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Over the past year, the number of men in Pleasantville
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09 Feb 2018, 09:01
09 Feb 2018, 09:01
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Question Stats:
76% (02:30) correct
23% (02:26) wrong based on 93 sessions
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Over the past year, the number of men in Pleasantville increased by 20% while the number of women in Pleasantville decreased by 20%. If the number of men and women in Pleasantville are now equal to each other, what was the percentage change in the total population of Pleasantville over the past year?
10% decrease
4% decrease
no change
4% increase
10% increase
10% decrease
4% decrease
no change
4% increase
10% increase
Re: Over the past year, the number of men in Pleasantville
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09 Feb 2018, 15:23
09 Feb 2018, 15:23
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Expert Reply
Let the number of men in the past be \(x\) and let number of women be \(y\). Also assume currently the number of both men and women are 100 each.
So with 20% increase for men we can say \(1.2 \times x = 100\) or \(x=83.33\).
Also with 20% decrease for women we can say \(0.8 \times y = 100\) or \(y=125\).
Population in the past\(=x+y=83.33+125=208.33\).
Present population =\(100+100=200\).
% decrease= \(\frac{208.33-200}{208.33} \approx 3.99\).
Hence option B is correct!
So with 20% increase for men we can say \(1.2 \times x = 100\) or \(x=83.33\).
Also with 20% decrease for women we can say \(0.8 \times y = 100\) or \(y=125\).
Population in the past\(=x+y=83.33+125=208.33\).
Present population =\(100+100=200\).
% decrease= \(\frac{208.33-200}{208.33} \approx 3.99\).
Hence option B is correct!
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Re: Over the past year, the number of men in Pleasantville
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10 Feb 2018, 08:59
10 Feb 2018, 08:59
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goutham v wrote:
Over the past year, the number of men in Pleasantville increased by 20% while the number of women in Pleasantville decreased by 20%. If the number of men and women in Pleasantville are now equal to each other, what was the percentage change in the total population of Pleasantville over the past year?
10% decrease
4% decrease
no change
4% increase
10% increase
10% decrease
4% decrease
no change
4% increase
10% increase
Let's assign some nice values to the number of men and women AFTER the increases and decreases occurred.
Let's say that AFTER the increases and decreases occurred, there were 24 men and 24 women.
So, AFTER the increases and decreases occurred, the TOTAL population = 48
Let M = number of men BEFORE the increase
Let W = number of women BEFORE the decrease
The number of men in Pleasantville increased by 20%
So, 1.2M = 24
So, M = 24/1.2 = 20
There were 20 men BEFORE the increase
The number of women decreased by 20%
So, 0.8F = 24
So, F = 24/0.8 = 30
There were 30 women BEFORE the decrease
TOTAL population BEFORE the increases and decreases = 20 + 30 = 50
What was the percentage change in the total population of Pleasantville over the past year?
The population decreased from 50 to 48
ELIMINATE C, D and E
Percent change = 100(new - old)/old
= (100)(48 - 50)/50
= -4%
= B
Cheers,
Brent
