So we have this biggest community for CAT Preparation, and we discuss almost everything about CAT here in this group called CAT Preparation – iQuanta .Anyone can be a part of it by sending a join request.

So here are few variety of questions on Past CAT Remainder Questions, discussed in group along with detailed solutions.

**1.What is the remainder when 4^96 is divided by 6?**

1) 0

2) 2

3) 3

4) 4

**Remark:** It can be done in 3 different ways, iQuanta shortcut, or Euler or Chinese remainder Theorem

**Solution here: https://www.facebook.com/groups/Rockthecat/permalink/1226230407544659/**

**2. The remainder, when (15^23 + 23^23) is divided by 19, is:**

1) 4

2) 15

3) 0

4) 18

Remark : It uses

Solution here: https://www.facebook.com/groups/Rockthecat/permalink/1226238654210501/

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

1) 0

2) 1

3) 69

4) 35

**Remark** : It uses concept of previous questions, but it has 1 extra condition to remember.

**Solution here:** https://www.facebook.com/groups/Rockthecat/permalink/1226247444209622/

**4. Let n! = 1 × 2 × 3 × … × n for integer n ≥ 1. If p = 1! + (2 × 2!) + (3 × 3!) + … +(10 × 10!), then p + 2 when divided by 11! leaves a remainder of**

1) 10

2) 0

3) 7

4) 1

**Remark :** It has 2 ways : One by general expanding and other is a generalised shortcut, both discussed in the link below

**Solution here: https://www.facebook.com/groups/Rockthecat/permalink/1226255684208798/**

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

1) 0

2) 9

3) 3

4) 6

**Remark :** It is one of the easiest questions on remainder asked in CAT.

**Solution here**: https://www.facebook.com/groups/Rockthecat/permalink/1226268600874173/

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

**Remark :** It is a very conceptual question and tricky one if one doesn’t know the solution already.

**Solution here :** https://www.facebook.com/groups/Rockthecat/permalink/1226277290873304/

**7. On dividing a number by 3, 4 and 7, the remainders are 2, 1 and 4 respectively. If the same number is divided by 84 then the remainder is**

1) 80

2) 76

3) 53

4) None of these

**Remark :** A question on Chinese remainder theorem

**Solution here:** https://www.facebook.com/groups/Rockthecat/permalink/1226287320872301/

**8. For all integers n > 0, 7^6n – 6^6n is divisible by**

1) 13

2) 127

3) 559

4) All of these

**Remark:** An application of algebraic formula a^2-b^2=(a-b)(a+b)

**Solution here:** https://www.facebook.com/groups/Rockthecat/permalink/1226297767537923/

**9. The remainder when 2^256 is divided by 17 is**

1) 7

2) 13

3) 11

4) 1

**Remark :** A simple question on Euler theorem

**Solution here:** https://www.facebook.com/groups/Rockthecat/permalink/1226305060870527/

**10. 101! Mod 103 [ CAT 2003]**

**Remark :** A simple question on Wilson Theorem

**Solution here : https://www.facebook.com/groups/Rockthecat/permalink/1226308500870183/**

**● CAT 20 Course Details: https://www.facebook.com/groups/Rockthecat/permalink/1182586281909072/**