AMC8 2027 - Self-practice Set 2

Suzanna rides at the constant rate shown, one mile per 5 minutes. How many miles will she ride in 30 minutes?

You walk 45 minutes at 4 miles per minute, then run 30 minutes at 10 miles per minute. How far do you travel in 1 hour 15 minutes?

Primes $a$, $b$, $c$ satisfyab=55 andbc=35. What is $abc$?

Suppose $a*b=2a-b$. What is $x$ if $4*(3*x)=10$?

Two $4\times4$ squares intersect as shown. At each intersection, their crossing sides are perpendicular and bisect each other. Draw a circle whose diameter joins the two intersection points. What is the area of the shaded region?

A gum machine contains $9$ red, $7$ white, and $8$ blue pieces of gum, dispensed randomly. What is the minimum number of purchases that guarantees four pieces of the same color?

Four friends sit in 4 distinct car seats. Only Bonnie or Carlo can drive. How many seating arrangements are possible?

The percentages working from home in 1960, 1970, 1980, 1990 are 5%, 8%, 15%, 30%. Which illustrated graph represents these values best?

Alex and Bob run around rectangle ABCD. Alex starts at A toward D at 30 metres per minute; Bob starts at B toward C at 42 metres per minute. They first meet after 3 minutes and meet again 4 minutes later. Find the perimeter.

For how many positive integers $x$ is 36/(x+3) also an integer?

Evaluate the following expression.
$$1^2-2^2+3^2-4^2+\ldots+2017^2-2018^2+2019^2.$$

In the diagram, $ABCD$ is a rectangle and $EFGH$ is a parallelogram. Using the labeled lengths, find the perpendicular distance $d$ between $HE$ and $FG$.

Bình (B), Đức (Đ), Hoa (H), and Lan (L) stand in line for ice cream. The person in the third position stands between Hoa and Bình. Đức stands immediately before Hoa, and Hoa is not last. What is their order?

Samantha lives at the lower-left corner and her school is at the upper-right corner of the illustrated map. She follows the two directions indicated by the compass. How many routes can she take?

Jacky tosses a fair coin 4 times. What is the probability that heads occur at least as often as tails?

June 24 of a leap year is a Wednesday. On which weekday is June 24 of the following year?

Find all nonnegative integers $x$ for which 8 x²+2 x−55 is prime.

Evaluate $100-97+94-91+\ldots+4-1$.

Triangle $ABC$ has area $8$ square meters. Points $M$ and $N$ are the midpoints of $AB$ and $AC$, respectively. Altitude $AD$ bisects $BC$. What is the shaded area?

Each half of the diagram contains $3$ red, $5$ blue, and $8$ white triangles. When the upper half is folded down along the horizontal line, two red-red pairs, three blue-blue pairs, and two red-white pairs overlap. How many white-white pairs overlap?