Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
391
In a class, the average age of all the boys is 15 years, and that of the girls is 12 years. If the ratio of boys to girls is 3:2, find the average age of the entire class.
Answer:
13.8 years
Let the number of boys be 3k and girls be 2k. Total age of boys = 3k * 15 = 45k. Total age of girls = 2k * 12 = 24k. Total age = 69k. Total students = 5k. Average = 69k / 5k = 13.8 years.
392
The average of x numbers is 3x. If x-1 is subtracted from each number, the new average will be:
Answer:
2x + 1
If a constant is subtracted from each number, the same constant is subtracted from the average. New average = 3x - (x - 1) = 3x - x + 1 = 2x + 1.
393
Find the average of the first 10 whole numbers.
Answer:
4.5
The first 10 whole numbers are 0, 1, 2, ..., 9. Their sum is 9*10/2 = 45. Average = 45 / 10 = 4.5.
394
A student's average marks in 5 subjects is 80. If the marks of one subject are excluded, the average drops to 78. What were the marks of the excluded subject?
Answer:
88
Total marks for 5 subjects = 5 * 80 = 400. Total marks for 4 subjects = 4 * 78 = 312. Excluded subject marks = 400 - 312 = 88.
395
The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one weighing 65 kg. The weight of the new person is:
Answer:
85 kg
Total increase in weight = 8 * 2.5 = 20 kg. Weight of the new person = Weight of replaced person + increase = 65 + 20 = 85 kg.
396
The average of 5 consecutive even numbers is M. If the next five even numbers are also included, the average of all ten numbers will be:
Answer:
M + 5
The average of an arithmetic progression increases by half the total common difference added. Adding 5 new even numbers shifts the midpoint by 5 positions (each representing half a step between elements). The new average is M + 5.
397
Average of 5 numbers is 20. If each number is multiplied by 2 and then 5 is added to each, the new average will be:
Answer:
45
When operations are uniformly applied to all elements, they apply to the average. Multiply average by 2: 20 * 2 = 40. Then add 5: 40 + 5 = 45.
398
The average age of a class of 40 students is 18 years. When the teacher's age is included, the average increases by 0.5 years. What is the teacher's age?
Answer:
38.5 years
Total age initially = 40 * 18 = 720. With teacher, total people = 41. New average = 18.5. New total age = 41 * 18.5 = 758.5. Teacher's age = 758.5 - 720 = 38.5 years.
399
The average temperature of the first 4 days of a week is 37°C and that of the last 4 days is 41°C. If the average temperature of the whole week is 39°C, the temperature of the fourth day is:
Answer:
39°C
Sum of first 4 days = 4 * 37 = 148. Sum of last 4 days = 4 * 41 = 164. Sum of all 7 days = 7 * 39 = 273. The fourth day is counted twice in the first and last sums. Temp of 4th day = (148 + 164) - 273 = 312 - 273 = 39°C.
400
The average of ten numbers is 7. If each number is multiplied by 12, then the average of the new set of numbers is:
Answer:
84
Multiplying each number by a constant multiplies the average by the same constant. New average = 7 * 12 = 84.