8. Peasants were often faced with a vicious cycle. The manure from their animals was essential for fertilizing their crops, but they often did not have enough crops to feed themselves and their animals, and hence had to slaughter the animals for food.
The cycle is called vicious because
(A) without the animals the peasants would lack the manure for growing their crops
(B) the peasants would become dependent on those who slaughtered the animals
(C) the peasants would want meat in their diet and would be forced to purchase it
(D) successful farming demanded that a farmer rotate crops from one field to another
(E) the animals are faced with starvation
Questions 9-14
Exactly five lights-a green one, a yellow one, a red one, a white one, and a blue one-are arrayed in a straight line on a control panel evenly spaced, going from left to right in the order given above. On the control panel, there can be two types of patterns of lights that are on, called X-sequences and Y-sequences.
An X-sequence of lights is a sequence of either three or four lights that are on and evenly spaced with respect to one another.
A Y-sequence of lights is any sequence of lights that are on that is not an X-sequence.
9. Which of the following could be the lights on in a Y-sequence of lights?
(A) Green, yellow, red
(B) Yellow, red, white
(C) Yellow, white, blue
(D) Red, white, blue
(E) Yellow, red, white, blue
10. Which of the following X-sequences of lights must remain an X-sequence if an additional light is turned on?
(A) Green. yellow, red
(B) Green, red, blue
(C) Yellow, red, white
(D) Red, white, blue
(E) Yellow, red, white, blue
11. Which of the following lights must be on in any X-sequence of lights?
(A) Green
(B) Yellow
(C) Red
(D) White
(E) Blue
12. Which of the following X-sequences of lights must turn into a Y-sequence if any one of the five lights is changed, whether the change is from on to off, or from off to on?
(A) Green, yellow, red
(B) Green, red, blue
(C) Yellow, red, white
(D) Green, yellow, red, white
(E) Yellow, red, white, blue
13. Which of the following operations, if performed on an X-sequence of lights, must result in a Y-sequence?
(A) Turning on one more of the lights
(B) Turning on two more of the lights
(C) Turning off one of the lights that are on
(D) Changing the green light to on if it is off, or to off if it is on
(E) Changing the blue light to on if it is off, or to off if it is on
14. Which of the following operations can be performed only on a Y-sequence of lights?
(A) Turning on two more of the lights
(B) Turing on three more of the lights
(C) Turning off two of the lights that are on
(D) Turning off three of the lights that are on
(E) Turning off four of the lights that are on