Integrated Programme in Management (IPM) by IIM Indore provides an excellent opportunity for students, who want to pursue a career in management. The program will help you get a brand name in the field of management much earlier than you could have through the more traditional approach of post-graduation. This program will also aid in your overall personality development as the environment in IIM will make you a more brighter and confident person.

Cracking the IPMAT exam and studying in an IIM is a highly coveted dream for many management aspirants. It is being sought by many but few. If you have the right preparation strategy, strong concept knowledge, and shortcut tricks to solve questions efficiently you are definitely going to succeed in IPMAT. One of the important concepts to save time in the Remainder aptitude questions asked in the Quantitative aptitude section is provided below.

# Remainders concept for IPM Aptitude

A lot of questions based on remainder concepts are generally asked in the examination. To help you tackle these questions with ease we have listed important tricks and theorems related to the remainder concept with previous year questions and solutions

Concept -1

Starting from the basics the general equation for finding remainders is.

Dividend(n) = Divisor(d) x Quotient(q) + Remainder(r)

Let’s understand this concept with the help of an example, if we divide 100/3 we will have:-

Divisor(d) = 3 Dividend(n) = 100

Quotient(q) = 33

Remainder(r) = 1

100 = 3 x 33 + 1

Concept 2 if x, y, and z be three random numbers, we know that

- (x z) gives remainder Rx
- (y z) gives remainder Ry then find

(i) remainder of (x + y) z

(ii) remainder of (x -y) z

(iii) remainder of (x * y) z

The Trick to solve this question is to replace the unknown number by their respective remainder i.e., (Rx + Ry) / z. The remainder of this term will be the answer now. Three cases are possible using this approach.

### IPM Aptitude Questions & Answers based on Remainders

**Question: In a division problem, the product of quotients and the remainder is 24 while their sum is 10. If the divisor is 5 then the dividend is __________. (IPMAT 2020)**

**Solution :**

In this problem, we have given that the product of quotient(q) and the remainder(r) is 24.

i.e q x r = 24 -( i )

And it is also given that their sum is 10

i.e q + r = 10 -( ii )

Divisor(d) = 5.

( i ) and ( ii ) represent the sum and product of a quadratic equation, from ( ii ) putting r = q - 10, in ( i ), we will get q x (10 - q) = 24,

i.e q2-10q + 24 = 0,

Which will give q = 6 or 4.

Therefore one of them will be 6 and the other one will be 4. We do not know yet whether Quotient is 6 and Remainder is 4 or vice versa.

We know that

Dividend(n) = divisor(d) x quotient(q) + remainder(r) .

From the given data, n = 5 x q + r. - ( iii ),

As the divisor is 5 we infer that the remainder obviously will be smaller than 5, therefore the remainder will be 4 and the quotient will be 6. Putting the above-decided value in ( iii ).

n = 5(6) + 4 , therefore n = 34.