Try this beautiful problem Based on Integer useful for ISI B.Stat Entrance.

## Integer| ISI B.Stat Entrance | Problem 72

The number of integer (positive ,negative or zero)solutions of \(xy-6(x+y)=0\) with \(x\leq y\) is

- 5
- 10
- 12
- 9

**Key Concepts**

Integer

Algebra

Divisor

## Check the Answer

Answer: 10

TOMATO, Problem 72

Challenges and Thrills in Pre College Mathematics

## Try with Hints

Factorize the given equation

Can you now finish the problem ……….

Find the divisor

can you finish the problem……..

Given equation is \(xy-6(x+y)=0\)

\(\Rightarrow xy-6x-6y=0\)

\(\Rightarrow xy-6x-6y+36=36\)

\(\Rightarrow (x-6)(y-6)=3^2 \times 2^2\)

Now the numbers of factpr of \(36=9\) i.e \(\{1,2,3,4,6,9,12,18,36\}\)

Thus we may say that 36 has 9 positive divisors, and 9 negative. and x=0 and y=0 is also a solution

the given condition \(x\leq y\) ,so there are 10 non-negetive solution

## Other useful links

- https://www.cheenta.com/trapezium-geometry-prmo-2018-problem-5/
- https://www.youtube.com/watch?v=qb4oN02rSxM