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

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Math Expert
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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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53% (01:47) correct 47% (01:41) wrong based on 192 sessions

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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) 25% of retirees in the country are college graduates.

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

Spoiler: :: OLD VERSION
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.

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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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1
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) 25% 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: 25%*(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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Re: 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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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 $$25$$%$$*(x+y) = x => 0.25x+0.25y=x$$

or $$0.75x=0.25y => \frac{x}{y}=\frac{0.25}{0.75}=\frac{1}{3}$$. 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 $$\frac{x}{y}=\frac{1.6}{4.8}=\frac{1}{3}$$. Hence we get the ratio
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Re: In a certain country, the average retirement age for college graduates  [#permalink]

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02 Aug 2018, 01:16
niks18 wrote:
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

Hey Niks,

Do we need to assume that there are only two classes of people in that country?

Question says, " Among retirees in that country, what is the ratio of college graduates to people who have not graduated from college?"

How can we assume that we have x + y = 63.1 and not x + y + z = 63.1

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

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

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02 Aug 2018, 01:48
a and b give 2 different ratios.

a gives 1:4 and b gives 1:3
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Re: In a certain country, the average retirement age for college graduates  [#permalink]

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02 Aug 2018, 01:53
niks18 wrote:
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

16/48= 1/3 and not 1/4.
the 2 options give differing ratios
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Re: In a certain country, the average retirement age for college graduates  [#permalink]

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02 Aug 2018, 02:12
rahulkashyap wrote:
16/48= 1/3 and not 1/4.
the 2 options give differing ratios

Hi rahulkashyap

thanks for pointing out. the question needs to be rectified.
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Posts: 49965
Re: In a certain country, the average retirement age for college graduates  [#permalink]

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02 Aug 2018, 03:18
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) 25% of retirees in the country are college graduates.

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

Spoiler: :: OLD VERSION
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.

Veritas Prep edited the question since it was first published. Now, (1) reads: 25% of retirees in the country are college graduates. (It was 20% before)

VERITAS PREP OFFICIAL SOLUTION:

Pay particular attention to the specific question being asked here: the question wants you to find a ratio, not an exact number. And weighted averages, the primary concept tested on this problem, lend themselves quite well to solving for ratios.

With statement 1, it is important to note that when categories are defined as "X" and "not X" (here that's "college graduates" and "people who have not graduated college"), that structure means that they add up to 100%. You'll see this setup in many word problems and probability problems. So when the world of retirees is divided into those two complementary categories, you know that if 25% of retirees are college graduates, then 75% are not college graduates. This then means that the ratio of college graduates to people who have not graduated from college is 1:3, and that the statement is sufficient.

With statement 2, recognize that the value supplied (63.1) is the weighted average of the retirement ages for college graduates (58.3) and people who have not graduated from college (64.7). As mentioned above, weighted averages are tailor-made for ratios. If you employ the weighted average mapping strategy, you can see that you have:

58.3-------------------63.1---------64.7
-----------4.8-----------------1.6---------

Since the distances from each individual average to the weighted average are 4.8 and 1.6, you know that the ratio between the groups is 3:1. And with the weighted average closer to "people who have not graduated from college," that group will take the larger value. The ratio, then, is 1:3.

Because both statements are sufficient to determine that 1:3 ratio, the answer is D.
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Re: In a certain country, the average retirement age for college graduates  [#permalink]

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02 Aug 2018, 06:30
AkshdeepS wrote:
niks18 wrote:
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

Hey Niks,

Do we need to assume that there are only two classes of people in that country?

Question says, " Among retirees in that country, what is the ratio of college graduates to people who have not graduated from college?"

How can we assume that we have x + y = 63.1 and not x + y + z = 63.1

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

I am confused.

Hi AkshdeepS

I have assumed: "x" college graduate retirees & "y" non graduate retirees

There could be 100s of colleges but among all the colleges the question bifurcates two types of retirees.

Let me know if you have any doubts.
Re: In a certain country, the average retirement age for college graduates &nbs [#permalink] 02 Aug 2018, 06:30
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