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
491
The average of 20 numbers is 50. If 10 is subtracted from each number, what is the new average?
Answer:
40
Similar to addition, when a constant value is subtracted from every number in a dataset, the average decreases by that exact constant. Thus, the new average is 50 - 10 = 40.
492
The average of 10 numbers is 25. If 5 is added to each number, what is the new average?
Answer:
30
When a constant value is added to every observation in a dataset, the average of the dataset increases by that same constant. Therefore, the new average will be 25 + 5 = 30.
493
The average of 15 numbers is 40. If each number is multiplied by 3, what will be the new average?
Answer:
120
If every number in a dataset is multiplied by a constant factor 'k', the new average also becomes 'k' times the original average. Here, the original average is 40 and k = 3. The new average is 40 * 3 = 120.
494
The average of four consecutive even numbers is 27. Find the largest of these numbers.
Answer:
30
Let the even numbers be x, x+2, x+4, and x+6. Their sum is 4x + 12. The average is (4x + 12) / 4 = x + 3. Given x + 3 = 27, we find x = 24. The largest number is x + 6 = 24 + 6 = 30.
495
The average of 7 consecutive odd numbers is 25. What is the smallest of these numbers?
Answer:
19
Since there are 7 numbers (an odd count), the average, 25, is the middle number. The sequence is: _, _, _, 25, _, _, _. The three odd numbers before 25 are 23, 21, and 19. Thus, the smallest number is 19.
496
The average of 5 consecutive numbers is 20. What is the largest of these numbers?
Answer:
22
For an odd number of consecutive integers, the average is always the middle number. So, the middle number is 20. The numbers are 18, 19, 20, 21, and 22. The largest number is 22.
497
What is the average of the first 10 odd numbers?
Answer:
10
The average of the first 'n' odd natural numbers is simply 'n'. Therefore, for the first 10 odd numbers, the average is 10. The sum of the first 10 odd numbers is 10^2 = 100, and 100 / 10 = 10.
498
What is the average of the first 10 even numbers?
Answer:
11
The formula for the average of the first 'n' even natural numbers is (n + 1). For the first 10 even numbers, the average is 10 + 1 = 11. Alternatively, the numbers are 2, 4, ..., 20. Sum = 110. Average = 110 / 10 = 11.
499
Find the average of the first 10 natural numbers.
Answer:
5.5
The sum of the first 'n' natural numbers is given by the formula n(n+1)/2. For n=10, the sum is 10(11)/2 = 55. The average is the sum divided by n, which is 55 / 10 = 5.5.
500
What is the average of the numbers 12, 15, 18, 21, and 24?
Answer:
18
To find the average, sum all the numbers and divide by the total count. Sum = 12 + 15 + 18 + 21 + 24 = 90. Total count = 5. Average = 90 / 5 = 18. Since these are consecutive multiples of 3, the middle number (18) is the average.