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
481
The average of 30 numbers is zero. At most, how many of these numbers may be greater than zero?
Answer:
29
For the average of 30 numbers to be zero, their total sum must be zero. It is possible for 29 numbers to be strictly greater than zero (positive), as long as the 30th number is a sufficiently large negative number to cancel out their sum. Thus, at most 29 can be greater than zero.
482
A batsman has a certain average of runs for 11 innings. In the 12th inning, he makes a score of 90 runs, thereby increasing his average by 5. What is his average after the 12th inning?
Answer:
35
Let the original average for 11 innings be 'x'. Total runs = 11x. After 12 innings, the average is 'x + 5'. Equation: (11x + 90) / 12 = x + 5. 11x + 90 = 12x + 60. Solving this gives x = 30. His new average after 12th inning is x + 5 = 30 + 5 = 35.
483
A student's marks were wrongly entered as 83 instead of 63. Due to this error, the average marks of the class increased by half a mark (0.5). How many students are there in the class?
Answer:
40
The difference in marks due to the wrong entry is 83 - 63 = 20. This extra 20 marks caused an overall increase of 0.5 marks per student. Number of students = Total increase in marks / Increase per student = 20 / 0.5 = 40 students.
484
In a family, the average age of a father and a mother is 35 years. The average age of the father, mother, and their only son is 27 years. What is the age of the son?
Answer:
11 years
Total age of father and mother = 2 * 35 = 70 years. Total age of father, mother, and son = 3 * 27 = 81 years. The age of the son is the difference between these two totals: 81 - 70 = 11 years.
485
The average temperature for Monday, Tuesday, and Wednesday was 40°C. The average for Tuesday, Wednesday, and Thursday was 41°C. If the temperature on Thursday was 42°C, what was the temperature on Monday?
Answer:
39°C
Sum for Mon+Tue+Wed = 3 * 40 = 120°C. Sum for Tue+Wed+Thu = 3 * 41 = 123°C. Difference: (Tue+Wed+Thu) - (Mon+Tue+Wed) = 123 - 120, which simplifies to Thu - Mon = 3°C. If Thu is 42°C, then Mon = 42 - 3 = 39°C.
486
The average of 11 results is 50. If the average of the first six results is 49 and that of the last six is 52, what is the sixth result?
Answer:
56
Total sum of all 11 results = 11 * 50 = 550. Sum of the first 6 results = 6 * 49 = 294. Sum of the last 6 results = 6 * 52 = 312. The sixth result is counted twice when adding these two sums. Sixth result = (294 + 312) - 550 = 606 - 550 = 56.
487
The average age of a class of 30 students is 15 years. If the teacher's age is included, the average age increases by 1 year. What is the age of the teacher?
Answer:
46 years
Total age of 30 students = 30 * 15 = 450 years. With the teacher, there are 31 people, and the new average is 16 years. Total age of 31 people = 31 * 16 = 496 years. Teacher's age = 496 - 450 = 46 years.
488
The average weight of 8 men is increased by 1.5 kg when one of the men who weighs 65 kg is replaced by a new man. What is the weight of the new man?
Answer:
77 kg
The total weight increase for all 8 men is 8 * 1.5 kg = 12 kg. This increase happens because the new man is heavier than the man he replaced. Weight of the new man = weight of the replaced man + total increase = 65 kg + 12 kg = 77 kg.
489
The average of 5 numbers is 27. If one number is excluded, the average becomes 25. What is the excluded number?
Answer:
35
The total sum of the initial 5 numbers = 5 * 27 = 135. After excluding one number, there are 4 numbers, and their sum = 4 * 25 = 100. The excluded number is the difference of the sums: 135 - 100 = 35.
490
The average of 8 numbers is 14. The average of 6 of these numbers is 16. What is the average of the remaining two numbers?
Answer:
8
Total sum of the 8 numbers = 8 * 14 = 112. Total sum of the 6 numbers = 6 * 16 = 96. Sum of the remaining 2 numbers = 112 - 96 = 16. The average of these 2 remaining numbers is 16 / 2 = 8.