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The MCQs below are drawn from the Mathematics subject category.
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7571
The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weight of all the boys in the class.
Total weight of 16 boys = 16 * 50.25 = 804 kg. Total weight of 8 boys = 8 * 45.15 = 361.2 kg. Total weight of 24 boys = 804 + 361.2 = 1165.2 kg. Average = 1165.2 / 24 = 48.55 kg.
7572
Average marks obtained by 120 students is 35. If the average marks of passed students is 39 and that of the failed students is 15, then the number of passed students is:
Using alligation or standard equation: Let passed students be P and failed be F. P + F = 120. Total marks = 120 * 35 = 4200. Also, 39P + 15F = 4200. Substitute F = 120 - P: 39P + 15(120 - P) = 4200 => 39P + 1800 - 15P = 4200 => 24P = 2400 => P = 100.
7573
Three years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average age of the family is the same today. The present age of the baby is:
Sum of ages 3 years ago for 5 members = 5 * 17 = 85 years. Without the baby, their total age today would be 85 + (5 * 3) = 100 years. The current average of the 6 members (including baby) is 17 years. So, current total age = 6 * 17 = 102 years. Age of the baby = 102 - 100 = 2 years.
7574
Average of 10 distinct numbers is 20. If each number is increased by 10%, the new average will be:
Total sum of 12 numbers = 12 * 15 = 180. Add 41: new sum = 180 + 41 = 221. New total numbers = 13. New average = 221 / 13 = 17.
7576
A student scored an average of 60% in his first 4 subjects. To get an overall average of 70% in 5 subjects, what percentage must he score in the 5th subject?
Total required percentage points for 5 subjects = 5 * 70 = 350. Points scored in 4 subjects = 4 * 60 = 240. Required points in 5th subject = 350 - 240 = 110. Since the maximum possible in one subject is 100%, he needs 110%, which means it's mathematically 110% (even if physically impossible in standard grading).
7577
The average of 5 consecutive odd numbers is 25. The product of the smallest and largest number is:
The average of an odd number of consecutive integers is the middle term. So the middle term is 25. The numbers are 21, 23, 25, 27, 29. The smallest is 21 and the largest is 29. Their product is 21 * 29 = 609.
7578
The average of three numbers is 135. The largest number is 195 and the difference between the other two is 20. The smallest number is:
Total sum of the three numbers = 3 * 135 = 405. Sum of the two smaller numbers = 405 - 195 = 210. Let the two smaller numbers be x and y (where x > y). x + y = 210 and x - y = 20. Adding the two gives 2x = 230, so x = 115. Then y = 210 - 115 = 95. The smallest is 95.
7579
If the average of x and y is 40, and the average of y and z is 60, then the difference between z and x is:
We have (x + y)/2 = 40 => x + y = 80. Also, (y + z)/2 = 60 => y + z = 120. To find z - x, subtract the first equation from the second: (y + z) - (x + y) = 120 - 80. This gives z - x = 40.
7580
If the average of a, b, c is M and ab + bc + ca = 0, then the average of a^2, b^2, c^2 is:
Given (a+b+c)/3 = M, so a+b+c = 3M. Squaring both sides: (a+b+c)^2 = 9M^2. This expands to a^2 + b^2 + c^2 + 2(ab+bc+ca) = 9M^2. Since ab+bc+ca = 0, we have a^2 + b^2 + c^2 = 9M^2. The average of these squares is (9M^2) / 3 = 3M^2.
