# Modulus Functions in Two Variables – 6 ## 18 thoughts on “Modulus Functions in Two Variables – 6”

1. jugapratim |

for excercise Q1: plugging in values of x as 0,-1,-2,-3,-4,-5,-6,-7,-8,-9,-10 we get 1,3,5,7,9,11,9,7,5,3,1 as values of y.Total values of y=61

2. Jan |

Dear J,

I would like to thank u a lot for the effort you are taking in each post. These posts have truly helped me in many ways for which i am grateful. I am having my CAT on Nov.1 and hope the methods taught here will come in more handy( as you have already saved us with the ant question ). 🙂

Thanks,
Jan

• catcracker |

Jan, glad it is helping, and hope that on your D-day you will find many questions which you can solve confidently 🙂

regards
J

3. jaspreet |

sir exercise 1 ka 20 arah… 😐

4. jaspreet |

i think inequality mein 61 hna chahiye ans <=5..maybe..havnt tried,equality k lie toh 20 hna chahiye.

5. catcracker |

Yes, should have been “enclosed by” only, Jaspreet. I have edited it now!

regards
J

6. Harsh Vardhan |

Sir after getting the range like x=2,3,4,5,6 and y=0,1,2,3,4 do we have to check after plugging each and every value or i there any quicker method in this to obtain. I mean do we need to form all the combination at hand to get the result.

• catcracker |

Harsh, look for patterns. Here if I see 1, 3, 5, 7…. samajhdar ko ishara kaafi hai na?

regards
J

7. Harsh |

Hello J,

Is the answer for integer co-ordinates satisfying |x| + |y| = 5, 50?

Regards 🙂
Harsh

• catcracker |

I make it 61, Harsh. You have possibly missed the case where x = 0 (which gives 11 values for y)

regards
J

8. Harsh |

Yes, I missed that one.
As you have pointed out in the post that the only difference between them is their centres, so I was checking the solutions….
So, effectively, in the test, can we solve for |x| + |y| = 5, if the question is |x+5| + |y-3| = 5? ;)(Integer co-ordinates)

Regards 🙂
Harsh

• catcracker |

Yes we can.

regards
J

9. Gaurav |

What goes wrong if we were to plot the graphs for the 2 variables, |x-4| and |y-2|, separately, in a way similar to the previous post on modulus addition? Thank You! These topics have been of great of help.

10. catcracker |

The problem is, how would you do that? Normally if you are plotting just |x-4| it means you are plotting y = |x-4| and so here you would be trying to do two separate things, both in x and y. Confusing. Here both x and y are interacting together and we can’t separate them out that easily since both are within modulus signs. So trial and error is simplest.

regards
J

11. Himanshu Srivastava |

Here, just draw the graph of |x|+|y|=5 and then shift the graph according to the given point and we know the graph of this given mod is simple rhombus .Using the concept of 90-45-45 find its one of the side which will be equal to the 5sqrt2=50.

• Himanshu Srivastava |

5sqrt2 is the side of rhombus.So area =side square=50

12. ankit kumar |

Hi J , As reasoning mentioned in the question above is it safe to infer that the no of points having integral coordinates for |x|+|y|=2 will be same as |x+a|+|y+b|=2

• catcracker |

As long as “a” and “b” are integers, yes 🙂

regards
J