section iv
time—35 minutes
23 questions
directions: each group of questions in this section is based on a set of conditions. in answering some of the questions it may be useful to draw a rough diagram. choose the response that most accurately and completely answers each questions and blacken the corresponding space on your answer sheet.
questions 1-5
in certain recipe contest each contestant submits submits two recipes. one for an appetizer and one for a main dish together the two recipes must include exactly seven flavorings—fenugreek, ginger, lemongrass, nutmeg, paprika, saffron, and turmeric—with no flavoring included in more than one of the two recipes. each contestant s recipes must satisfy the following conditions
the appetizer recipe includes at most three of the flavorings.
fenugreek is not included in the same recipe as nutmeg.
saffron is not included in the same recipe as turmeric
ginger is included in the same recipe as nutmeg
1. which one of the following could be a complete and accurate list of the flavorings included in one contestant s main-dish recipe?
(a) fenugreek, lemongrass, saffron
(b) fenugreek, ginger, nutmeg, turmeric
(c) ginger, lemongrass, nutmeg, paprika
(d) ginger, nutmeg, paprika, turmeric
(e) lemongass nutmeg, saffron, turmeric
2. if a contestant s appetizer recipe does not include fenugreek, then the contestant s appetizer recipe must include
(a) ginger
(b) lemongrass
(c) paprika
(d) saffron
(e) turmeric
3. which one of the following could be a list of all of the flavorings included in one contestant s appetizer recipe?
(a) fenugreek, saffron
(b) ginger, nutmeg
(c) fenugreek, nutmeg, turmeric
(d) lemongrass, nutmeg, saffron
(e) fenugreek, lemongrass, paprika, turmeric
4. if a contestant includes lemongrass in the same recipe as paprika, which one of the following is a flavoring that must be included in the contestant s main-dish recipe?
(a) ginger
(b) lemongrass
(c) nutmeg
(d) saffron
(e) turmeric
5. if the condition that requires ginger to be included in the same recipe as nutmeg is suspended but all of the other original conditions remain in effect. then which one of the following could be a list of all of the flavorings included in one contestant s main-dish recipe?
(a) ginger, lemongrass, nutmeg, paprika
(b) ginger, lemongrass, paprika, turmeric
(c) fenugreek, ginger, lemongrass, paprika, saffron
(d) fenugreek, ginger, lemongrass, saffron, turmeric
(d) fenugreek,lemongrass, nutmeg, paprika, saffron
questions 6-10
seven singer—jamine, ken, lalitha, maya, norton, olive, and patrick—will be scheduled to perform in the finals of a singing competition. during the evening of the competition, each singer, performing alone, will give exactly one performance. the schedule for the evening must conform to the following requirements.
jamle performs immediately after ken
parick performs at some time after maya
lalitha performs third only if norton performs fifth.
if patrick does not perform second, he performs fifth
6. which one of the following is an acceptable schedule for the evening s performers, from first through seventh?
(a) ken, jamie, maya, lalitha, patrick norton, olive
(b) lalitha, patrick, norton, olive maya, ken, jamie
(c) norton, olive ken, jamie, maya, patrick, lalitha
(d) olive, maya, ken, lalitha, patrick, norton, jamie
(e) olive, maya, lalitha, norton,patrick, ken jamie
7. if lalitha is scheduled for the third performance which one of the following must be scheduled for the sixth performance?
(a) jame
(b) ken
(c) norton
(d) olive
(e) patrick
8. if norton is scheduled for the fifth performance, which one of the following could be true?
(a) jamie is scheduled for the sixth performance
(b) ken is scheduled for the second performance
(c) lalitha is scheduled for the fourth performance.
(d) maya is scheduled for the third performance
(e) olive is scheduled for the first performance
9. if maya is scheduled for the performance. which one of the following could be true?
(a) jamie is scheduled for the sixth performance
(b) ken is scheduled forthe fourth performance
(c) lalitha is scheduled for the third performance
(d) norton is scheduled for the fifth performance
(e) olive is scheduled for the fourth performance
10. if jamie s performance is scheduled to be immediately before lalitha s performance, jamie s performance cannot be scheduled to be
(a) second
(b) third
(c) fourth
(d) fifth
(e) sixth
questions 11-17
at a small press, six texbooks, three introductory—f. g. and h—and three advanced—x, y, and z—will each be evaluated once by the editor, juarez, and once by the publisher. rosenberg, during six consecutive wees—week 1 through week 6 each evaluator evatuates exactly one textbook per week. no textbook will be evaluated by juarez and rosenberg during the same week. the following additional constraints apply.
rosenbery cannot evaluate any introductory textbook until juarez has evaluated that textbook.
juarez cannot evaluate any advanced textbook until
rosenberg has evaluated that textbook
rosenberg cannot evaluate any two introductory textbooks consecutively
juarez must evaluate x during week 4.
