BALANCE - Editorial

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

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