olymmath

HMMT November 2022 H8

  • Theme
  • Answer

Alice thinks of four positive integers a≤b≤c≤da \leq b \leq c \leq d satisfying {ab+cd,ac+bd,ad+bc}={40,70,100}\{a b+c d, a c+b d, a d+b c\}=\{40,70,100\}. What are all the possible tuples (a,b,c,d)(a, b, c, d) that Alice could be thinking of?

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

(1,4,6,16)

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.

Add a solution

Similar problems

These problems have the most words in common with this statement.

Locator hmnt/2022/h8 · Tag SH3W63RWX3 · Edit this page on GitHub · Keys: j next, k previous