he puts on his shirt.


Option “C” is correct.
There is not enough information to verify the third statement.

33. If the first two statements are true, the third statement is :
I. Three pencils cost the same as two erasers.
II. Four erasers cost the same as one ruler.
III. Pencils are more expensive than rulers.


Option “B” is correct.
Rulers are the most expensive item.

34. If the first two statements are true, the third statement is :
I. Taking the train across town is quicker than taking the bus.
II. Taking the bus across town is slower than driving a car.
III. Taking the train across town is quicker than driving a car.


Option “C” is correct.
Both the car and the train are quicker than the bus, but there is no way to make a comparison between the train and the car.

35. If the first two statements are true, the third statement is :
I. Cloudy days tend to be more windy than sunny days.
II. Foggy days tend to be less windy than cloudy days.
III. Sunny days tend to be less windy than foggy days.


Option “C” is correct.
Cloudy days are the most windy, but there is not enough information to compare the wind on the foggy days with the wind on the sunny days.

36. If the first two statements are true, the third statement is :
I. At a parking lot, a sedan is parked to the right of a pickup and to the left of a sport utility vehicle.
II. A minivan is parked to the left of the pickup.
III. The minivan is parked between the pickup and the sedan.


Option “B” is correct.
This is the order of the cars from left to right: minivan, pickup, sedan, sport utility vehicle.

37.If the first two statements are true, the third statement is :
I. The bookstore has a better selection of postcards than the newsstand does.
II. The selection of postcards at the drugstore is better than at the bookstore.
III. The drugstore has a better selection of postcards than the bookstore or the newsstand.


Option “A” is correct.
Of the three, the drugstore has the best selection of postcards.

38. If the first two statements are true, the third statement is :
I. A jar of jelly beans contains more red beans than green.
II. There are more yellow beans than red.
III. The jar contains fewer yellow jelly beans than green ones.


Option “B” is correct.
The first two statements indicate there are more yellow jelly beans than red and green.

39. Fact 1: All dogs like to run.
Fact 2: Some dogs like to swim.
Fact 3: Some dogs look like their masters.

If the first three statements are facts, which of the following statements must also be a fact?
I: All dogs who like to swim look like their masters.
II: Dogs who like to swim also like to run.
III: Dogs who like to run do not look like their masters.


Option “B” is correct.
Statement II is the only true statement. Since all dogs like to run, then the ones who like to swim also like to run. There is no support for statement I or statement III.

40. Fact 1: Jessica has four children
Fact 2: Two of the children have blue eyes and two of the children have brown eyes.
Fact 3: Half of the children are girls.

If the first three statements are facts, which of the following statements must also be a fact?
I: At least one girl has blue eyes.
II: Two of the children are boys.
III: The boys have brown eyes.


Option “B” is correct.
Since one-half of the four children are girls, two must be boys. It is not clear which children have blue or brown eyes.

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119 thoughts on “Logical Problems”

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