11. which one of the following is an acceptable evaluation schedule with the textbooks listed in order of evaluation from week 1 through week 6?
(a) juarez f. g. x. z. h. y
rosenberg x. f. z. g. y. h
(b) juarez: f, y, g, x, h, z
rosenberg, y, f, x, g, z, h
(c) juarez g, h, f, x, y, z
rosenberg x, g, h, y, z, f
(d) juarez g, z, f, z, h, y,
rosenberg z, f, x, g, y, h
(e) juarez h, y, f, x, g, z
rosenberg x, h, z, f, y, g
12. if juarez evaluates h during week 3 and rosenberg evaluates g during week 6, which one fo the following must be true?
(a) juarez evaluates f during week 1
(b) juarez evaluates g during week 2.
(c) juarez evaluates z during week 6.
(d) rosenberg evaluates x during week 1
(e) rosenberg evaluates y during week 5.
13. if juarez evaluates z during week 2, then rosenberg must evaluate which one of the following textbooks during week 5?
(a) f
(b) h
(c) x
(d) y
(e) z
14. which one of the following must be true?
(a) rosenberg evaluates h during week 6
(b) rosenberg evaluates an advanced textbook during week 3
(c) juarez evaluates an advanced textbook during week 2.
(d) juarez evaluates y before evaluating g.
(e) juarez does not evaluate any two introductroy textbooks consecutively
15. if rosenberg evaluates x during week 1 and f during week 2, which one of the following could be true?
(a) x is the third of the advanced textbooks to be evaluated by juarez.
(b) y is the first of the advanced textbooks to be evaluated by juarez.
(c) juarez does not evaluate any two introductory texbooks in a row.
(d) juarez evaluates g during week 5.
(e) juarez evaluates z during week 6.
16. which one of the following is a complete and accurate list of the those weeks during which juarez must evaluate an introductory textbook?
(a) week 1
(b) week 6
(c) week 1, week 5
(d) week 1, week 2, week 3
(e) week 1, week 3, week 5.
17. which one of the following could be true?
(a) juarez evaluates f during week 6
(b) juarez evaluates z during week 1
(c) rosenberg evaluates f during week 3.
(d) rosenberg evaluates h during week 2.
(e) rosenberg evaluates x during week 5
questions 18-23
nine different treatments are available for a certain illness: three antibioties—f, g, and h—three dietary regimens—m, n and o—and three physical therapies—u, y, and w, for each case of the illness, a doctor will prescribe exactly five of the treatments, in accordance with the following conditions.
if two of the antibioties are prescribed, the remaining antibiotie cannot be prescribed
there must be exactly one dietary regimen prescribed
if o is not prescribed f cannot be prescribed
if w is prescribed f cannot be prescribed
g cannot be prescribed if both n and u are prescribed
v cannot be prescribed unless both h and m are prescribed
18. which one of the following could be the five treatments prescribed for a given case?
(a) f, g, h, m, v
(b) f, g, m, o, v
(c) f, h, m, o, w
(d) g, h, n, u, w
(e) g, h, o, u, w
19. which one fo the following could be the antibioties and physical therapies prescribed for a given case?
(a) f, g, h, w,
(b) f, g, u, v
(c) f, u, v, w
(d) g, u, v, w
(e) h, u, v, w
20. if o is prescribed for a given case, which one of the following is a pair of treatments both of which must also be prescribed for that case?
(a) f, m
(b) g, v
(c) n, u
(d) u, v
(e) u, w
21. if g is prescribed for a given case which one of the following is a pair of treatments both of which could also be prescribed for that case?
(a) f, m
(b) f, n
(c) n, v
(d) o, v
(e) v, w
22. which one of the following is a list of three treatments that could be prescribed together for a given case?
(a) f, m, u
(b) f, o, w
(c) g, n, v
(d) g, v, w
(e) h, n, v
23. which one of the following treatments cannot be prescribed for any case?
(a) g
(b) m
(c) n
(d) u
(e) w