Mixed Deck — All AMC 8 Topics Flashcards

Two angles of a triangle are 55° and 75°. What is the third angle?

Answer: 50°

The angles sum to 180°, so the third angle = 180° − 55° − 75° = 50°.

A square has area 144. What is its perimeter?

Answer: 48

Side = √144 = 12, so perimeter = 4 × 12 = 48.

What is the greatest common factor (GCF) of 48 and 36?

Answer: 12

The GCF of 48 and 36 is 12, since 12 divides both and no larger number does.

Express 0.625 as a fraction in lowest terms.

Answer: 5/8

0.625 = 625/1000 = 5/8 after dividing numerator and denominator by 125.

Mike read 1/4 of a book on Monday and 1/3 on Tuesday. What fraction of the book remains?

Answer: 5/12

He read 1/4 + 1/3 = 3/12 + 4/12 = 7/12, leaving 1 − 7/12 = 5/12.

Carlo's car consumes a gallon of gas every 35 miles and has a gas tank capacity of 14 gallons when full. Karl started with a full tank of gas, traveled 350 miles, stopped to buy 8 gallons of gas, and then drove the rest of the way to his destination. His gas tank was half full when he arrived. Karl drove how many miles that day?

Answer: 525

The correct answer: He had consumed 350/35 = 10 gallons of gas after 350 miles since he uses a gallon of gas every 35 miles. As a result, he had 14 – 10 = 4 gallons of gas left after the first leg of his journey. Then he went out and bought another 8 gallons of gas, bringing his total gas tank capacity to 12 gallons. He had 1/2 14 = 7 gallons of gas when he arrived. As a result, on the second part of his journey, he used 5 gallons of gas. As a result, the second leg of his journey covered 5 35 = 175 miles. When we add this to the 350 miles, we get 350 + 175 = 525 miles.

A container holds 50 red, 40 blue, and 10 green marbles. What percent are blue?

Answer: 40%

Total marbles = 100, and 40 are blue, so blue percent = 40/100 = 40%.

How many 3-digit even numbers can be formed from {2, 4, 5, 6} with no repetition?

Answer: 18

Choose an even units digit (3 options: 2, 4, 6), then arrange the remaining 3 digits in the first two positions (3 × 2 = 6 ways): 3 × 6 = 18.

Which correctly orders 3/5, 7/10, and 0.65 from least to greatest?

Answer: 3/5, 0.65, 7/10

Converting to decimals: 3/5 = 0.60, 0.65, 7/10 = 0.70, so the order is 3/5 < 0.65 < 7/10.

Two fair dice are rolled. What is the probability that their sum is 7?

Answer: 1/6

There are 6 pairs that sum to 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 equally likely outcomes.

What is the value of 3a − 2b when a = 4 and b = −1?

Answer: 14

3(4) − 2(−1) = 12 + 2 = 14.

A sequence follows the rule: each term is 3 less than twice the previous term. If the first term is 5, what is the 4th term?

Answer: 19

t₁ = 5, t₂ = 2(5)−3 = 7, t₃ = 2(7)−3 = 11, t₄ = 2(11)−3 = 19.

What is the largest of the following values?

Answer: 2 + 0 + 1 + 7

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

A rectangle's length is increased by 20% and its width is decreased by 10%. By what percent does the area change?

Answer: 8% increase

New area = 1.2 × l × 0.9 × w = 1.08lw, which is an 8% increase.

Alice is 5 years older than Bob. The sum of their ages is 37. How old is Bob?

Answer: 16

If Bob = b, then b + (b+5) = 37 gives 2b = 32, so b = 16.

The longest professional tennis match took 11 hours and 5 minutes to complete. What is the time in minutes?

Answer: 665

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.

The sum of three consecutive integers is 75. What is the largest of the three?

Answer: 26

With integers n, n+1, n+2: 3n + 3 = 75 gives n = 24, so the largest is 26.

If a number leaves a remainder of 3 when divided by 7, what remainder does twice that number leave when divided by 7?

Answer: 6

If n ≡ 3 (mod 7), then 2n ≡ 6 (mod 7).

The mean of a data set is 15 and the median is 13. If the largest value (an outlier of 30) is removed, what is most likely true?

Answer: The mean decreases more than the median

Removing a large outlier has a greater effect on the mean (which depends on all values) than on the median (which depends only on position).

A box has 6 red and 4 blue balls. Two balls are drawn without replacement. What is the probability both are red?

Answer: 1/3

P = (6/10) × (5/9) = 30/90 = 1/3.