Is the average age of a class of 60 . . .

[Vincen]

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.

C is the OA.

How can I use both statements to establish that they together are sufficient?

[Jay@ManhattanReview]

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.

C is the OA.

How can I use both statements to establish that they together are sufficient?

Statement 1: 59 students in the class are exactly 30 years of age each.

We have no information about the age of the 60th student.

If the age of the 60th students less than 30, the class average is less than 30; however, if the age of the 60th students more than 30, the class average is more than 30.

No unique answer. Insufficient.

Statement 2: The average age of 5 of the students in the class is less than 30 years.

We do not have information about the ages of 25 students. Insufficient.

Statement 1 & 2:

Since the age of 59 students is EXACTLY 30, and the average age of 5 of the students in the class is less than 30 years, it implies that the age of the 60th student must be less than 30, otherwise the average age of 5 of the students in the class cannot be less than 30 years.

So, we have the average age of 59 students equal to 30 and the age of the 60th student is less than 30, thus, the average age of all the 60 students is less than 30. The answer is No. Sufficient.

The correct answer: C

Hope this helps!

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-Jay
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[Brent@GMATPrepNow]

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