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Statement 1: Elizabeth has four children.<br />Statement 2: Two of the children have blue eyes and two of the children have brown eyes.<br />Statement 3: Half of the children are girls.<br />If the first three statements are facts, which of the following statements must also be a fact? a. At least one girl has blue eyes.<br />b. Two of the children are boys.<br />c. The boys have brown eyes.

Correct Answer: b only

Since half of the four children are girls, two must be boys. It is not clear which children have blue or brown eyes. So only statement (b) follows.

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.

The film director wants an actress for the lead role of Lucy who perfectly fits the description that appears in the original screenplay. He is not willing to consider actresses who do not resemble the character as she is described in the screenplay, no matter how talented they are. The screenplay describes Lucy as an average-sized, forty something redhead, with deep brown eyes, very fair skin, and a brilliant smile. The casting agent has four actresses in mind.

Actress #1 : is a stunning red-haired beauty who is 5'9" and in her mid-twenties. Her eyes are brown and she has an olive complexion.
Actress #2 : has red hair, big brown eyes, and a fair complexion. She is in her mid-forties and is 5'5".
Actress #3 : is 5'4" and of medium build. She has red hair, brown eyes, and is in her early forties.
Actress #4 : is a blue-eyed redhead in her early thirties. She's of very slight build and stands at 5'.

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.

Fact 1: All hats have brims.
Fact 2: There are black hats and blue hats.
Fact 3: Baseball caps are hats.

If the first three statements are facts, which of the following statements must also be a fact?
I: All caps have brims.
II: Some baseball caps are blue.
III: Baseball caps have no brims.

Fact 1: Robert has four vehicles.
Fact 2: Two of the vehicles are red.
Fact 3: One of the vehicles is a minivan.

If the first three statements are facts, which of the following statements must also be a fact?
I: Robert has a red minivan.
II: Robert has three cars.
III: Robert's favorite color is red.

h,J,K,L,M,N and O are the only legislators eligible to vote on Bills 1,2 and 3, each of which will be passed if at least four legislators eligible vote in favor of it. each legislator must vote on all three bills; on abstentions are possible. The following is known : *H must vote against all three bills; each of the other legislators must vote in favor of at least one bill and against at lest one bill. *j must vote against Bills 1. *O Must vote against Bills 2 and 3. * L must the same way that K dose on all three bills.*N must vote the same way that O dose on all three bills. If M votes the same way that O dose on all three bills, which of the following can be determined ?

h,J,K,L,M,N and O are the only legislators eligible to vote on Bills 1,2 and 3, each of which will be passed if at least four legislators eligible vote in favor of it. each legislator must vote on all three bills; on abstentions are possible. The following is known : *H must vote against all three bills; each of the other legislators must vote in favor of at least one bill and against at lest one bill. *j must vote against Bills 1. *O Must vote against Bills 2 and 3. * L must the same way that K dose on all three bills.*N must vote the same way that O dose on all three bills. which of the following must vote in favor of Bill 1 ?

h,J,K,L,M,N and O are the only legislators eligible to vote on Bills 1,2 and 3, each of which will be passed if at least four legislators eligible vote in favor of it. each legislator must vote on all three bills; on abstentions are possible. The following is known : *H must vote against all three bills; each of the other legislators must vote in favor of at least one bill and against at lest one bill. *j must vote against Bills 1. *O Must vote against Bills 2 and 3. * L must the same way that K dose on all three bills.*N must vote the same way that O dose on all three bills. If any bill is to be passed,which of the following must be among the legislators who vote in favor of it?

h,J,K,L,M,N and O are the only legislators eligible to vote on Bills 1,2 and 3, each of which will be passed if at least four legislators eligible vote in favor of it. each legislator must vote on all three bills; on abstentions are possible. The following is known : *H must vote against all three bills; each of the other legislators must vote in favor of at least one bill and against at lest one bill. *j must vote against Bills 1. *O Must vote against Bills 2 and 3. * L must the same way that K dose on all three bills.*N must vote the same way that O dose on all three bills. which of the following cannot be true ?

h,J,K,L,M,N and O are the only legislators eligible to vote on Bills 1,2 and 3, each of which will be passed if at least four legislators eligible vote in favor of it. each legislator must vote on all three bills; on abstentions are possible. The following is known : *H must vote against all three bills; each of the other legislators must vote in favor of at least one bill and against at lest one bill. *j must vote against Bills 1. *O Must vote against Bills 2 and 3. * L must the same way that K dose on all three bills.*N must vote the same way that O dose on all three bills. The maximum number of favorable votes that Bill 2 could receive is ---