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
421
The average of 5 consecutive odd numbers is 95. What is the fourth number in descending order?
Answer:
93
The middle number is 95. The sequence is 91, 93, 95, 97, 99. In descending order, the sequence is 99, 97, 95, 93, 91. The fourth number is 93.
422
A library has an average of 265 visitors on Sundays and 130 visitors on other days. The average number of visitors per day in a month of 30 days beginning with a Monday is:
Answer:
148
A 30-day month starting on Monday will have 4 Sundays and 26 other days. Total visitors = (4 * 265) + (26 * 130) = 1060 + 3380 = 4440. Average per day = 4440 / 30 = 148.
423
Average of 15 numbers is 0. Among them, how many numbers can be greater than 0 at most?
Answer:
14
If the average of 15 numbers is 0, their sum must be 0. We can have 14 positive numbers whose sum is S. The 15th number can then be -S, making the total sum 0. Therefore, at most 14 numbers can be greater than 0.
424
The arithmetic mean of 1, 2, 3, ..., n is:
Answer:
(n+1)/2
The numbers 1, 2, ..., n form an arithmetic progression. The mean of an AP is (first term + last term) / 2. Therefore, the mean is (1 + n) / 2 or (n+1)/2.
425
The average of the reciprocals of x and y is:
Answer:
(x + y) / (2xy)
The reciprocals of x and y are 1/x and 1/y. Their sum is 1/x + 1/y = (y + x) / xy. The average is the sum divided by 2, which gives (x + y) / (2xy).
426
A student finds the average of 10 two-digit numbers. If the digits of one of the numbers is interchanged, the average increases by 3.6. The difference between the digits of the two-digit number is:
Answer:
4
Increase in average = 3.6. Total increase in sum = 10 * 3.6 = 36. A two-digit number is 10x + y. The interchanged number is 10y + x. The difference is (10y + x) - (10x + y) = 9(y - x). This difference equals 36. So, 9(y - x) = 36, meaning y - x = 4. The difference between the digits is 4.
427
The average of first 99 even natural numbers is:
Answer:
100
The average of the first 'n' even natural numbers is 'n + 1'. Thus, for the first 99 even natural numbers, the average is 99 + 1 = 100.
428
The average of first 50 odd natural numbers is:
Answer:
50
The average of the first 'n' odd natural numbers is exactly 'n'. Therefore, for the first 50 odd numbers, the average is 50.
429
In a T20 cricket match, the average runs scored by the first 5 batsmen was 30. The average of the next 4 batsmen was 15. The 10th and 11th batsmen scored 0 and 5 respectively. What was the average score of the team (11 players)?
Answer:
19.5
Sum of first 5 = 5 * 30 = 150. Sum of next 4 = 4 * 15 = 60. Sum of last 2 = 0 + 5 = 5. Total runs = 150 + 60 + 5 = 215. Average score = 215 / 11 = 19.54, approximately 19.5.
430
The average monthly expenditure of a family was Rs. 2200 during the first 3 months, Rs. 2250 during the next 4 months, and Rs. 3120 during the last 5 months. If the total savings during the year were Rs. 1260, the average monthly income was:
Answer:
Rs. 2605
Total expenditure for the year = (3 * 2200) + (4 * 2250) + (5 * 3120) = 6600 + 9000 + 15600 = Rs. 31,200. Total income = Total expenditure + Savings = 31200 + 1260 = Rs. 32,460. Average monthly income = 32460 / 12 = Rs. 2605.