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The MCQs below are drawn from the Mathematics subject category.
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7601
A library has an average of 510 visitors on Sundays and 240 on other days. What is the average number of visitors per day in a month of 30 days beginning with a Sunday?
A 30-day month beginning with a Sunday will have 5 Sundays and 25 other days. Total visitors = (5 * 510) + (25 * 240) = 2550 + 6000 = 8550. Average visitors per day = 8550 / 30 = 285.
The first 10 multiples of 3 are 3, 6, 9, ..., 30. This is an arithmetic progression. For an AP, the average is (first term + last term) / 2 = (3 + 30) / 2 = 33 / 2 = 16.5.
7603
In an exam, the average marks of 40 students is 72. Later, it was found that the marks of three students were misread as 68, 75, and 73 instead of 64, 62, and 84 respectively. Find the correct average.
Original sum = 40 * 72 = 2880. The misread sum was 68 + 75 + 73 = 216. The correct sum should be 64 + 62 + 84 = 210. Difference = 210 - 216 = -6. Correct sum = 2880 - 6 = 2874. Correct average = 2874 / 40 = 71.85.
7604
The average age of three boys is 15 years. If their ages are in the ratio 3:5:7, what is the age of the youngest boy?
Total age of the three boys = 3 * 15 = 45 years. Let their ages be 3x, 5x, and 7x. 3x + 5x + 7x = 45, which gives 15x = 45, so x = 3. The age of the youngest boy is 3x = 3 * 3 = 9 years.
7605
The average of 50 numbers is 38. If two numbers, namely 45 and 55, are discarded, the average of the remaining numbers is:
Total sum of 50 numbers = 50 * 38 = 1900. Sum of the two discarded numbers = 45 + 55 = 100. Sum of the remaining 48 numbers = 1900 - 100 = 1800. Average of remaining numbers = 1800 / 48 = 37.5.
7606
The average of 5 quantities is 10 and the average of 3 of them is 8. What is the average of the remaining 2 quantities?
Total sum of the 5 quantities = 5 * 10 = 50. Sum of the 3 quantities = 3 * 8 = 24. Sum of the remaining 2 quantities = 50 - 24 = 26. Average of the remaining 2 quantities = 26 / 2 = 13.
When distances are equal, average speed is calculated using the formula 2xy / (x + y). Here, x = 40 and y = 60. Average speed = 2(40)(60) / (40 + 60) = 4800 / 100 = 48 km/h.
7609
Find the average of the cubes of the first 4 natural numbers.
The sum of the cubes of the first n natural numbers is [n(n+1)/2]^2. For n=4, the sum is [4(5)/2]^2 = 10^2 = 100. The average is 100 / 4 = 25. Alternatively: (1+8+27+64)/4 = 100/4 = 25.
7610
Find the average of the squares of the first 5 natural numbers.
The formula for the sum of squares of the first n natural numbers is n(n+1)(2n+1)/6. For n=5, the sum is 5(6)(11)/6 = 55. The average is 55 / 5 = 11. Alternatively: (1+4+9+16+25)/5 = 55/5 = 11.
