Arcturus
11-18-2010, 12:04 AM
This was a logic subtest of an old version of some academic aptitude test -- I believe the LSAT. Note the peculiar subject references (encasing children in cubicles, etc).
Five children, three girls and two boys, are playing. Sometimes they arrange themselves in a circle for a game. Sometimes they arrange themselves in pairs so that one child is either left out or plays the game without a partner. Sometimes they line up in front of, behind, or beside one another. Sometimes they wear colored hats. A child is adjacent to another child when that child is immediately next to the other child.
7. In a certain game, two of the girls wear red hats; the other children wear among themselves two blue hats and one yellow hat. If they line up one behind the other, all facing the same direction, and the child fourth in line sees two girls and one boy, each wearing a different colored hat, which of the following must be true?
I. The fourth child is either a boy in a blue hat or a girl in a red hat.
II. Both boys are wearing blue hats.
III. Only one boy is wearing a blue hat.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
8. In a certain game, one girl wears a yellow hat, one boy wears a blue hat, and the other children wear red hats, but only four children play at any one time. If the four children form pairs so that the members of any one pair match in terms of sex or in terms of hat color, but not in terms of both sex and hat color, which of the following must be true?
I. If both pairs match in terms of sex, the girl in the yellow hat sits out.
II. If a girl in a red hat sits out, both pairs match in terms of hat color.
III. If one pair matches in terms of hat color and the other pair matches in terms of sex, the boy in the blue hat sits out.
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II and III only
9. In a certain game, there are three red hats, one yellow hat, and one blue hat, and both boys wear red hats. If the children form a straight line so that either the three red hats are adjacent or the three girls are adjacent, but not both, which of the following must be true?
I. The two boys are not adjacent.
II. If the first child in line is a girl in a red hat, the second in line must be a boy.
III. If there is a red hat at each end of the line, there is a girl exactly in the middle of the line.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
10. In a certain game, two of the girls wear red hats; the other children wear among themselves two blue hats and one yellow hat. If the five form a straight line so that the boys are not adjacent, and the two blue hats are not adjacent, and the two red hats are not adjacent, which of the following must be true?
(A) If two girls are adjacent, both boys must wear blue hats.
(B) If no girls are adjacent, the first child in line must be a girl in a red hat.
(C) If no girls are adjacent, both boys must wear blue hats.
(D) If no girls are adjacent and one boy wears the yellow hat, a girl in a blue hat must be either first or fifth in line.
(E) If both boys wear blue hats, the first child in line must be a girl.
11. If the five children join hands in a circle, which of the following could be true?
I. The boys are not adjacent.
II. No girl has a girl on both sides of her if no girl has a boy on both sides of her.
III. One of the girls is not holding a boy's hand.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
12. In a certain game, one child wears a yellow hat, two children wear red hats, and two children wear blue hats. The children are grouped into two pairs and one single player so that each child sees the hats on at least three other children, but neither his or her own hat nor his or her partner's hat. Two of the children are asked what they see. The first child to speak says, "I see a boy in a blue hat and two girls in red hats." The second child to speak says, "I see a girl in a yellow hat and two boys in blue hats." Which of the following must be true?
I. The child with no partner is a girl.
II. The partner of the first child to speak wears a yellow hat.
III. The partner of the second child to speak is a girl in a red hat.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
13. In a certain game one child wears a yellow hat, two children wear red hats and two children wear blue hats. The five children are placed in closed, separate cubicles, numbered 1 through 5, so that they cannot see each other. Only the children outside of the boxes can be seen. To begin the game, the children from cubicles 1, 2, and 3 come out. One of these children says, "I see two girls wearing blue hats," and then these children go back into their respective cubicles. Next, the children from cubicles 3, 4, and 5 come out. One of these children says, "I see two boys wearing red hats." Which of the following must be true?
