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CAT Questions – Averages [VIDEO Solutions]

QUESTION 1
Last year, the average age of the class of 25 students was 13 years. If the age of the class teacher was included, the new average of the class became 14 years. Exactly a year later (i.e. this year), the class teacher leaves the school and if the age of the new class teacher is included, then the new average of the class this year becomes 14.5 years. Find the age of the new class teacher.
  1. 27
  2. 41
  3. 43
  4. 67
Option: 1
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QUESTION 2
If $S=\left\{ 10,12,14,16,18,20,22 \right\}$ , another set A is formed whose elements are the average of all the possible pairs of the elements taken from set S.
What is the average of the all elements of set A.
Answer: 16
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QUESTION 3
The difference of weight between the heaviest student and the lightest student in a class of 26 students is 15 kg. If the lightest student is excluded, the new average weight of the class increases by 1% of the original average weight. If the heaviest student is excluded, the new average weight of the class drops to 99% of the original average weight. Find the original average weight (in Kg) of the class.
Answer: 30
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QUESTION 4
A family consists of a mother, a father, and some children. The average age of the members of the family is 20, the father is 48 years old, and the average age of the mother and children is 16. How many children are in the family?
Answer: 6
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QUESTION 5
On a certain math exam, 10% of the students got 70 points, 25% got 80 points, 20% got 85 points, 15% got 90 points, and the rest got 95 points. What is the difference between the mean and the median score on this exam?
Answer: 1
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