## Logical Problems

#### Logical Problems

Direction: Pick the correct option for the given questions.

1. Children are in pursuit of a dog whose leash has broken. James is directly behind the dog. Ruby is behind James. Rachel is behind Ruby. Max is ahead of the dog walking down the street in the opposite direction. As the children and dog pass, Max turns around and joins the pursuit. He runs in behind Ruby. James runs faster and is alongside the dog on the left. Ruby runs faster and is alongside the dog on the right. Which child is directly behind the dog?

1. After all the switches were made, Max is directly behind the dog, James is alongside the dog on the left.

##### Correct Option: D

After all the switches were made, Max is directly behind the dog, James is alongside the dog on the left, Ruby is alongside the dog on the right, and Rachel is behind Max.

Direction: The logic problems in this set present you with three true statements : Fact 1, Fact 2, and Fact 3. Then, you are given three more statements (labeled I, II, and III), and you must determine which of these, if any, is also a fact. One or two of the statements could be true; all of the statements could be true; or none of the statements could be true. Choose your answer based solely on the information given in the first three facts.

1. 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.

1. 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.

##### Correct Option: B

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.

1. Fact 1 : Mary said, “Ann and I both have cats.”
Fact 2 : Ann said, “I don’t have a cat.”
Fact 3 : Mary always tells the truth, but Ann sometimes lies.
If the first three statements are facts, which of the following statements must also be a fact?
I. Ann has a cat.
II. Mary has a cat.
III. Ann is lying.

1. If Mary always tells the truth, then both Ann and Mary have cats

##### Correct Option: C

If Mary always tells the truth, then both Ann and Mary have cats (statements I and II), and Ann is lying (statement III).

1. Fact 1 : Some pens don’t write.
Fact 2 : All blue pens write.
Fact 3 : Some writing utensils are pens.
If the first three statements are facts, which of the following statements must also be a fact?
I. Some writing utensils don’t write.
II. Some writing utensils are blue.
III. Some blue writing utensils don’t write.

1. Since some pens don’t write, some writing utensils don’t write (statement I). Since there are blue pens and since pens are writing utensils, some writing utensils are blue (statement II).

##### Correct Option: B

Since some pens don’t write, some writing utensils don’t write (statement I). Since there are blue pens and since pens are writing utensils, some writing utensils are blue (statement II). There is not enough information to support statement III.

1. Fact 1 : Eyeglass frames cost between \$35 and \$350.
Fact 2 : Some eyeglass frames are made of titanium.
Fact 3 : Some eyeglass frames are made of plastic.
If the first three statements are facts, which of the following statements must also be a fact?
I. Titanium eyeglass frames cost more than plastic frames.
II. Expensive eyeglass frames last longer than cheap frames.
III. Only a few eyeglass frames cost less than \$35.

1. There is no information in the facts to support statements I or II.

##### Correct Option: D

There is no information in the facts to support statements I or II. Statement III is clearly wrong because, according to Fact 1, no frames cost less than \$35.