Aptitude - Numbers - Discussion

Answer should be 4 and 1.

Here 29 is fit for this by hit and trail method when 29/4 give reminder 1 and when 29/5 gives reminder 4 so why 4, 1 is not answer.

I am unable to understand the solution.

When dividing a positive integer n by another positive integer D (divider) , we obtain a quotient Q, which is a non-negative integer and a remainder R, which is an integer such that 0\leq{R}<D. We can write n = DQ+R.

When dividing our number n by 4 we obtain a remainder of 1, so, if the quotient is some integer Q, we can write n = 4Q+1.

Now, dividing Q by 5, we obtain another quotient say q and remainder 4, thus we can write
Q = 5q+4.

It follows that n = 4(5q+4)+1 = 20q+17.

Since n = 20q+17 = 5(4q+3)+2, it means that when dividing n by 5 first, we get a quotient 4q+3 and remainder 2.

Then dividing 4q+3 by 4 we obviously obtain a remainder of 3.

37/4=remainder 1.

Then how 1 - 3? I don't understand it, please explain it.

Divident=9, and next time it divided by 7 and 6. (not 5 and 4).

Let a no x.

It is divided by 4 remainder is 1.

So x = 4*y + 1;
y = 5*z+ 4;( anther division).

Now,
x=4(5*z +4)+1= 20*z+17;

We can write above no.as
x=5(4*z +3)+2;

So above no gives remainder 2 when divided by 5. And then successive division gives remainder 3 from ( 4*z +3).

Let the number be X. when it is divided by 4, remainder is 1 and quotient is Y(assume). now further when Y is divided by 5, remainder is 4 and quotient will be 1(successively divided). Now according to formula,

Y=(5*1)+4=9 and
X=(4*y)+1=(4*9)+1=37

So we got the values of X and Y..rest you can find out easily.

@Sasikala.

Why b=1?

Thanks @Jay.