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# Integer | ISI-B.stat Entrance(Objective from TOMATO) | Problem 72

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

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

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