–24RESULTS WERE POSTED IN 1975 AND 1990 FOR 8 DENTAL PATIE...
Questions 19–24Results were posted in 1975 and 1990 for 8 dental patients: Quincy, Sonntag,Tav, Ulmer, Vinton, Waud, Yu, and Zimino.In 1975, Ulmer’s cavities outnumbered Vinton’s cavities and outnumberedYu’s cavities; in 1990, Vinton’s cavities outnumbered Zimino’s cavities andoutnumbered Tav’s cavities.In 1975, Zimino’s cavities outnumbered Tav’s cavities; in 1990, Zimino’scavities outnumbered Waud’s cavities.In 1975, Yu’s cavities outnumbered Sonntag’s cavities; in 1990, Waud’s cavities outnumbered Yu’s cavities.In 1975, Waud’s cavities outnumbered Ulmer’s cavities and outnumberedZimino’s cavities; in 1990, Tav’s cavities outnumbered Sonntag’s cavitiesand outnumbered Ulmer’s cavities.Using the information in the conditions, the following charts could be drawn:
1975
V
W
Z
T
U
Z
Q?
V ? Y
Q?
W
S
?
U
T
S
Y
19.
Of the following, who could NOT have had the fewest number of cavitiesin either year, 1975 or 1990?A. TavB. UlmerC. VintonD. YuE. Zimino20.
A complete and accurate listing of those who could have had the fourthlowest number of cavities in 1990 would includeA. Quincy, Sonntag, and Waud.B. Quincy, Sonntag, Ulmer, and Waud.C. Quincy, Sonntag, Tav, Ulmer, and Waud.D. Quincy, Sonntag, Ulmer, Waud, Yu, and Zimino.E. Quincy, Sonntag, Tav, Ulmer, Waud, Yu, and Zimino.E is correct. Because Quincy and Sonntag are in each of the choices, you do notneed to consider them. Only Vinton, who is highest or second highest (if Quincywas highest) could not be the fourth lowest in 1990.21.
Ulmer’s number of cavities must have been greater than Yu’s in 1990 if,in 1990,A. Quincy had more cavities than Waud.B. Waud had more cavities than Sonntag.C. Tav had more cavities than Waud.D. Waud had more cavities than Ulmer.E. Ulmer had more cavities than Waud.E is correct. If Ulmer had more cavities than Waud, then Ulmer must also havemore cavities than Yu.22.
Which of the following must be true?I. Waud’s cavities in 1975 and 1990 outnumbered Ulmer’s cavities inthose years.II. Waud’s cavities in 1975 and 1990 outnumbered Yu’s cavities in thoseyears.III. Quincy’s cavities in 1975 and 1990 outnumbered Sonntag’s cavities inA. I onlyB. II onlyC. III onlyD. I and II onlyB is correct. The only definitive information in both years can be drawn betweenWaud and Yu. Waud had more cavities than Yu in both 1975 and 1990.23.
Suppose that each patient’s cavities are totaled for the two years, 1975 and1990. Which must be true?A. Waud’s total cavities are more than Quincy’s total.B. Ulmer’s total cavities are more than Sonntag’s total.C. Tav’s total cavities are more than Sonntag’s total.D. Waud’s total cavities are more than Yu’s total.E. Zimino’s total cavities are more than Yu’s total.D is correct. Only Waud’s cavities definitely outnumbered Yu’s cavities in each ofthe years; therefore, Waud’s total must be greater than Yu’s.24.
Disregarding Quincy, suppose that three patients had the same number forthe fewest cavities in 1975, and three patients had the same number for thefewest cavities in 1990. Who must have had the fewest total cavities in 1975and 1990 combined?A. SonntagB. TavC. UlmerD. VintonE. YuA is correct. Disregarding Quincy, if three patients had the same number of fewestcavities in 1975, those three patients must have been Vinton, Sonntag, and Tav,since those are the only three who could be tied with the fewest number in thatyear. Disregarding Quincy, if three patients had the same number of fewest cavi-ties in 1990, those patients must have been Yu, Sonntag, and Ulmer. SinceSonntag is the only patient who had fewest in both years, Sonntag must have hadthe fewest total cavities in both years.