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# A family of 5 people: A, B, C, D, E had an average age of 34 years

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Joined: 22 Aug 2013
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A family of 5 people: A, B, C, D, E had an average age of 34 years  [#permalink]

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02 Mar 2018, 00:06
00:00

Difficulty:

65% (hard)

Question Stats:

61% (02:45) correct 39% (02:08) wrong based on 58 sessions

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A family of 5 people: A, B, C, D, E had an average age of 34 years as on 1st January, 2009. All ages are considered in integers and none of the family members has a birthday in either December or in January. On 1st January 2010, E left the country for studies and on 1st January 2012, oldest member of this family B died at the age of 55 years. E returned on 1st January 2015 with his wife F, who is now a part of this family. F also does not have a birthday in either December or January. If no other changes in this family happened apart from those mentioned here, then what was the average age of this family with A, C, D, E, F on 1st January 2016?

(1) E was 24 years old as on 1st January 2010.

(2) F was 23 years old as on 1st January 2010.
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Joined: 02 Aug 2009
Posts: 8202
A family of 5 people: A, B, C, D, E had an average age of 34 years  [#permalink]

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02 Mar 2018, 08:00
2
amanvermagmat wrote:
A family of 5 people: A, B, C, D, E had an average age of 34 years as on 1st January, 2009. All ages are considered in integers and none of the family members has a birthday in either December or in January. On 1st January 2010, E left the country for studies and on 1st January 2012, oldest member of this family B died at the age of 55 years. E returned on 1st January 2015 with his wife F, who is now a part of this family. F also does not have a birthday in either December or January. If no other changes in this family happened apart from those mentioned here, then what was the average age of this family with A, C, D, E, F on 1st January 2016?

(1) E was 24 years old as on 1st January 2010.

(2) F was 23 years old as on 1st January 2010.

info ;-
5 people have an average age of 34 in 2009..
One person goes out and joins back, so does not effect or result in any change..

the oldest person dies in 2012 at age of 55
so he would have been 52 in 2009..
so average of REMAINING four A,C,D,E is $$\frac{34*5-52}{4} = \frac{170-52}{4}=\frac{118}{4}=29.5$$

so their average age in 2016 becomes 29.5+7=36.5

a new person F comes and now we have to find the average which is $$\frac{F+4*36.5}{5}$$

so WHAT is required..
AGE of F

(1) E was 24 years old as on 1st January 2010.
not required and age of F is not given
Insuff

(2) F was 23 years old as on 1st January 2010.
YES as can be seen by explanation above
new average = $$\frac{36.5*4+(23+6)}{5}=\frac{146+29}{5}=\frac{175}{5}=35$$
suff

B
_________________
A family of 5 people: A, B, C, D, E had an average age of 34 years   [#permalink] 02 Mar 2018, 08:00
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