raunakrajan wrote: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.
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