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
351
Find the average of the first five multiples of 3.
Answer:
9
The first five multiples of 3 are 3, 6, 9, 12, and 15. Their sum is 45. Dividing by the number of terms (5) gives the average: 45 ÷ 5 = 9.
352
If the average of x, y, z is 15 and x+y=20, then z equals:
Answer:
25
The sum x+y+z = 3 * 15 = 45. We know x+y = 20. Therefore, 20 + z = 45, which gives z = 25.
353
Average of 5 consecutive integers is 21. If the highest and lowest numbers are removed, what is the average of the remaining numbers?
Answer:
21
For any symmetric sequence, removing the highest and lowest values symmetrically does not change the average. The middle term remains the same. The average remains 21.
354
The average of 8, 11, 6, 14, x, and 13 is 10. Find the value of x.
Answer:
8
The sum of the 6 numbers is 6 * 10 = 60. Sum of given 5 numbers = 8 + 11 + 6 + 14 + 13 = 52. So, x = 60 - 52 = 8.
355
What is the average of the squares of the first 3 natural numbers?
Answer:
4.67
The squares of the first 3 natural numbers are 1, 4, 9. Their sum is 1+4+9=14. Average = 14 / 3 = 4.666..., which rounds to 4.67.
356
If the average of two numbers is ab and one number is a, the other number is:
Answer:
2ab - a
Let the two numbers be x and y. Their average is (x+y)/2 = ab. Therefore, x+y = 2ab. If x = a, then a + y = 2ab, so y = 2ab - a.
357
The average of 5 positive numbers is 100. If the first number is 20, what is the average of the remaining 4 numbers?
Answer:
120
Total sum = 5 * 100 = 500. Sum of the remaining 4 numbers = 500 - 20 = 480. Average of the remaining 4 = 480 / 4 = 120.
358
If the average of 5 terms is 10 and the average of 10 terms is 5, what is the combined average of these 15 terms?
Answer:
6.67
Total sum = (5 * 10) + (10 * 5) = 50 + 50 = 100. Total terms = 15. Combined average = 100 / 15 = 20 / 3 = 6.67.
359
The average marks of 30 students are 45. A student who scored 80 marks is mistakenly entered as 50. Find the correct average.
Answer:
46
Difference = Correct Mark - Incorrect Mark = 80 - 50 = +30. This difference is distributed among the 30 students. Increase in average = 30 / 30 = +1. Correct average = 45 + 1 = 46.
360
The average of x and y is 40. If z = 10, what is the average of x, y, and z?
Answer:
30
Since the average of x and y is 40, their sum x + y = 80. Adding z (10) makes the total sum 80 + 10 = 90. The average of the three numbers is 90 / 3 = 30.