MathDB

16

Part of 2019 India PRMO

Problems(2)

Minimizing the difference between variables in a linear equation

Source:

8/11/2019
A pen costs Rs. 13\mathrm{Rs.}\, 13 and a note book costs Rs. 17\mathrm{Rs.}\, 17. A school spends exactly Rs. 10000\mathrm{Rs.}\, 10000 in the year 2017−182017-18 to buy xx pens and yy note books such that xx and yy are as close as possible (i.e., ∣x−y∣|x-y| is minimum). Next year, in 2018−192018-19, the school spends a little more than Rs. 10000\mathrm{Rs.}\, 10000 and buys yy pens and xx note books. How much more did the school pay?
linear equationalgebra
Simple Divisibility

Source: PRMO Leg 2 P16

8/25/2019
Let NN denote the number of all natural numbers nn such that nn is divisible by a prime p>np> \sqrt{n} and p<20p<20. What is the value of NN ?
algebra