Aptitude - Numbers - Discussion

I took number as 37. I calculated by trial and error.

When a number is divided by 4 remainder is 1 and successive division (this is nothing but QUOTIENT OF FIRST division). Initially, I used 5 as the number and divided by 4 5 5/4 I got remainder 1 and quotient also 1. Now a successive division of 1/5 (here 1 is the quotient of previous division) won't give rem 1. So I used 9 so that 9/5 remainder is 4. Now 9 quotient of step 1 division 4*9 =36 so if I take 37 as the number remainder is 1.

See now 37/4 = 9 quo and 1 rem matches the rem in question.

Successive division 9/5 1 quo and 4 rem, matches rem in question.

Now as asked in the question first div by 5 and then 4 find rem.

37/5 = 2 rem quo is7 and 7/4 1 quo 3 rem.

So the answer is 2, 3.

Original number is assumed as x.

The quotient after dividing by 5 is assumed in the given solution as 1. This could be assumed as any number and has no effect on the remainder. This is because there are many numbers such as 17, 37, 57 etc. that satisfy the criteria of leaving 1 and 4 as remainders after successively dividing by 4 and 5.

If we assume 1 as the quotient after division by 5, we get two equations:
4 | x
5 | y (remainder: 1)
|1 <== assume any number here (remainder: 4)

1*5 + 4 =y ===> y=9;
y*4+1=x ====> x=37;

Once we get the original number as 37, divide by 5, get the remainder 2 and quotient 7. Divide 7 by 4, get the remainder 3. Hence the answer 2,3.

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.

Let a number X which is divisible by 4 and 5 respective gives 1 and 4.

Step 1:

Now, first divide by 4. We take Y as dividend. When you divide X by 4 it gives remainder 1.

4 | X | Y.
______

1.

So X = 4 * Y + 1 --- equation(1).

Step 2:

Now, divide by 5. We take 1 as dividend because it divides completely. When you divide Y by 5 it gives only remainder 4.

5 | Y | 1.
______

4.

So Y = 5*1+4.

Step 3:

Y = 9.

And put this value in equation (1).

X = 4*9+1.
X = 37.

Step 4:

Now 37 divide by 5 and 4 respective it will gives 2 and 3.

@Ripa Roy.

x=4a+1 and a=5b+4.
when successively divide a number, quotient will be taken as dividend.
to find the number:
a=5(1)+4=9,
a=9.

Substitute a value to x then x=4(9)+1=36+1=37.
x=37.
when 37 is successfully divided by 5 and 4,
37/5=quotient 7 and remainder 2,
then 7/4=quotient 1 and remainder 3,
so answer is 2 and 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.

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).

It is said that "divided SUCCESSIVELY by 4 and 5" .
SUCCESSIVE: Following one another
So from the given solution we see that at first any number (X) has been divided by 4 and then the result (Y-1) is divided by 5 .

When a number is successively divided by 7, 5 and 4 it leaves remainders of 4, 2 and 3 respectively. What will be the respective remainders when the smallest such number is successively divided by 8, 5 and 6?

Can you please tell the answer for this?

A number x when divided by 9 leaves a remainder 8. What is the remainder when we divide x^24 by 9?

A. 3
B. 2
C. 7
D. 1