The population of the town of Paxton continuously increased in the two decades 1960 through 1969and 1970 through 1979. Was the percentage increase greater in the first decade than in the second decade?
(1)The population increase in the first decade was 10,082.
(2)The population increased by the same amount in both decades.

• Statement (2) alone answers the question.
  
  Let p be the population of Paxton in 1960.
  
  Then from Statement (1) alone, the population increased by 10,082 in the first decade.
  So, the new population is p+ 10,082.
  Hence, the percentage increase in the population is 10,082/p x 100
  
  Since we don't know the population increase in the second decade, we cannot calculate the percentage increase and therefore Statement (1) alone is not sufficient.
  From Statement (2) alone, we have that the population increase was the same (say,i) in each decade.
  
  Hence, the population should be p+i at the end of the year 1969 and
  
  (p+i)+i= p+2i at the end of the second decade.
  
  So, the percentage increase in population in the first decade equals
  
  (Increase in population in the first decade)
  --------------------------------------------- x100 =i/p x100
  (The population in 1960)
  
  
  Also, the percentage increase in population in the second decade equals
  
  (Increase in population in the second decade)
  ----------------------------------------------- x 100 = i/(p+i)x 100
  (The population in 1970)
  
  Now, since both p and i are positive,i/p is greater than i/(p+i)
  
  since the numerator is the same in bothfractions and the denominator is lesser and positive.
  
  Hence, Statement (2) alone answers the question.
  
  
  The answer to the question is “Yes.Percentage increase was greater in first decade than in second decade.”
• 12 years agoHelpfull: Yes(10) No(2)
• The population of the town be initially x
  the percentage increase in the first decade=10082*100/x
  the percentage increase in the 2nd decade=10082*100/(x+10082)
  so the percentage increase greater in the first decade
• 12 years agoHelpfull: Yes(4) No(0)
• let the population of paxton in 1960 b 1,00,000(say).
  so at the end of the 1st decade population will be 1,10,082.
  therefore % increase in population will b (10,082*100)/1,00,000=10.082%
  from statement 2 increase in population in second decade is same as the 1st decade.
  i.e % increase in second decade will b (10,082*100)/1,10,082=9.15%
  hence ans is yes.
• 12 years agoHelpfull: Yes(4) No(1)
• percentage increase is greater in the first decade.
• 12 years agoHelpfull: Yes(2) No(0)