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Joined: 20 Feb 2017
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In 1972, country X had a population of P and M cases of meni
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02 Jan 2020, 00:07
02 Jan 2020, 00:07
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In 1972, country X had a population of P and M cases of meningitis, for a per capita rate of meningitis of M/P . If, over the next ten years, the number of cases of meningitis decreased by 50% and the population of country X increased by 50%, what is the percentage change in the per capita rate of meningitis over the ten-year period?
(A) 33 1/3 % increase
(B) no change
(C) 33 1/3 % decrease
(D) 50% decrease
(E) 66 2/3 % decrease
(A) 33 1/3 % increase
(B) no change
(C) 33 1/3 % decrease
(D) 50% decrease
(E) 66 2/3 % decrease
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Re: In 1972, country X had a population of P and M cases of meni
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02 Jan 2020, 08:30
02 Jan 2020, 08:30
2
In 1972
Population = P
Meningitis = M
per capita rate of meningitis = M/P
In 10 years
The number of cases of meningitis decreased by 50% => Cases of meningitis in 10 years = 50% of cases of meningitis inn 1972 = 50% of M = 0.5M
The population of country X increased by 50% => Population in 10 years = Population in 1972 + 50% of Population in 1972 = P + 50%*P = P + 0.5P = P(1+0.5) = 1.5P
per capita rate of meningitis = cases of meningitis/Population = 0.5M/1.5P = M/3P
Percentage change in per capita rate of meningitis = (Old Value - New Value)*100/Old Value = ((M/P) - (M/3P))*100 / (M/P) = (1-(1/3)) * 100 = 200/3% = 66.67% or 66 2/3% decrease
So, Answer will be E
Hope it helps!
Population = P
Meningitis = M
per capita rate of meningitis = M/P
In 10 years
The number of cases of meningitis decreased by 50% => Cases of meningitis in 10 years = 50% of cases of meningitis inn 1972 = 50% of M = 0.5M
The population of country X increased by 50% => Population in 10 years = Population in 1972 + 50% of Population in 1972 = P + 50%*P = P + 0.5P = P(1+0.5) = 1.5P
per capita rate of meningitis = cases of meningitis/Population = 0.5M/1.5P = M/3P
Percentage change in per capita rate of meningitis = (Old Value - New Value)*100/Old Value = ((M/P) - (M/3P))*100 / (M/P) = (1-(1/3)) * 100 = 200/3% = 66.67% or 66 2/3% decrease
So, Answer will be E
Hope it helps!
Re: In 1972, country X had a population of P and M cases of meni
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04 Sep 2020, 20:47
04 Sep 2020, 20:47
2
Let original population = P = 100
Let original meningitis cases = M = 100
Original P = 100
New P (after 50% inc) = 150
Original M = 100
New M (after 50% dec) = 50
Original M/P = 100/100 = 1
New M/P = 50/150 = 1/3
Percent Change = (New - Old)/Old
= (1/3 - 1)/1
= -0.66 decrease - Option E
Let original meningitis cases = M = 100
Original P = 100
New P (after 50% inc) = 150
Original M = 100
New M (after 50% dec) = 50
Original M/P = 100/100 = 1
New M/P = 50/150 = 1/3
Percent Change = (New - Old)/Old
= (1/3 - 1)/1
= -0.66 decrease - Option E
