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
471
The average of first 10 multiples of 3 is:
Answer:
16.5
The first 10 multiples of 3 are 3, 6, 9, ..., 30. This is an arithmetic progression. For an AP, the average is (first term + last term) / 2 = (3 + 30) / 2 = 33 / 2 = 16.5.
472
In an exam, the average marks of 40 students is 72. Later, it was found that the marks of three students were misread as 68, 75, and 73 instead of 64, 62, and 84 respectively. Find the correct average.
Answer:
71.85
Original sum = 40 * 72 = 2880. The misread sum was 68 + 75 + 73 = 216. The correct sum should be 64 + 62 + 84 = 210. Difference = 210 - 216 = -6. Correct sum = 2880 - 6 = 2874. Correct average = 2874 / 40 = 71.85.
473
The average age of three boys is 15 years. If their ages are in the ratio 3:5:7, what is the age of the youngest boy?
Answer:
9 years
Total age of the three boys = 3 * 15 = 45 years. Let their ages be 3x, 5x, and 7x. 3x + 5x + 7x = 45, which gives 15x = 45, so x = 3. The age of the youngest boy is 3x = 3 * 3 = 9 years.
474
The average of 50 numbers is 38. If two numbers, namely 45 and 55, are discarded, the average of the remaining numbers is:
Answer:
37.5
Total sum of 50 numbers = 50 * 38 = 1900. Sum of the two discarded numbers = 45 + 55 = 100. Sum of the remaining 48 numbers = 1900 - 100 = 1800. Average of remaining numbers = 1800 / 48 = 37.5.
475
The average of 5 quantities is 10 and the average of 3 of them is 8. What is the average of the remaining 2 quantities?
Answer:
13
Total sum of the 5 quantities = 5 * 10 = 50. Sum of the 3 quantities = 3 * 8 = 24. Sum of the remaining 2 quantities = 50 - 24 = 26. Average of the remaining 2 quantities = 26 / 2 = 13.
476
The average of first 5 prime numbers is:
Answer:
5.6
The first 5 prime numbers are 2, 3, 5, 7, and 11. Their sum is 2 + 3 + 5 + 7 + 11 = 28. The average is 28 / 5 = 5.6.
477
A man drives to a city at a speed of 40 km/h and returns along the same route at a speed of 60 km/h. What is his average speed for the entire journey?
Answer:
48 km/h
When distances are equal, average speed is calculated using the formula 2xy / (x + y). Here, x = 40 and y = 60. Average speed = 2(40)(60) / (40 + 60) = 4800 / 100 = 48 km/h.
478
Find the average of the cubes of the first 4 natural numbers.
Answer:
25
The sum of the cubes of the first n natural numbers is [n(n+1)/2]^2. For n=4, the sum is [4(5)/2]^2 = 10^2 = 100. The average is 100 / 4 = 25. Alternatively: (1+8+27+64)/4 = 100/4 = 25.
479
Find the average of the squares of the first 5 natural numbers.
Answer:
11
The formula for the sum of squares of the first n natural numbers is n(n+1)(2n+1)/6. For n=5, the sum is 5(6)(11)/6 = 55. The average is 55 / 5 = 11. Alternatively: (1+4+9+16+25)/5 = 55/5 = 11.
480
The average salary of 20 workers in an office is Rs. 15,000 per month. If the manager's salary is added, the average salary becomes Rs. 16,000. What is the manager's monthly salary?
Answer:
Rs. 36,000
Total salary of 20 workers = 20 * 15,000 = Rs. 300,000. With the manager, there are 21 people. Total salary = 21 * 16,000 = Rs. 336,000. Manager's salary = 336,000 - 300,000 = Rs. 36,000.