Author: Shivam Pawase
Tester: Rushang Gajjal
Editorialist: Sangram Desai
DIFFICULTY:
CAKEWALK, SIMPLE-EASY .
PREREQUISITES:
Math
PROBLEM:
There are two items potatoes and tomatoes, we need to tell whether it is possible to buy equal quantity of potatoes and tomatoes from market or not.
QUICK EXPLANATION:
So we just want to check LCM(x,y)/x and LCM(x,y)/y must be less than n and m respectively.
EXPLANATION:
Weight = Item weight * Number of tomatoes / potatoes
let’s consider a variable such that after multiplying with x and y gives an equal weight of potatoes and tomatoes.
Also, weight must be less than the total weight of items in the market.
LCM of x and y gives that number which satisfies the conditions
for example,
we have x = 3 y = 5 n = 5 and m = 3
x = 3,9,12,15,..
y = 5,10,15,20,..
we get 15 as equal weight so LCM becomes 15, now no. of potatoes = 15/x and no. of tomatoes = 15/y . Which is less than the total number items n and m respectively.
AUTHOR’S AND TESTER’S SOLUTIONS:
Author’s solution can be found here
Tester’s solution can be found here