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
371
A family consists of grandparents, parents, and 3 grandchildren. The average age of the grandparents is 67 years, parents is 35 years, and grandchildren is 6 years. Find the average age of the family.
Answer:
31 5/7 years
Total members = 2 + 2 + 3 = 7. Total age = (2 * 67) + (2 * 35) + (3 * 6) = 134 + 70 + 18 = 222. Average = 222 / 7 = 31 5/7 years.
372
The average age of 24 boys and their teacher is 15 years. If the teacher's age is excluded, their average age decreases by 1. What is the teacher's age?
Answer:
39 years
Total age of 25 people = 25 * 15 = 375. After excluding the teacher, average is 14. Total age of 24 boys = 24 * 14 = 336. Teacher's age = 375 - 336 = 39 years.
373
The average of four numbers is 20. If one number is 14, what is the average of the other three numbers?
Answer:
22
Total sum of the 4 numbers = 4 * 20 = 80. Sum of the other three numbers = 80 - 14 = 66. Average of the other three = 66 / 3 = 22.
374
What is the average of 1/2, 1/3, and 1/6?
Answer:
1/3
Sum = 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1. Average = Sum / 3 = 1 / 3.
375
The average of the first five multiples of 9 is:
Answer:
27
The first five multiples of 9 are 9, 18, 27, 36, 45. The average is the middle term of this AP, which is 27.
376
If the average of 6 numbers is 12, what is the sum of these numbers?
Answer:
72
Sum = Average * Quantity. Sum = 12 * 6 = 72.
377
The average weight of A, B, C is 40 kg. If the average weight of A and B is 35 kg and that of B and C is 38 kg, find the weight of B.
Answer:
26 kg
Sum of A, B, C = 120. A + B = 70. B + C = 76. (A + B) + (B + C) = 146 => A + 2B + C = 146. Subtract (A + B + C): B = 146 - 120 = 26 kg.
378
The mean of 11 numbers is 35. If the mean of first 6 numbers is 32 and that of the last 6 numbers is 37, find the sixth number.
Answer:
29
Sum of 11 numbers = 11 * 35 = 385. Sum of first 6 = 6 * 32 = 192. Sum of last 6 = 6 * 37 = 222. The 6th number = (192 + 222) - 385 = 414 - 385 = 29.
379
If average of 20 observations is x1, and average of another 30 observations is x2, what is the average of all 50 observations?
Answer:
(2x1 + 3x2) / 5
Total sum = 20(x1) + 30(x2). Total observations = 50. Average = (20x1 + 30x2) / 50 = (2x1 + 3x2) / 5.
380
The average of a non-zero number and its square is 5 times the number. What is the number?
Answer:
9
Let the number be x. Average = (x + x^2) / 2 = 5x. Multiply by 2: x + x^2 = 10x. Divide by x (since x != 0): 1 + x = 10. Therefore, x = 9.