AMC8 Test 2
An test is taken by four pupils. Their scores are 70, 80, and 90, respectively. What is the remaining score if the average of their four scores is 70?
The correct answer:
Solution
The remaining score is abbreviated as r. We also know that 70 equals 70 + 80 + 90 + r / 4. To solve for r, we can use simple algebra:
70 + 80 + 90 + r / 4 = 70
240 + r / 4 = 70
240 + r = 280
r = 40
Solution 2
Because 90 is 20 more than 70 and 80 is ten more than 70, the other number must be thirty less than 70, or 40, in order for 70 to be the average.
Adam used to be able to run 15 miles in 3 hours and 30 minutes when he was a kid. He can now walk 10 kilometers in four hours as an elderly man. How much longer does it take him to walk a mile now than it did when he was a kid?
The correct answer:
Adam used to be able to run 15 miles in 3 hours and 30 minutes (3 x 60 + 30 minutes = 210 minutes), resulting in a mile time of 210/15 = 14 minutes. He can now walk 10 miles in 4 hours = 4 x 60 minutes = 240 minutes, resulting in a mile time of 240/10 = 24 minutes. As a result, walking a mile now takes him 10 minutes longer than it did when he was a child.
A and b have a least common multiple of 12, whereas b and c have a least common multiple of 15. What is the smallest feasible value of a and c's least common multiple?
The correct answer:
We're looking for possible a, b, and c values. By determining the highest common factor of 12 and 15, we can deduce that it's a multiple of b, and since we know it's 3, we can deduce that b is 3. Moving on to a and c, we want to find the smallest such that the least common multiple of a and 3 is 12, which leads to 4. We get 5 in the same way we got 3 and c. Twenty is the least common multiple of four and five.
10,000 is the sum of 25 consecutive even integers. Which of these 25 consecutive integers is the largest?
The correct answer:
Assume that n is the 13th consecutive even integer to be added. Because (n – 2k) +... + (n – 4) + (n – 2) + (n) + (n + 2) + (n + 4) +... +(n + 2k) = 25n, we can see that the sum of all 25 even numbers will reduce to 25n. 25n = 10000, which equals n=400. We want to discover the 25th integer, which is 400 + 2(25 – 13) = 424, keeping in mind that this is the 13th integer.
What is the largest of the following values?
The correct answer:
The values of the expressions are, in order, 10, 8, 9, 9, and 0.
Mary's marbles are all blue, red, green, or yellow in color. a 1/3 of her total The majority of the marbles are blue, with a quarter of them being red and six being green. What is the least amount of yellow marbles Mary may possibly possess?
The correct answer:
As a result, the total number of Mary's marbles must be divisible by three and four.
It has to be a 12th multiple. If she only has 12 marbles, four of them will be blue and three will be red.
She couldn't have 6 green marbles because she only had 5 other marbles. If she has 24 marbles, eight are left.
She could have 6 green marbles and 4 yellow marbles if 6 are blue and 6 are red.
marbles. Mary's fewest number of yellow marbles would be four..
The smallest positive integer bigger than 1 with a remainder of one. Which of the following is true when 1 is divided by 4, 5, and 6? numbers in pairs?
The correct answer:
60 is the least common multiple of the numbers 4, 5, and 6. Numbers that leave an impression
When divided by 4, 5, and 6, the residue is one more than a whole number multiple of 60.
As a result, the smallest positive number larger than 1 that divides to 1 leaves a leftover of 1 is
The sum of 4, 5, and 6 is 61.
The longest professional tennis match took 11 hours and 5 minutes to complete. What is the time in minutes?
The correct answer:
1st Option:
It's preferable to divide the 11 hours and 5 minutes into two pieces, one 11 hours and one 5 minutes. We all know that an hour is divided into 60 minutes. As a result, in 11 hours, there are 11 60 = 660 minutes. 660 + 5 = 665 is the result of adding the second part (the 5 minutes).
2nd Option
When you recall your multiplication tables, you'll have the best way. As a result, our answer of 665 is trivial.
Lindsay traveled for one hour each day for four days at a speed of As a result, she was able to cover one mile in an integer number of minutes. Her speed slowed each day after the first, and the number of people she could see reduced. Over the previous year, the time it took to go one mile increased by 5 minutes. day. Her total distance traveled over the four days was also an integer. the distance between two points How many miles did the four of them cover in total trips
The correct answer:
Each journey took her 60 minutes. The 60 factors are 1, 2, 3, 4, 5, and 6.
10, 12, 15, 20, 30, and 60 are the numbers. Her daily minutes for a mile make a four-part pattern.
numerals where each number is 5 higher than the one before it. These figures must also be accurate.
Because the amount of kilometers traveled must be an integer, each must be a factor of 60. The only one of its kind
The order of the 60 factors is 5, 10, 15, 20, and so on. For the four days, her rates in miles per minute were 1/5, 1/10, 1/15, 1/20
and multiplied by 60 minutes gives her distances in minutes for a total distance of 25 miles as 12, 6, 4, and 3.
