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The total number of musicians, not counting soloists, whom the SSO must contract for the entire spring season is 97.: Yes
The average number of strings required by the compositions in the program for Performance C is smaller than the average number of strings required by the compositions in the program of either of the other two performances.: Yes
If a composition requires 8 woodwinds, the probability that it was not composed by Sanford, M. is 33%.: No
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Difficulty:
95%
(hard)
Question Stats:
29% (03:38) correct
71%
(03:33)
wrong
based on 326
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The Springfield Symphony Orchestra (SSO) is planning three performances in the spring: Performance A, B, and C. The table shows the compositions included in the program for each performance as well as the number of instruments of each instrument group needed for each composition. The number of instruments required for each composition also equals the number of musicians for that composition: No musician will play more than one instrument in each piece. Each musician will be contracted for the entire spring season, even though he or she may not need to play on all compositions.
(Sort ↕ the table by clicking on the headers)
For each of the following statements, select Yes if the statement can be shown to be true based on the information in the table. Otherwise, select No.
| Composition | Composer | Performance | Woodwinds | Brass | Percussion | Strings | Solo Instrument |
|---|---|---|---|---|---|---|---|
| Concerto for 3 Violins | Kwan | B | 16 | 15 | 2 | 62 | 3 |
| Concerto for Cello | Sanford, M. | C | 8 | 6 | 1 | 21 | 1 |
| Concerto for Clarinet | Sanford, M. | A | 9 | 6 | 1 | 21 | 1 |
| Concerto for Piano #4 | Baranko | B | 8 | 4 | 1 | 51 | 1 |
| Phaedra Overture | Sanford, L. | A | 8 | 12 | 1 | 45 | 0 |
| Romance for Strings | Zlatan | B | 0 | 0 | 0 | 21 | 0 |
| Serenade for Strings | Mysel | C | 0 | 0 | 0 | 31 | 0 |
| Symphony #2 | Baranko | A | 14 | 14 | 2 | 51 | 0 |
| Symphony #7 | Limoges | C | 16 | 16 | 3 | 54 | 0 |
For each of the following statements, select Yes if the statement can be shown to be true based on the information in the table. Otherwise, select No.
| Yes | No | |
| The total number of musicians, not counting soloists, whom the SSO must contract for the entire spring season is 97. | ||
| The average number of strings required by the compositions in the program for Performance C is smaller than the average number of strings required by the compositions in the program of either of the other two performances. | ||
| If a composition requires 8 woodwinds, the probability that it was not composed by Sanford, M. is 33%. |
ShowHide Answer
Official Answer
The total number of musicians, not counting soloists, whom the SSO must contract for the entire spring season is 97.: Yes
The average number of strings required by the compositions in the program for Performance C is smaller than the average number of strings required by the compositions in the program of either of the other two performances.: Yes
If a composition requires 8 woodwinds, the probability that it was not composed by Sanford, M. is 33%.: No
17 Dec 2023, 12:33
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Official Explanation
The total number of musicians, not counting soloists, whom the SSO must contract for the entire spring season is 97.
Explanation
The most woodwinds players that the SSO needs is 16, for Kwan’s Concerto for 3 Violins and for Limoges’ Symphony #7. The most brass players that it needs is 16, also for Limoges’ Symphony #7. The most percussion players that it needs is 3, again for Limoges’ Symphony #7. The most string players it needs is 62, for Kwan’s Concerto for 3 Violins. The total number of musicians, not counting soloists, whom the SSO must contract for the entire spring season is the sum of these four numbers, which is 97.
Answer: Yes
The average number of strings required by the compositions in the program for Performance C is smaller than the average number of strings required by the compositions in the program of either of the other two performances.
Explanation
Sort by “Performance.” You don’t need to calculate the averages: rather, eyeball the table and save some time. One of the compositions in each program requires 21 strings, so these compositions cancel one another out. The other two compositions for each performance require 51 and 45 strings (Performance A), 51 and 62 strings (Performance B), and 54 and 31 (Performance C). It is clear that the 31 strings required by Performance C’s Serenade for Strings bring the average number of strings for Performance C down considerably, compared to those averages for the other two performances.
Answer: Yes
If a composition requires 8 woodwinds, the probability that it was not composed by Sanford, M. is 33%.
Explanation
Three compositions require 8 woodwinds, and two of them were not composed by Sanford, M.; one was composed by Sanford, L. and the other by Baranko. Thus, if a composition requires 8 woodwinds, the probability that it was not composed by Sanford, M. is 67%, not 33%.
Answer: No
The total number of musicians, not counting soloists, whom the SSO must contract for the entire spring season is 97.
Explanation
The most woodwinds players that the SSO needs is 16, for Kwan’s Concerto for 3 Violins and for Limoges’ Symphony #7. The most brass players that it needs is 16, also for Limoges’ Symphony #7. The most percussion players that it needs is 3, again for Limoges’ Symphony #7. The most string players it needs is 62, for Kwan’s Concerto for 3 Violins. The total number of musicians, not counting soloists, whom the SSO must contract for the entire spring season is the sum of these four numbers, which is 97.
Answer: Yes
The average number of strings required by the compositions in the program for Performance C is smaller than the average number of strings required by the compositions in the program of either of the other two performances.
Explanation
Sort by “Performance.” You don’t need to calculate the averages: rather, eyeball the table and save some time. One of the compositions in each program requires 21 strings, so these compositions cancel one another out. The other two compositions for each performance require 51 and 45 strings (Performance A), 51 and 62 strings (Performance B), and 54 and 31 (Performance C). It is clear that the 31 strings required by Performance C’s Serenade for Strings bring the average number of strings for Performance C down considerably, compared to those averages for the other two performances.
Answer: Yes
If a composition requires 8 woodwinds, the probability that it was not composed by Sanford, M. is 33%.
Explanation
Three compositions require 8 woodwinds, and two of them were not composed by Sanford, M.; one was composed by Sanford, L. and the other by Baranko. Thus, if a composition requires 8 woodwinds, the probability that it was not composed by Sanford, M. is 67%, not 33%.
Answer: No
General Discussion
13 Dec 2023, 19:00
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Sir Explanation please
