 # If two natural numbers, x and y are selected at random, then the total number of ways suchthat x2 + y2 is divisible by 10 is? Askiitians Expert Sahil Arora - IITD
19 Points
12 years ago

IF both x and y are divisible by 10.then obviously

 x2 + y2 will also be  divisible by 10 ... now how many natural no. u can find divisible by 10.. obviously infinite...... so there are infinite ways in which we can select x and y  I think the question doesn't make sense..there  should be some subset of natural no. given ```Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best s adhithya !!! Regards, Askiitians Experts Sahil Arora```

12 years ago

Consider the set of possible remainders on division by 10 i.e.{1,2,...,10}. When you square the possible remainders are {0,1,4,5,6,9}.

If we consider the ordered pairs of remainders (x,y), we get 100 possibilities

Thus x2+y2 will be divisible in the following cases:

(1) (0,0) - 1 case

(2) (1,9) - 4 cases

(3) (4,6) - 4 cases

(4) (5,5) - 1 case

(5) (6,4) - 4 cases

(6) (9,1) - 4 cases

making 18 favourable cases out of 100 possible cases giving a probability of 18/100 = 9/50