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The MCQs below are drawn from the Mathematics subject category.
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7551
The average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew, who weighs 53 kg is replaced by a new man. The weight of the new man is:
Total weight increase = 10 * 1.8 = 18 kg. This increase is because the new man is heavier. Weight of the new man = weight of replaced man + increase = 53 + 18 = 71 kg.
7552
The average of 5 consecutive odd numbers is 95. What is the fourth number in descending order?
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.
7553
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:
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.
7554
Average of 15 numbers is 0. Among them, how many numbers can be greater than 0 at most?
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.
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.
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).
7557
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:
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.
The average of the first 'n' odd natural numbers is exactly 'n'. Therefore, for the first 50 odd numbers, the average is 50.
7560
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)?
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.
