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

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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.
[Reveal] Spoiler: OA

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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.

Answer C.
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Re: Sarah is in a room with 6 other children. If the other child [#permalink]

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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.




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.

So, the answer is (C).
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Re: Sarah is in a room with 6 other children. If the other child [#permalink]

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New post 27 Oct 2016, 10:00
so should we assume that average age is an integer ....?cant we just round it to the nearest

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Re: Sarah is in a room with 6 other children. If the other child [#permalink]

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New post 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.

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Re: Sarah is in a room with 6 other children. If the other child   [#permalink] 25 Oct 2017, 00:27
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