{"id":779,"date":"2022-02-01T11:46:00","date_gmt":"2022-02-01T15:46:00","guid":{"rendered":"http:\/\/mathfun4kids.com\/mlog\/?p=779"},"modified":"2024-10-25T15:09:44","modified_gmt":"2024-10-25T19:09:44","slug":"amc-8-exercises-1-october-20-2020","status":"publish","type":"post","link":"https:\/\/mathfun4kids.com\/mlog\/?p=779","title":{"rendered":"AMC 8 Exercises 1 – 02\/01\/2024"},"content":{"rendered":"\n
  1. The sum of the first three prime number greater than 50 is $$ $$ $\\textbf{(A) }169 \\qquad\\textbf{(B) }171 \\qquad\\textbf{(C) }173 \\qquad\\textbf{(D) }175 \\qquad \\textbf{(E) } 177$ $$ $$<\/li>
  2. In a regular hexagon, the ratio between the shortest diagonal and the longest diagonal is $$ $$ $\\textbf{(A) }\\dfrac{1}{3} \\qquad\\textbf{(B) }\\dfrac{1}{2} \\qquad\\textbf{(C) }\\dfrac{1}{\\sqrt{3}} \\qquad\\textbf{(D) }\\dfrac{2}{3} \\qquad \\textbf{(E) } \\dfrac{\\sqrt{3}}{2}$ $$ $$<\/li>
  3. In a box there are 5 red balls and 10 white balls. If two balls are taken at the same time, the chance of getting two balls of the same color is $$ $$ $\\textbf{(A) }\\dfrac{1}{2} \\qquad\\textbf{(B) }\\dfrac{1}{4} \\qquad\\textbf{(C) }\\dfrac{2}{21} \\qquad\\textbf{(D) }\\dfrac{10}{21} \\qquad \\textbf{(E) } \\dfrac{11}{21}$ $$ $$<\/li>
  4. Let $x=\\dfrac{1}{2+\\dfrac{1}{2+\\dfrac{1}{2}}}$, then $x$ = $$ $$ $\\textbf{(A) }\\dfrac{2}{9} \\qquad\\textbf{(B) }\\dfrac{5}{12} \\qquad\\textbf{(C) }\\dfrac{4}{9} \\qquad\\textbf{(D) }\\dfrac{9}{4} \\qquad \\textbf{(E) } \\dfrac{12}{5}$ $$ $$<\/li>
  5. In $\\triangle{ABC}$, point $F$ divides $AC$ in the ratio of $1: 2$. Suppose $G$ is the middle point of $BF$ and $E$ is the point of intersection between $BC$ and $AG$. Then point $E$ divides $BC$ in the ratio of $$ $$ $\\textbf{(A) }\\dfrac{1}{4} \\qquad\\textbf{(B) }\\dfrac{1}{3} \\qquad\\textbf{(C) }\\dfrac{2}{5} \\qquad\\textbf{(D) }\\dfrac{4}{11} \\qquad \\textbf{(E) } \\dfrac{3}{8}$ $$ $$<\/li>
  6. In a gathering, 28 handshakes were made. Every two people shake hands at most once. The least number of people who attended the gathering was $$ $$ $\\textbf{(A) }28 \\qquad\\textbf{(B) }27 \\qquad\\textbf{(C) }14 \\qquad\\textbf{(D) }8 \\qquad \\textbf{(E) }7 $ $$ $$<\/li>
  7. Kevin’s salary is 20% more than William’s. After William earns a salary increase, his salary is more than $20%$ of Kevin’s salary. William’s salary increase percentage is $$ $$ $\\textbf{(A) }0.44 \\qquad\\textbf{(B) }20 \\qquad\\textbf{(C) }44 \\qquad\\textbf{(D) }144 \\qquad \\textbf{(E) } \\text{Cannot be determined}$ $$ $$<\/li>
  8. Let $P$ be the set of all points on the $xy$-plane satisfying $|x|+|y|\\le4|$. The area of $P$ is $$ $$ $\\textbf{(A) }4 \\qquad\\textbf{(B) }8 \\qquad\\textbf{(C) }12 \\qquad\\textbf{(D) }16 \\qquad \\textbf{(E) } 32$ $$ $$<\/li>
  9. How many 3-digit natural numbers are there with its value 30 times of the sum of its digits? $$ $$ $\\textbf{(A) }0 \\qquad\\textbf{(B) }1 \\qquad\\textbf{(C) }2 \\qquad\\textbf{(D) }5 \\qquad \\textbf{(E) }10 $ $$ $$<\/li>
  10. Denote $a\\oplus b=a+b+1$, for all integers $a$ and $b$. If $a\\oplus p=a$ for all integers $a$, then $p=$ $$ $$ $\\textbf{(A) }-1 \\qquad\\textbf{(B) }0 \\qquad\\textbf{(C) }1 \\qquad\\textbf{(D) }-2 \\qquad \\textbf{(E) } \\text{No solution}$ $$ $$<\/li>
  11. Ten ice hockey teams participate in a tournament. Each team meets every other team once. The winner of each match gets a 3 point, while the loser gets a score of 0. For a match that ends in a draw, both teams score 1 each. At the end of the tournament, the total score for all teams is 124. The number of matches that end in a draw is $$ $$ $\\textbf{(A) }8 \\qquad\\textbf{(B) }9 \\qquad\\textbf{(C) }10 \\qquad\\textbf{(D) }11 \\qquad \\textbf{(E) } 12 $ $$ $$<\/li>
  12. Each $dong$ is a $ding$. Some $dung$ are $dong$. The following statements are made $ding$, $dong$, and $dung$: