–18FIVE PEOPLE ARE TO SERVE ON A COMMITTEE TO CHOOSE A NEW...
Questions 16–18Five people are to serve on a committee to choose a new school principal. W,X, Y, and Z are teachers. S, T, U, and R are parents. The committee must haveat least two parents and at least two teachers. The committee must conform tothe following conditions:If either W or X serves on the committee, Z will not serve on the committee.If S serves on the committee, U will not serve on the committee.If U serves on the committee, R must serve on the committee.Look for similarities and differences to help you make your groups. Also considerusing lines and other marks to connect people or items that can or cannot be together.From the information given in the conditions, you can draw the following dia-gram to help you answer the questions:
2 or more
Parents
Teachers
S
W
T
X
U
Y
R
Z
5
16.
If Z serves on the committee, which of the following must also serve on thecommittee?I. SII. UIII. YA. I onlyB. II onlyC. III onlyD. I and II onlyE. I, II, and IIIC is correct. If Z serves on the committee, that eliminates W and X from serving,which leaves Y to serve as the second teacher on the committee.17.
Which of the following groups could serve as members of the committee?A. S, U, R, W, XB. S, U, W, X, YC. S, R, W, X, YD. S, R, W, X, ZE. S, T, R, X, ZC is correct. Choices A and B violate the second condition, “If S serves on thecommittee, U will not serve on the committee.” Choices D and E violate the firstcondition, “If either W or X serves on the committee, Z will not serve on the com-mittee.” This answer could have been more easily spotted by looking at the display.18. If Z is chosen to serve on the committee, each of the following lists couldcomprise the other committee members EXCEPTI. Y, S, T, RII. Y, S, U, RIII. Y, T, U, RD. I and III onlyB is correct. Option II contains S with U, which is a violation of the second condi-tion. Because the question is phrased in the negative (EXCEPT), choice B is thecorrect choice.