# 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

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}

 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.