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Bunuel
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Twenty-five percent of the residents of City Y are 65 years old or old 06 May 2019, 21:18
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84% (01:58) correct 16% (02:12) wrong based on 169 sessions

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Twenty-five percent of the residents of City Y are 65 years old or older. Twenty percent of the residents of City Y who are under the age of 65 are age 18 or younger. What percent of the residents of City Y are between the ages of 18 and 65?

A. 15%
B. 25%
C. 45%
D. 60%
E. 75%
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D
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Twenty-five percent of the residents of City Y are 65 years old or old 06 May 2019, 22:03
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Bunuel
Twenty-five percent of the residents of City Y are 65 years old or older. Twenty percent of the residents of City Y who are under the age of 65 are age 18 or younger. What percent of the residents of City Y are between the ages of 18 and 65?

A. 15%
B. 25%
C. 45%
D. 60%
E. 75%
Show more

We can divide the population in three age brackets: \(\leq18\), \(18-65\)\(\) and \(\geq65\).
\(\geq65\) =25%. Therefore other two categories (i.e. <65 years of age) have 75% people
\(\leq18\)= 20% of 75% (i.e. <65 years of age)= 15%
Therefore, people in 18-65 age bracket= 100%-25%-15%=60%.

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Twenty-five percent of the residents of City Y are 65 years old or old 07 May 2019, 03:17
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Twenty-five percent of the residents of City Y are 65 years old or older. Twenty percent of the residents of City Y who are under the age of 65 are age 18 or younger. What percent of the residents of City Y are between the ages of 18 and 65?

A. 15%
B. 25%
C. 45%
D. 60%
E. 75%
Show more

solve using 2x2 matrix

------->=65-----<65-----total
<=18--- 15------15--------30
>18----10-------60--------70
total---25-------75--------100

percent of the residents of City Y are between the ages of 18 and 65 ; = 60
IMO D
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Twenty-five percent of the residents of City Y are 65 years old or old 07 May 2019, 03:31
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Bunuel
Twenty-five percent of the residents of City Y are 65 years old or older. Twenty percent of the residents of City Y who are under the age of 65 are age 18 or younger. What percent of the residents of City Y are between the ages of 18 and 65?

A. 15%
B. 25%
C. 45%
D. 60%
E. 75%

solve using 2x2 matrix

------->=65-----<65-----total
<=18--- 15------15--------30
>18----10-------60--------70
total---25-------75--------100

percent of the residents of City Y are between the ages of 18 and 65 ; = 60
IMO D
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Dear Archit3110,

\(\leq65\) and \(\leq18\)\(\) are mutually exclusive categories, how can a person be both >65 year of age and <18 at the same time? A 2x2 matrix is not appropriate for this situation. How did you get the numbers 30 and 70 mentioned in the 2x2 matrix and also the number 15 in >65 and <18 cell. Please explain.
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Twenty-five percent of the residents of City Y are 65 years old or old 07 May 2019, 03:43
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Rakesh1987
Archit3110
Bunuel
Twenty-five percent of the residents of City Y are 65 years old or older. Twenty percent of the residents of City Y who are under the age of 65 are age 18 or younger. What percent of the residents of City Y are between the ages of 18 and 65?

A. 15%
B. 25%
C. 45%
D. 60%
E. 75%

solve using 2x2 matrix

------->=65-----<65-----total
<=18--- 15------15--------30
>18----10-------60--------70
total---25-------75--------100

percent of the residents of City Y are between the ages of 18 and 65 ; = 60
IMO D

Dear Archit3110,

\(\leq65\) and \(\leq18\)\(\) are mutually exclusive categories, how can a person be both >65 year of age and <18 at the same time? A 2x2 matrix is not appropriate for this situation. How did you get the numbers 30 and 70 mentioned in the 2x2 matrix and also the number 15 in >65 and <18 cell. Please explain.
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I usually find solving 2 set cases using 2x2 matrix easier than venn diag..
yes you are right ; below will be the 2x2 matrix ..
30,70 were just only possible values which to make sum = 100 ; so i plugged in ; they are of no use though ..

------->=65-----<65-----total
<=18--- a------15--------15+a
>18----b-------60--------60+b
total---25-------75--------100
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Twenty-five percent of the residents of City Y are 65 years old or old 07 May 2019, 03:55
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Archit3110
I usually find solving 2 set cases using 2x2 matrix easier than venn diag..
yes you are right ; below will be the 2x2 matrix ..
30,70 were just only possible values which to make sum = 100 ; so i plugged in ; they are of no use though ..

------->=65-----<65-----total
<=18--- a------15--------15+a
>18----b-------60--------60+b
total---25-------75--------100
Show more


Hi Archit3110,

I agree 2x2 matrix are easier to solve. And see without punching values for a or b, still you can solve the question. The answer we wanted was for age group (>18, <65) which you correctly got as 60.

You should remove a and b, after that the matrix looks fine to me.
------->=65-----<65-----total
<=18--- NA------15--------15
>18----25-------60--------85
total---25-------75--------100

25 whatever is >65 is surely >18.
+1 Kudos for the matrix.

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Twenty-five percent of the residents of City Y are 65 years old or old 02 Aug 2024, 02:42
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Bunuel
Twenty-five percent of the residents of City Y are 65 years old or older. Twenty percent of the residents of City Y who are under the age of 65 are age 18 or younger. What percent of the residents of City Y are between the ages of 18 and 65?

A. 15%
B. 25%
C. 45%
D. 60%
E. 75%
Show more
Let total residents = 100x
­Residents older than 65 Years =25% = 25x
A. Residents younger than 65 yrs= 75% = 75x
B. Residents under 18yrs= 25% of residents under 65 yrs = 20% of 75x = 75x /5 = 15x
Residents between 18 to 65 years = A-B = 60 x
Percentage = 60x/100x *100 =60%
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