The composers whose works were performed a greater number of times tha

Question

For each of the 20 composers of classical music, the table gives the year of birth, the year of death, and the number of live performances of the composer’s works in 2010.

Composer  
  Year of birth  
  Year of death  
  Number of performances  
 
  Bach 
 1685 
 1750 
 1388 
 
  Beethoven 
 1770 
 1827 
 2859 
 
  Brainns 
 1833 
 1897 
 1848 
 
  Chopin 
 1810 
 1849 
 748 
 
  Dvorak 
 1841 
 1904 
 1071 
 
  Handel  
 1685 
 1759 
 757 
 
  Haydn  
 1732 
 1809 
 989 
 
  Mendelssohn  
 1809 
 1847 
 865 
 
  Mozart 
 1756 
 1791 
 3035 
 
  Prokofiev 
 1891 
 1953 
 931 
 
  Puccini 
 1858 
 1924 
 723 
 
  Raclunaninov 
 1873 
 1943 
 673 
 
  Ravel 
 1875 
 1937 
 864 
 
  Schubert 
 1797 
 1828 
 1023 
 
  Schumann 
 1810 
 1856 
 1460 
 
  Shostakovich 
 1906 
 1975 
 779 
 
  Strauss 
 1864 
 1949 
 720 
 
  Stravinsky 
 1882 
 1971 
 849 
 
  Tchaikovsky 
 1840 
 1893 
 2295 
 
  Verdi 
 1813 
 1901 
 845 
 
  Total 
 - 
 - 
 24722

For each of the following statements about the composers listed in the table, select  Yes  if the statement accurately reflects the information in the table. Otherwise, select  No .

Usernamevisible · Answer

The composers whose works were performed a greater number of times than the median number of performances were all born in the 1700s or the 1800s. — No
The 5 composers with the least number of performances accounted for less than 15 percent of the total number of performances. — Yes
For the composer whose works were performed the greatest number of times, the number of performances is at least 300 percent greater than for the composer whose works were performed the least number of times. — Yes
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Verification

1. Median number of performances

* 20 composers ⇒ median = average of 10th and 11th values.
* Median = ((865 + 931)/2 = 898).
* Composers with more than 898 performances include Bach, who was born in 1685.
* Therefore, they were not all born in the 1700s or 1800s. → No

---

2. Five least-performed composers

* (673 + 720 + 723 + 748 + 757 = 3621)
* Percentage of total:
 3621/24722} = 0.1465 = 14.65% ]
* (14.65% < 15%). → Yes

---

3. Greatest vs. least performances

* Greatest = 3035 (Mozart)
* Least = 673 (Rachmaninov)
* “300% greater than” means at least (4 	imes) as many:
  
* (3035 > 2692). → Yes

abhargav23 · Answer

Any particular method how this question could be solved quickly? Especially 2nd part?

peeps88 · Answer

Yes, It took me 4 mins to solve this and such kind of questions, how can i solve such questions quickly

alamin8 · Answer

The second one was easy because you need to just add the five numbers and then divide by the total. It takes 30 seconds.

FrozenDragon · Answer

My suggestion would be to notice --- what exactly we need here before opening calculator or doing mental maths. Example for this 2nd part of the question we need to know if 5 least number of performance account to less than 15 percent of total performance ?

So before doing anything, find total number of performance because that's the most crucial part in this question. once we get that number, do the calculation : 15% of 24722 = 3708

So now our question is : is addition of 5 least number of performance less than 3708

Here you can notice that average of 5 performance is somewhere around 720 ( Lowest is 673 and highest is 757. we don't need calculator for this, we can rely on approximation)

720 *5 =3600 (which is less than 3708)

I hope this helps

egmat · Answer

Hi abhargav23,

Good instinct to look for a shortcut here. The efficient move on  all three  parts is to turn a "compute the exact figure" task into a "compare against a benchmark" task, and your Part  2  worry is the clearest example of that.

Part 2 - the fast route

The slow way (what the thread does) is: add the five smallest, then divide by the total and read off a percentage like  14.65% . You don't need the exact percentage at all - the statement only asks  less than 15%?

So flip it:

1.  Sort the "Number of performances" column ascending.  The five smallest jump to the bottom instantly - no visual hunting across  20  rows.
2.  Turn 15% into a raw benchmark.15%  of the total (~ 24,722 ) is about  3,708 . That's your finish line.
3.  Sum the five smallest and just compare.  Their sum (~ 3,621 ) sits  below  3,708 , so the share is under  15%  - the comparison alone answers it. No division needed.

Computing  15%  of the total  once  is much lighter than computing a precise percentage from an awkward sum.

Same trick on Parts 1 and 3

-  Part 1 (median):  sort the column, average the  10th  and  11th  values, then scan only the rows  above  that line and check their birth years - you never touch the rows below.
-  Part 3 ("300% greater"):  "300% greater" means "at least  4× ." Multiply the smallest value by  4  and compare to the largest - one multiplication, no percentage formula.

Mini-rehearsal

Values  10, 20, 30, 40 , total  100 . "Do the bottom two make up less than  25% ?"  25%  of  100  =  25  (benchmark first). Bottom two =  10  +  20  =  30  >  25  - No. Notice you decided it by comparing sums, never by computing an exact percent.

Apply that benchmark-first habit to your table's values and each part collapses to one quick comparison.

The composers whose works were performed a greater number of times tha

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Composer	Year of birth	Year of death	Number of performances
Bach	1685	1750	1388
Beethoven	1770	1827	2859
Brainns	1833	1897	1848
Chopin	1810	1849	748
Dvorak	1841	1904	1071
Handel	1685	1759	757
Haydn	1732	1809	989
Mendelssohn	1809	1847	865
Mozart	1756	1791	3035
Prokofiev	1891	1953	931
Puccini	1858	1924	723
Raclunaninov	1873	1943	673
Ravel	1875	1937	864
Schubert	1797	1828	1023
Schumann	1810	1856	1460
Shostakovich	1906	1975	779
Strauss	1864	1949	720
Stravinsky	1882	1971	849
Tchaikovsky	1840	1893	2295
Verdi	1813	1901	845
Total	-	-	24722

Yes	No
		The composers whose works were performed a greater number of times than the median number of performances were all born in the 1700s or the 1800s.
		The 5 composers with the least number of performances accounted for less than 15 percent of the total number of performances.
		For the composer whose works were performed the greatest number of times, the number of performances is at least 300 percent greater than for the composer whose works were performed the least number of times.

GMAT Graphs and Tables (G&T) Questions

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