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

Question

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.

EvaJager · Accepted Answer

(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.

premnath · Answer

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).

sanaexam · Answer

so should we assume that average age is an integer ....?cant we just round it to the nearest

Tpral · Answer

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.

avocado310 · Answer

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

kaladin123 · Answer

A = {2, 4, 5, 8, 10, 13, S}

Is S=7?

From S1: Mean=Median. (4th element is the median in a set of 7 elements)
Mean =\frac{42+S}{7}=6+\frac{S}{7} 
S=7, 14, etc. (a multiple of 7)
If S=7, A = {2, 4, 5, S= 7 , 8, 10, 13}, Mean= Median =7
If S=14, A = {2, 4, 5,  8 , 10, 13, S=14}, Mean= Median =8

Insufficient

From S2: Sarah is not the oldest child. 
Insufficient.

S1 & S2: S=7
Sufficient

DonBosco7 · Answer

Hi sanaexam, we do not have to assume age as an integer, age is always an integer, when you tell someone's age you don't generally say he/she is 20.5 yr old or 61.7 yr old, we simply say he/she is 12 or 15 or 30 yrs old.

bumpbot · Answer

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

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