Gnpth 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 30Consider 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 30Case b: the ages are {30, 30, 30, 30, 30, 30, ......30, 29}, in which case

the average age is less than 30Since 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 30Case 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 30Since 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 30Since we can answer the

target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,

Brent

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