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/
