BTGmoderatorLU wrote: ↑Fri Jun 19, 2020 5:08 am
Source: Manhattan Prep
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 age
2) Sarah is not the oldest child in the room
The OA is
C
Sum of the six children = 42.
Let's take each statement one by one.
1) The age of the fourth oldest child is equal to the average (arithmetic mean) of the seven children's age.
Case 1: Say Sara is 7 years old.
We see that the age of the fourth oldest child is also 7 years.
=> 7 = (42 + 7)/7 => 5 = 7. The answer is yes.
Case 2: Say Sara is x years old, where x < 5.
We see that the age of the fourth oldest child is 5 years.
=> 5 = (42 + x)/7 => x = negative number. Not a valid case. Sara is not less than 5 year old.
Case 3: Say Sara is x years old, where x > 8.
We see that the age of the fourth oldest child is 8 years.
=> 8 = (42 + x)/7 => x = 14. Sara is not 7 year old. The answer is no.
No unique answer. Insufficient.
2) Sarah is not the oldest child in the room.
Certainly insufficient.
(1) and (2) together
Case 3 in statement 1 is not applicable. So, only statement 1 is applicable. Sufficient.
Correct answer:
C
Hope this helps!
-Jay
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