IPM Aptitude Questions Based on Remainders

Attempting IPMAT itself is a challenge and having less time for each paper becomes another. But if you know the right trick, you can manage your time quite easily.

The questions from the remainders concept in the IPMAT maths section are of a certain standard to check your mathematical reasoning. Practising more and more questions from this concept will help you fetch more marks than others.

With the right preparation strategy, students with non-math backgrounds have cleared the exam easily in the past. To ease your preparation, we have compiled the important IPM aptitude questions and answers based on remainders in this post.

So, what are you looking for? Check out the questions from the post below and enhance your preparation.

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What is a Remainder?

In arithmetic, the remainder is defined as the integer left over after dividing one integer by another to produce an integer quotient.

A lot of questions based on the remainder concept are generally asked in the competitive examinations including IPMAT. Therefore, following some IPMAT Maths Preparation Tips and tricks would definitely help you solve these questions in a matter of seconds.

To help you tackle these questions with ease, we have listed important tricks and theorems related to the remainders along with previous year questions and solutions below.

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 

1. (x z) gives remainder Rx 
2. (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 that are possible using this approach are explained below.

Read more: Short tricks to crack IPMAT verbal ability section

Read more: Important cross multiplication questions for IPMAT 2023

Practice More Questions on Remainders for IPMAT

IPM Aptitude Questions & Answers based on Remainders

To help you get an idea about the type of questions asked in the exam, we have provided few sample questions that are curated from the previous year Question Papers for IPMAT.

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 __________. 

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. 

Question:

What is the remainder when 123 x 124 x 125 is divided by 9?

Solution :

When 123 is divided by 9, the remainder will be  -3.

While it is -2 when 124 is divided by 9.

Similarly, when 123 is divided by 9, the remainder will be -1

Therefore, final remainder = (-3)(-2)(-1)

= -6

The required positive remainder = 9-6

= 3