You can find Top 20+ Remainders Questions with detailed video and text explanations on this page. There are many tricks, shortcuts and formulas that help you to solve the questions quickly. One can find those solving tips in the video solutions explained by CAT experts and IIM Alumni. You can get the complete resources for practising the Concepts of Remainders. Keep practising free CAT mocks where you'll get a fair idea of how questions are asked, and type of questions asked.

**The Remainder theorem** is a part of the Number Systems** **topic in the **CAT Quant Section**. You can check out these** CAT Remainder Questions from Previous years.** The best part about our page is you can download the questions PDF for free without signing up**. **Click on the link below to download all the remianders questions from CAT previous papers

**CAT Remainder theorem Questions - Tip 1: **If you're starting the prep, firstly understand the CAT Number System Syllabus; Based on our analysis of the previous years CAT number system questions, only a few questions were asked from CAT Remainder theorem questions.

**CAT Remainder theorem Questions - Tip 2:** If you're not very strong in this topic, don't spend too much time on these theorems. Only after you have completed all other topics, you can go to CAT remainder theorem questions and concepts.

You can practice these CAT remainder theorem questions in PDF with video solutions. Learn all the major formulae from these concepts and the **Important Number System for CAT tricks Formulas PDF here**.

How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

correct answer:-**2**

The number of integers x such that $$0.25 \leq 2^x \leq 200$$ and $$2^x + 2$$ is perfectly divisible by either 3 or 4, is

correct answer:-**5**

Let $$n!=1*2*3* ...*n$$ for integer $$n \geq 1$$.

If $$p = 1!+(2*2!)+(3*3!)+... +(10*10!)$$, then $$p+2$$ when divided by 11! leaves a remainder of

correct answer:-**4**

If x = $$(16^3 + 17^3+ 18^3+ 19^3 )$$, then x divided by 70 leaves a remainder of

correct answer:-**1**

The remainder, when $$(15^{23} + 23^{23})$$ is divided by 19, is

correct answer:-**3**

How many even integers n, where $$100 \leq n \leq 200$$ , are divisible neither by seven nor by nine?

correct answer:-**3**

The number of positive integers n in the range $$12 \leq n \leq 40$$ such that the product (n -1)*(n - 2)*…*3*2*1 is not divisible by n is

correct answer:-**2**

When $$2^{256}$$ is divided by 17, the remainder would be

correct answer:-**1**

After the division of a number successively by 3, 4 and 7, the remainders obtained are 2, 1 and 4 respectively. What will be the remainder if 84 divides the same number?

correct answer:-**4**

$$7^{6n} - 6^{6n}$$, where n is an integer > 0, is divisible by

correct answer:-**4**

Let $$b$$ be a positive integer and $$a = b^2 - b$$. If $$b \geq 4$$ , then $$a^2 - 2a$$ is divisible by

correct answer:-**3**

Let n be the number of different five-digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being repeated in the numbers. What is the value of n?

correct answer:-**3**

Let N = 1421 * 1423 * 1425. What is the remainder when N is divided by 12?

correct answer:-**3**

The integers 34041 and 32506 when divided by a three-digit integer n leave the same remainder. What is n?

correct answer:-**4**

Let N = $$55^3 + 17^3 - 72^3$$. N is divisible by:

correct answer:-**4**

The remainder when $$7^{84}$$ is divided by $$342$$ is :

correct answer:-**2**

A certain number, when divided by 899, leaves a remainder 63. Find the remainder when the same number is divided by 29.

correct answer:-**1**

A number is formed by writing first 54 natural numbers next to each other as 12345678910111213 ... Find the remainder when this number is divided by 8.

correct answer:-**3**

If m and n are integers divisible by 5, which of the following is not necessarily true?

correct answer:-**3**

Find the minimum integral value of n such that the division $$\frac{55n}{124}$$ leaves no remainder.

correct answer:-**1**

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