Vincen wrote:Is the average age of a class of 60 students more than 30 years?
(1) 59 students in the class are exactly 30 years of age each.
(2) The average age of 5 of the students in the class is less than 30 years.
Target question: Is the average age of a class of 60 students more than 30 years?
Statement 1: 59 students in the class are exactly 30 years of age each.
OBSERVE:
i) If the 60th person is also 30 years old, then the average age = 30
ii) If the 60th person is YOUNGER THAN 30 years old, then the average age = LESS THAN 30
iii) If the 60th person is OLDER THAN 30 years old, then the average age = GREATER THAN 30
Consider these two scenarios (that satisfy statement 1):
Case a: the ages are {30, 30, 30, 30, 30, 30, ......30, 31}, in which case
the average age is greater than 30
Case b: the ages are {30, 30, 30, 30, 30, 30, ......30, 29}, in which case
the average age is less than 30
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The average age of 5 of the students in the class is less than 30 years.
There are several values of x and y that satisfy statement 2. Here are two:
Consider these two scenarios (that satisfy statement 2):
Case a: {five people are 29 years old and the other fifteen people are 100 years old}, in which case
the average age is greater than 30
Case b: five people are 25 years old and the other fifteen people are 26 years old}, in which case
the average age is less than 30
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that 59 people are exactly 30 years old
Statement 2 tells us that there is at least 1 person who is less than 30 years old.
So, we have
case ii here, which means
the average age is less than 30
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer:
C
Cheers,
Brent
