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# Sarah is in a room with 6 other children. If the other child

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Manager
Joined: 02 Nov 2009
Posts: 104
Sarah is in a room with 6 other children. If the other child  [#permalink]

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07 Sep 2012, 20:36
3
20
00:00

Difficulty:

85% (hard)

Question Stats:

43% (01:13) correct 57% (00:53) wrong based on 437 sessions

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Sarah is in a room with 6 other children. If the other children are 2, 4, 5, 8, 10, and 13 years old, is Sarah 7 years old?

(1) The age of the fourth oldest child is equal to the average (arithmetic mean) of the seven children’s ages.

(2) Sarah is not the oldest child in the room.
Director
Joined: 22 Mar 2011
Posts: 600
WE: Science (Education)
Re: Sarah is in a room with 6 other children. If the other child  [#permalink]

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07 Sep 2012, 22:55
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venmic wrote:
Sarah is in a room with 6 other children. If the other children are 2, 4, 5, 8, 10, and 13 years old, is Sarah 7 years old?

(1) The age of the fourth oldest child is equal to the average (arithmetic mean) of the seven children’s ages.

(2) Sarah is not the oldest child in the room.

Can an expert please explain vvhy C

(1) The sum of the ages of the six other children is 42.
If $$x$$ is the age of Sarah and $$x\geq{8}$$ then $$(42+x)/7=8,$$ as the fourth age in the sequence is $$8.$$ Then $$x=14.$$
If $$5\leq{x}<8$$ then $$(42+x)/7=x,$$ as now the fourth age in the sequence is $$x.$$ This gives $$x=7.$$
If $$x<5$$ then $$(42+x)/7=5,$$ as now the fourth age in the sequence is $$5.$$ This gives $$x=-7$$, impossible.
Not sufficient.

(2) Obviously, not sufficient.

(1) and (2):
Sufficient, because we can now choose between $$7$$ and $$14,$$ and Sarah must be of age $$7,$$ as she cannot be the eldest.

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##### General Discussion
Manager
Joined: 24 Jul 2011
Posts: 66
Location: India
Concentration: Strategy, General Management
GMAT 1: 670 Q49 V33
WE: Asset Management (Manufacturing)
Re: Sarah is in a room with 6 other children. If the other child  [#permalink]

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12 Sep 2012, 07:59
4
2
venmic wrote:
Sarah is in a room with 6 other children. If the other children are 2, 4, 5, 8, 10, and 13 years old, is Sarah 7 years old?

(1) The age of the fourth oldest child is equal to the average (arithmetic mean) of the seven children’s ages.

(2) Sarah is not the oldest child in the room.

Consider Statement 1:
Sum of ages of all six children (except Sarah) is 2+4+5+8+10+13= 42

Sum of ages of all seven children is a multiple of 7 as the average is equal to the age of one of the children.
Also Sum > 42.
Possible values of Sum is 49, 56, 63 .....
If Sum=49, Age of Sarah is (49-42)= 7. She becomes the fourth oldest child.
If Sum=56, Age of Sarah is (56-42) = 14, She becomes the oldest chile
All other possible ages of Sarah is > 14
As we are not getting unique value, the statement is NOT SUFFICIENT

Consider Statement 2:
Sarah is not the oldest child in the room. This statement alone does not tell us anything about the age of Sarah. Hence, it is also NOT SUFFICIENT.

Now, Consider (1) + (2):
Sarah is not the oldest child. Then obvious Age of Sarah is 7 and this makes her fourth oldest child also.

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Intern
Joined: 01 Sep 2016
Posts: 29
Re: Sarah is in a room with 6 other children. If the other child  [#permalink]

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27 Oct 2016, 10:00
so should we assume that average age is an integer ....?cant we just round it to the nearest
Intern
Joined: 17 Mar 2017
Posts: 9
GMAT 1: 510 Q47 V15
GMAT 2: 600 Q49 V22
Re: Sarah is in a room with 6 other children. If the other child  [#permalink]

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25 Oct 2017, 00:27
I do Agree with you Sanaexam. It is not written anywhere that the age of Sarah is an integer. Thus, even if Sarah is not the oldest as per statement (2) Sarah could be anything ... this question I believe is unclear.
Intern
Joined: 30 Jun 2018
Posts: 16
Re: Sarah is in a room with 6 other children. If the other child  [#permalink]

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20 Dec 2018, 12:42
Question: why can't you just set up statement 1 in this case since they are saying that the new addition, will be equal to the average mean?

(1) The age of the fourth oldest child is equal to the average (arithmetic mean) of the seven children’s ages.

(42+missing age)/8 = missing age
Re: Sarah is in a room with 6 other children. If the other child &nbs [#permalink] 20 Dec 2018, 12:42
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