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
381
Out of 4 numbers, the average of the first three is 16 and that of the last three is 15. If the last number is 20, the first number is:
Answer:
23
a+b+c = 3*16 = 48. b+c+d = 3*15 = 45. Subtracting gives (a+b+c) - (b+c+d) = a - d = 3. Since d = 20, a - 20 = 3, meaning a = 23.
382
The average of 3 numbers is 77. The first number is twice the second and the second is twice the third. Find the first number.
Answer:
132
Let the third number be x. Then second is 2x, first is 4x. Sum = x + 2x + 4x = 7x. Average = 7x/3 = 77. So, 7x = 231, x = 33. The first number is 4x = 4 * 33 = 132.
383
Average marks of 10 students is 60. If the marks of one student is accidentally read as 30 instead of 80, what is the correct average?
Answer:
65
Difference = 80 - 30 = +50. This means the sum is short by 50. Adding 50 to the sum increases the average by 50 / 10 = 5. Correct average = 60 + 5 = 65.
384
The average of 8 numbers is 20. The average of the first two numbers is 15.5 and the average of the next three is 21 1/3. If the 6th number is 4 less than the 7th and 7 less than the 8th, what is the 8th number?
Answer:
25
Total sum = 160. Sum of first 2 = 31. Sum of next 3 = 3*(64/3) = 64. Sum of remaining 3 = 160 - 31 - 64 = 65. Let 6th be y, 7th be y+4, 8th be y+7. y + y+4 + y+7 = 65 => 3y + 11 = 65 => 3y = 54 => y = 18. The 8th number is y+7 = 18+7 = 25.
385
If the average of 5 observations x, x+2, x+4, x+6, x+8 is 11, then what is the average of the last three observations?
Answer:
13
The average of this arithmetic sequence is the middle term, x+4. So x+4 = 11, which gives x=7. The last three observations are 11, 13, 15. Their average is the middle one, 13.
386
The average temperature from Monday to Thursday is 38°C and from Tuesday to Friday is 40°C. If the temperature on Monday was 30°C, what was the temperature on Friday?
Answer:
38°C
M+T+W+Th = 4 * 38 = 152. T+W+Th+F = 4 * 40 = 160. Subtracting the first from the second gives F - M = 8. If M = 30, then F = 30 + 8 = 38°C.
387
If the average of a, b, c is 12 and the average of b, c is 15, what is the value of a?
Answer:
6
Sum of a,b,c = 3 * 12 = 36. Sum of b,c = 2 * 15 = 30. Therefore, a = 36 - 30 = 6.
388
A car travels from A to B at 60 km/h and returns at 40 km/h. What is the average speed of the car for the round trip?
Answer:
48 km/h
Using the formula for average speed over equal distances: 2xy / (x+y) = 2*60*40 / (60+40) = 4800 / 100 = 48 km/h.
389
The average age of 5 children is 8 years. If the age of their father is included, the average age becomes 13 years. What is the father's age?
Answer:
38 years
Total age of 5 children = 5 * 8 = 40. Total age with father (6 people) = 6 * 13 = 78. Father's age = 78 - 40 = 38 years.
390
The average of 5 consecutive odd integers is 15. What is the sum of the highest and lowest numbers?
Answer:
30
For any symmetric sequence, the sum of the highest and lowest is twice the average. Thus, 2 * 15 = 30. (The numbers are 11, 13, 15, 17, 19. 11+19 = 30).