I. The first child to speak is a girl in a yellow hat.
II. If the first child to speak comes from cubicle 1, the second child to speak is a girl in a blue hat.
III. If the first child to speak is a girl in a yellow hat, the child from cubicle 3 is a girl in a blue hat.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III only
answers:
ACCDECB
Five children, three girls and two boys, are playing. Sometimes they arrange themselves in a circle for a game. Sometimes they arrange themselves in pairs so that one child is either left out or plays the game without a partner. Sometimes they line up in front of, behind, or beside one another. Sometimes they wear colored hats. A child is adjacent to another child when that child is immediately next to the other child.
7. In a certain game, two of the girls wear red hats; the other children wear among themselves two blue hats and one yellow hat. If they line up one behind the other, all facing the same direction, and the child fourth in line sees two girls and one boy, each wearing a different colored hat, which of the following must be true?
I. The fourth child is either a boy in a blue hat or a girl in a red hat.
II. Both boys are wearing blue hats.
III. Only one boy is wearing a blue hat.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
8. In a certain game, one girl wears a yellow hat, one boy wears a blue hat, and the other children wear red hats, but only four children play at any one time. If the four children form pairs so that the members of any one pair match in terms of sex or in terms of hat color, but not in terms of both sex and hat color, which of the following must be true?
I. If both pairs match in terms of sex, the girl in the yellow hat sits out.
II. If a girl in a red hat sits out, both pairs match in terms of hat color.
III. If one pair matches in terms of hat color and the other pair matches in terms of sex, the boy in the blue hat sits out.
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II and III only
9. In a certain game, there are three red hats, one yellow hat, and one blue hat, and both boys wear red hats. If the children form a straight line so that either the three red hats are adjacent or the three girls are adjacent, but not both, which of the following must be true?
I. The two boys are not adjacent.
II. If the first child in line is a girl in a red hat, the second in line must be a boy.
III. If there is a red hat at each end of the line, there is a girl exactly in the middle of the line.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
10. In a certain game, two of the girls wear red hats; the other children wear among themselves two blue hats and one yellow hat. If the five form a straight line so that the boys are not adjacent, and the two blue hats are not adjacent, and the two red hats are not adjacent, which of the following must be true?
(A) If two girls are adjacent, both boys must wear blue hats.
(B) If no girls are adjacent, the first child in line must be a girl in a red hat.
(C) If no girls are adjacent, both boys must wear blue hats.
(D) If no girls are adjacent and one boy wears the yellow hat, a girl in a blue hat must be either first or fifth in line.
(E) If both boys wear blue hats, the first child in line must be a girl.
11. If the five children join hands in a circle, which of the following could be true?
I. The boys are not adjacent.
II. No girl has a girl on both sides of her if no girl has a boy on both sides of her.
III. One of the girls is not holding a boy's hand.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
12. In a certain game, one child wears a yellow hat, two children wear red hats, and two children wear blue hats. The children are grouped into two pairs and one single player so that each child sees the hats on at least three other children, but neither his or her own hat nor his or her partner's hat. Two of the children are asked what they see. The first child to speak says, "I see a boy in a blue hat and two girls in red hats." The second child to speak says, "I see a girl in a yellow hat and two boys in blue hats." Which of the following must be true?
I. The child with no partner is a girl.
II. The partner of the first child to speak wears a yellow hat.
III. The partner of the second child to speak is a girl in a red hat.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
13. In a certain game one child wears a yellow hat, two children wear red hats and two children wear blue hats. The five children are placed in closed, separate cubicles, numbered 1 through 5, so that they cannot see each other. Only the children outside of the boxes can be seen. To begin the game, the children from cubicles 1, 2, and 3 come out. One of these children says, "I see two girls wearing blue hats," and then these children go back into their respective cubicles. Next, the children from cubicles 3, 4, and 5 come out. One of these children says, "I see two boys wearing red hats." Which of the following must be true?
I. The first child to speak is a girl in a yellow hat.
II. If the first child to speak comes from cubicle 1, the second child to speak is a girl in a blue hat.
III. If the first child to speak is a girl in a yellow hat, the child from cubicle 3 is a girl in a blue hat.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III only
answers:
ACCDECB