AMC8 Test 2

Question 1

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?

Accepted Answer

40

Answer

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.

Question 2

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?

Accepted Answer

10

Answer

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.

Question 3

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?

Accepted Answer

20

Answer

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.

Question 4

10,000 is the sum of 25 consecutive even integers. Which of these 25 consecutive integers is the largest?

Accepted Answer

424

Answer

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.

Question 5

What is the largest of the following values?

Accepted Answer

2 + 0 + 1 + 7

Answer

The correct answer:
The values of the expressions are, in order, 10, 8, 9, 9, and 0.

AMC 8 - American Mathematics Competition 8 Practice Test

AMC 8 - American Mathematics Competition 8 Practice Test

AMC8 Test 2