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# In a certain country, the average retirement age for college graduates

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Math Expert
Joined: 02 Sep 2009
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In a certain country, the average retirement age for college graduates [#permalink]

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18 May 2017, 00:12
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In a certain country, the average retirement age for college graduates is 58.3 years old and the average retirement age for people who have not graduated from college is 64.7 years old. Among retirees in that country, what is the ratio of college graduates to people who have not graduated from college?

(1) 20% of retirees in the country are college graduates.

(2) The average retirement age in the country is 63.1.
[Reveal] Spoiler: OA

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Re: In a certain country, the average retirement age for college graduates [#permalink]

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18 May 2017, 11:53
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Bunuel wrote:
In a certain country, the average retirement age for college graduates is 58.3 years old and the average retirement age for people who have not graduated from college is 64.7 years old. Among retirees in that country, what is the ratio of college graduates to people who have not graduated from college?

(1) 20% of retirees in the country are college graduates.

(2) The average retirement age in the country is 63.1.

Let there be "x" college graduate retirees & "y" non graduate retirees.
We need to find out x:y

Statement 1: 20%*(x+y) = x . This equation will give us a ratio between x & y. Hence Sufficient

Statement 2: Total retirement age of college graduates = 58.3x
Total retirement age of non college graduates = 64.7y
Total no of retirees = x+y
So, Average retirement age in country = (58.3x+64.7y) / (x+y) = 63.1
Solving this equation we will get a relation between x & y. Hence sufficient

Option D
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In a certain country, the average retirement age for college graduates [#permalink]

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19 Nov 2017, 08:56
niks18 Bunuel VeritasPrepKarishma ENGRTOMBA2018

As per niks18 approach

Quote:
Let there be "x" college graduate retirees & "y" non graduate retirees.
We need to find out x:y

while analyzing the statements,

Quote:
Statement 1: 20%*(x+y) = x . This equation will give us a ratio between x & y. Hence Sufficient

Please elaborate this a step further as to how did you know we can find ratio of x/y from this.

Quote:
Statement 2: Total retirement age of college graduates = 58.3x
Total retirement age of non college graduates = 64.7y
Total no of retirees = x+y
So, Average retirement age in country = (58.3x+64.7y) / (x+y) = 63.1
Solving this equation we will get a relation between x & y. Hence sufficient

I believe now you have taken info from Q stem as average for retirement age for college graduates = sum of retirement ages/ total no of retirement ages
But again I am confused how can we deduce ratio x/y from this
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Joined: 25 Feb 2013
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In a certain country, the average retirement age for college graduates [#permalink]

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19 Nov 2017, 09:12
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niks18 Bunuel VeritasPrepKarishma ENGRTOMBA2018

As per niks18 approach

Quote:
Let there be "x" college graduate retirees & "y" non graduate retirees.
We need to find out x:y

while analyzing the statements,

Quote:
Statement 1: 20%*(x+y) = x . This equation will give us a ratio between x & y. Hence Sufficient

Please elaborate this a step further as to how did you know we can find ratio of x/y from this.

Quote:
Statement 2: Total retirement age of college graduates = 58.3x
Total retirement age of non college graduates = 64.7y
Total no of retirees = x+y
So, Average retirement age in country = (58.3x+64.7y) / (x+y) = 63.1
Solving this equation we will get a relation between x & y. Hence sufficient

I believe now you have taken info from Q stem as average for retirement age for college graduates = sum of retirement ages/ total no of retirement ages
But again I am confused how can we deduce ratio x/y from this

Statement 1

solve $$20$$%$$*(x+y) = x => 0.2x+0.2y=x$$

or $$0.8x=0.2y => \frac{x}{y}=\frac{0.2}{0.8}=\frac{1}{4}$$. Hence we get the ratio here

Statement 2:

$$\frac{(58.3x+64.7y)}{(x+y)} = 63.1$$

or $$58.3x+64.7y=63.1(x+y) => 58.3x+64.7y= 63.1x+63.1y$$

or $$64.7y-63.1y=63.1x-58.3x => 1.6y=4.8x$$

or $$\frac{x}{y}=\frac{1.6}{4.8}=\frac{1}{4}$$. Hence we get the ratio
In a certain country, the average retirement age for college graduates   [#permalink] 19 Nov 2017, 09:12
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