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
431
Average of 100 observations is 40. It was found that 53 was misread as 83. The correct average is:
Answer:
39.7
The value was misread as 83 instead of 53. The difference is 53 - 83 = -30. The total sum needs to be reduced by 30. The reduction in the average is 30 / 100 = 0.3. Correct average = 40 - 0.3 = 39.7.
432
The average of 2, 7, 6, and x is 5. The average of 18, 1, 6, x, and y is 10. What is the value of y?
Answer:
20
First, find x: (2 + 7 + 6 + x) / 4 = 5 => 15 + x = 20 => x = 5. Now substitute x in the second equation: (18 + 1 + 6 + 5 + y) / 5 = 10 => 30 + y = 50 => y = 20.
433
A batsman makes a score of 87 runs in the 17th match and thus increases his average by 3. Find his average after 17 matches.
Answer:
39
Let the average before the 17th match (i.e., for 16 matches) be x. Total runs = 16x. After 17 matches, the average is x + 3. (16x + 87) / 17 = x + 3. 16x + 87 = 17x + 51. So, x = 36. His average after 17 matches is x + 3 = 36 + 3 = 39.
434
If the average of m numbers is n^2 and that of n numbers is m^2, then the average of (m+n) numbers is:
Answer:
mn
Total sum of the m numbers = m * n^2. Total sum of the n numbers = n * m^2. The sum of all (m+n) numbers = mn^2 + nm^2 = mn(n+m). The average is the total sum divided by the number of items: mn(n+m) / (m+n) = mn.
435
Find the average of all prime numbers between 30 and 50.
Answer:
39.8
Prime numbers between 30 and 50 are 31, 37, 41, 43, and 47. There are 5 such primes. Their sum is 31 + 37 + 41 + 43 + 47 = 199. Average = 199 / 5 = 39.8.
436
A train covers the first 16 km at a speed of 20 km/hr, and another 20 km at 40 km/hr. Find the average speed for the whole journey.
Answer:
27.7 km/hr
Time for first part = Distance / Speed = 16 / 20 = 0.8 hours. Time for second part = 20 / 40 = 0.5 hours. Total distance = 16 + 20 = 36 km. Total time = 0.8 + 0.5 = 1.3 hours. Average speed = Total Distance / Total Time = 36 / 1.3 ≈ 27.69 km/hr, which rounds to 27.7.
437
The average of three numbers is 40. The first number is twice the second and the second is 3 times the third. The largest number is:
Answer:
72
Let the third number be x. Then the second is 3x, and the first is 2(3x) = 6x. The average is (6x + 3x + x) / 3 = 40. So 10x / 3 = 40, which means 10x = 120, x = 12. The largest number is the first one, which is 6x = 6 * 12 = 72.
438
In a class of 40 students, 45% are girls and the remaining are boys. If the average of the girls' marks is 54 and that of the boys is 46, what is the average of the whole class?
Answer:
49.6
Number of girls = 45% of 40 = 18. Number of boys = 40 - 18 = 22. Total marks of girls = 18 * 54 = 972. Total marks of boys = 22 * 46 = 1012. Total marks of the class = 972 + 1012 = 1984. Average = 1984 / 40 = 49.6.
439
The average of 5 numbers is 7. If three new numbers are added, the new average becomes 8.5. The average of the three new numbers is:
Answer:
11
Sum of the first 5 numbers = 5 * 7 = 35. Total numbers now = 5 + 3 = 8. Sum of all 8 numbers = 8 * 8.5 = 68. Sum of the 3 new numbers = 68 - 35 = 33. Average of these 3 new numbers = 33 / 3 = 11.
440
The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weight of all the boys in the class.
Answer:
48.55 kg
Total weight of 16 boys = 16 * 50.25 = 804 kg. Total weight of 8 boys = 8 * 45.15 = 361.2 kg. Total weight of 24 boys = 804 + 361.2 = 1165.2 kg. Average = 1165.2 / 24 = 48.55 kg.