When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.btg_13423 wrote:
If the average age of three people is 21 years, is the youngest older than 13?
(1) The oldest is 25.
(2) One person is 24.
How's this . . .
Target question: Is the youngest older than 13?
Given: The average age of three people is 21 years
If the average (arithmetic mean) the 3 ages is is 21, then the SUM of all 3 ages must = (3)(21) = 63
If we let A, B and C be the ages, in ascending order, then A + B + C = 63
Statement 1: The oldest is 25
So, C = 25
This means that A + B + 25 = 63
In other words, A + B = 38
Let's see what happens if we minimize the value of A.
To MINIMIZE the value of A, we must MAXIMIZE the value of B.
Since 25 is the greatest age, we know that B < 25
So, the MAXIMUM value of B is 24, in which case the MINIMUM value of C is 14 (since A + B = 38).
In other words, C must be greater than or equal to 14
So, the youngest person is definitely older than 13
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: One person is 24
Consider these 2 possible cases:
case a: the ages are 3, 24, 36 in which case the youngest person is NOT older than 13
case b: the ages are 14, 24, 25 in which case the youngest person IS older than 13
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent
