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In 1972, country X had a population of P and Meases of meningitis, fo

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Bunuel
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In 1972, country X had a population of P and Meases of meningitis, fo [#permalink] New post   12 Feb 2018, 00:45
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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
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E
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In 1972, country X had a population of P and Meases of meningitis, fo [#permalink] New post   Updated on: 12 Feb 2018, 02:18
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In 1972

Population= P
meningitis= M

Original Per capita= \(\frac{M}{P}\)
After 10 years

Population= 1.5P (Increased by 50%)
meningitis= 0.5M (Decreased by 50%)

New Per Capita= \(\frac{0.5M}{1.5P}\)= \(\frac{M}{3P}\)


Changed per capita= \(\frac{M}{P}\)- \(\frac{M}{3P}\)= \(\frac{2M}{3P}\)

% Change= \(\frac{2M}{3P}\)*\(\frac{P}{M}\) *100= 66.66%

Answer: E.

Originally posted by varun4s on 12 Feb 2018, 01:42.
Last edited by varun4s on 12 Feb 2018, 02:18, edited 1 time in total.
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gmatexam439
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In 1972, country X had a population of P and Meases of meningitis, fo [#permalink] New post   Updated on: 12 Feb 2018, 01:56
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Bunuel wrote:
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


IMO Answer=E

Original per capita rate=\(\frac{M}{P}\)
New per capita rate = \(\frac{0.5M}{1.5P}\)

%Change= (\(\frac{0.5M}{1.5P}\) - \(\frac{M}{P}\))/\(\frac{M}{P}\) = \(\frac{(0.5-1.5)}{1.5}\) =\(\frac{-1}{1.5}\) = \(\frac{-10}{15}\)*100 = -66.66%

Originally posted by gmatexam439 on 12 Feb 2018, 01:50.
Last edited by gmatexam439 on 12 Feb 2018, 01:56, edited 2 times in total.
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Re: In 1972, country X had a population of P and Meases of meningitis, fo [#permalink] New post   12 Feb 2018, 01:52
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Bunuel wrote:
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


It can never be same

Initial rate M/P
Change.. M to 0.5M and P to 1.5P
New rate = 0.5M/1.5P= M/3P..

Change = M/P-M/3P= 2M/3P..
% change =2*100/3=66 2/3%
E
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Re: In 1972, country X had a population of P and Meases of meningitis, fo [#permalink] New post   12 Feb 2018, 02:19
Edited my solution. Thanks
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Re: In 1972, country X had a population of P and Meases of meningitis, fo [#permalink] New post   13 Feb 2018, 18:01
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Bunuel wrote:
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


The original rate was M/P and the new rate was 0.5M/1.5P = (M/2)/(3P/2) =2M/6P = M/3P. The percent change was:

(M/3P - M/P)/(M/P) x 100

(M/3P - 3M/3P)/(M/P) x 100

-2M/3P x P/M x 100

-2/3 x 100 = 66 2/3 percent decrease

Answer: E
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Re: In 1972, country X had a population of P and Meases of meningitis, fo [#permalink] New post   09 Aug 2020, 01:07
Hello from the GMAT Club BumpBot!

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Re: In 1972, country X had a population of P and Meases of meningitis, fo [#permalink]
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