Aptitude - Numbers - Discussion

Discussion :: Numbers - General Questions (Q.No.131)

131. 

A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be

[A]. 1, 2
[B]. 2, 3
[C]. 3, 2
[D]. 4, 1

Answer: Option B

Explanation:

 4 | x            y = (5 x 1 + 4) = 9
 --------
 5 | y -1         x = (4 x y + 1) = (4 x 9 + 1) = 37
 --------
   | 1 -4

 Now, 37 when divided successively by 5 and 4, we get

 5 | 37
 ---------
 4 | 7 - 2
 ---------
   | 1 - 3
 
 Respective remainders are 2 and 3.

Rakhi Sharma said: (Sep 4, 2011)  
I am unable to understand the solution.

Amy said: (Aug 20, 2012)  
Someone, please explain.

Debashish Halder said: (Sep 8, 2012)  
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 .

Debashish Halder said: (Sep 8, 2012)  
Earlier I mentioned (Y-1) which will be only (Y), that is when (X) is divided by 4 the result is (Y).

Jay said: (Dec 27, 2012)  
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.

Thirupathi Reddy said: (Jul 14, 2013)  
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).

Tushar said: (Mar 10, 2014)  
Divident=9, and next time it divided by 7 and 6. (not 5 and 4).

Akml said: (Dec 27, 2014)  
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.

Rohit Jain said: (Apr 20, 2015)  
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.

Antara said: (Aug 27, 2015)  
Answer should be 4 and 1.

Gaurav said: (Mar 1, 2016)  
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.

Alam Milan said: (Aug 14, 2016)  
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

Kunal Madankar said: (Sep 24, 2016)  
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?

Ripa Roy said: (Apr 21, 2017)  
37/4=remainder 1.

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

Sasikala said: (Jun 24, 2017)  
@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.

Mr. Mp said: (Aug 29, 2017)  
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.

Neeraj said: (May 8, 2019)  
4Q+1=n.
5q+4=Q.
n = 4(5q+4)+1 = 20q+17= 5 * 4q + 5 * 3 + 2.
Now n is devided by 5 so the remainder is 2.
And now devide 4q+3 by 4 so remainder is 3.

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