IPMAT Aptitude Questions Based on Remainders

Overview: Several Exams, including the IPMAT, feature questions on the remainder concept. Enhance your skills with our guide on IPMAT Aptitude Questions Based on Remainders, which offers essential formulas, strategies, and practice problems to help you excel in your preparations!

Taking the IPMAT is difficult, and having less preparation time adds to the difficulty.

You can manage your time, though, if you know the right strategy for preparing each section of the paper.

The IPMAT aptitude questions based on remainders assess your mathematical reasoning skills.  

Practising more questions from this concept will help you fetch more marks and outrun your competitors. 

Students with non-math backgrounds have previously passed the exam with the proper preparation methods.

To ease your IPMAT preparation, we have compiled the important IPM aptitude questions and answers based on the remaining problems in this post.

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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.

To better understand the concepts of IPMAT Aptitude Questions Based on Remainders MCQ), watch the above video. 

Many questions based on the remainder concept are generally asked in competitive examinations, including IPMAT.

Therefore, following IPMAT Maths Preparation Tips would help you solve these questions in seconds.

We have listed important tips and theorems related to the remainders and previous year's IPMAT aptitude questions based on remainders with solutions.

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IPMAT Aptitude Questions Based on Remainders: Concepts

IPMAT Aptitude Questions Based on Remainders 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

IPMAT Aptitude Questions Based on Remainders Concept - 2 and 3

If x, y, and z are 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 solving these IPM aptitude questions based on remainders is to replace the unknown number by its 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.

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IPMAT Aptitude Questions Based on Remainders Concepts - 4 and 5

IPMAT Aptitude Questions Based on Remainders Concept - 6

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IPMAT Aptitude Questions Based on Remainders: Theorems-based questions

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IPMAT Aptitude Questions Based on Remainders with Answers

To help you understand the type of questions asked in the exam, we have provided a few sample IPM aptitude questions based on remainders curated from the previous year's IPMAT question papers.

Question 1:

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 )

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 six and Remainder is four 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. 

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Question 2:

When 123 x 124 x 125 is divided by 9, what is the remainder?

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

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Question 3:

What is the remainder when 2^50 is divided by 49?

Solution: 

Using Euler's theorem, the remainder when 2^50 is divided by 49 is 1.

Explanation: Euler’s theorem states that if a and n are relatively prime (i.e., the greatest common divisor of a and n is 1), then a^(ϕ(n)) ≡ 1 (mod n). Here, ϕ(49) is 42 since 49 is a prime number. Therefore, 2^42 gives a remainder of 1 when divided by 49. We know that 50 > 42, and the next multiple is 84, which is too high, so the highest multiple of 42 under 50 is 42. So, we can rewrite 2^50 as 2^(42+8) = 2^42 * 2^8. As per Euler's theorem, 2^42 will give us 1, so the equation simplifies to 2^8, which is 256. The remainder, when 256 is divided by 49, is 18.

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Question 4:

What is the remainder when 7^200 is divided by 6?

Solution: 

The remainder is 1.

Explanation: 7^n leaves a remainder of 1 when divided by 6 for all natural numbers n. Therefore, 7^200 will also leave a remainder of 1 when divided by 6.

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Question 5:

What is the remainder if the divisor is 14 and the dividend is 214?

Solution: 

The remainder is 2. 

Explanation: When you divide 214 by 14, the quotient is 15, and the remainder is 2.

Question 6:

What is the remainder when 5^99 is divided by 13?

Solution: 

The remainder is 8.

Explanation: If you notice the pattern, the remainder of powers of 5 is divided by 13 cycles for every four numbers: 5^1 (remainder 5), 5^2 (remainder 12), 5^3 (remainder 8), and 5^4 (remainder 1). Thus, when you find the remainder of 5^n divided by 13, if n is divisible by 4 (like 5^96), the remainder is 1. Since 99 = 96 + 3, the remainder of 5^99 divided by 13 will be the same as the remainder of 5^3 divided by 13, which is 8.

The article on IPMAT aptitude questions based on remainders guides students preparing for the IPMAT, explicitly focusing on mathematical reasoning involving remainder problems.

It explains concepts, tips, strategies, and practice problems to enhance preparation.

Following the guidance, students can significantly improve their performance in this exam section.

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Key Takeaways:

• Fundamental Concepts: Understanding the basic formula for remainders is essential for effectively solving related IPMAT aptitude questions based on remainders.
• Application of Techniques: Utilizing specific techniques and theorems can significantly speed up problem-solving and enhance accuracy.
• Focused Practice: Regular practice with targeted remainder questions is crucial as they are commonly featured in competitive exams.
• Utilizing Past Questions: Reviewing IPMAT aptitude questions based on remainders helps familiarize with the question patterns and difficulty levels.
• Leveraging Resources: The article highlights the importance of using study materials, educational videos, and SuperGrads IPMAT Online Coaching expert guidance.