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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