Math topic中文

Indeterminate equations

Find integer solutions using divisibility, parity and bounding to shrink the search space.

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Letters represent numbers

Practice questions

  1. 1一个除法算式，把被除数、除数、商相加得124，被除数是（ ） A. 62 B. 124 C. 不能确定
  2. 2A classroom has a row of 35 coat hooks. Paulina likes coats to be equally spaced, so that there is the same number of em…
  3. 3Greta Grasshopper sits on a long line of lily pads in a pond. From any lily pad, Greta can jump 55 pads to the right or…
  4. 4In a sequence of positive integers, each term after the second is the product of the previous two terms. The sixth term…
  5. 5Ralph went to the store and bought 12 pairs of socks for a total of 24.Someofthesocksheboughtcost24. Some of the socks he bought cost 1 a pair, som…
  6. 6In trapezoid ABCDABCD, angles BB and CC measure 60∘60^\circ and AB=DCAB = DC. The side lengths are all positive integers and…
  7. 7Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by…
  8. 8末八位数是18421997且能被71整除的最小自然数为 ．
  9. 9Steph scored 15 baskets out of 20 attempts in the first half of a game, and 10 baskets out of 10 attempts in the second…
  10. 10After Euclid High School's last basketball game, it was determined that 14\frac{1}{4} of the team's points were scored b…
  11. 11How many positive integers can fill the blank in the sentence below? “One positive integer is ___ more than twice anothe…
  12. 12The land of Catania uses gold coins and silver coins. Gold coins are 1mm thick and silver coins are 3 mm thick. In how m…
  13. 13A baseball league consists of two four-team divisions. Each team plays every other team in its division NN games. Each…
  14. 14Laila took five math tests, each worth a maximum of 100 points. Laila's score on each test was an integer between 0 and…
  15. 15Nicolas is planning to send a package to his friend Anton, who is a stamp collector. To pay for the postage, Nicolas wou…