D.S

[raunakrajan]

Mrs. K's class has 10 students. If the average age of the students is 12, then how many of the students are 12 years of age?

(1) None of the students are younger than 12.

(2) None of the students are older than 12.



OA D

[Patrick_GMATFix]

Hi Raunakrajan,

No calculation is required here. This is a reasoning problem. We know that average age is 12.

(1) if no one is younger than 12, then no one can be older than 12 either. Otherwise the average age would be greater than 12. This would be true even if 9 of the 10 were exactly 12yrs old and only the 10th were older. This statement thus guarantees that all students are exactly 12. SUFFICIENT

(2) Same logic as one, from the flip side. If no one is older than 12, then no one can be younger than 12 either. Otherwise, even if only 1 student were younger than 12 and all the others were 12yrs old, the average age would be less than 12. This statement guarantees that all students are exactly 12. SUFFICIENT

The answer is D

[GMATGuruNY]

Mrs. K's class has 10 students. If the average age of the students is 12, then how many of the students are 12 years of age?

(1) None of the students are younger than 12.

(2) None of the students are older than 12.

A helpful technique for average problems:

Find the total.

In this case, total = sum of all the ages.

Since Average = total/(number of things), total = average * number of things

In this problem the average age is 12 and we have 10 students. So total = 12 * 10 = 120. The sum of all the ages is 120.

Statement 1:
Tells us that the minimum age of each student is 12. If each of the 10 students actually is 12, then the sum of all the ages = 10 * 12 = 120. This means that none of the students can be older than 12, or the sum would be too big. So every student is 12. SUFFICIENT.

Statement 2:
Tells us that the maximum age of each student is 12. If each of the 10 students actually is 12, then the sum of all the ages = 10 * 12 = 120. This means that none of the students can be younger than 12, or the sum would be too small. So every student is 12. SUFFICIENT.

The correct answer is D.