CAT Remainders Questions & Solutions

A sample of real CAT Remainders past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 26 Remainders questions in all — sign up free to practise them timed.

Q1.CAT 2024
When $3^{333}$ is divided by 11, the remainder is
- 5
- 10
- 1
- 6
Q2.CAT 2024
If $10^{68}$ is divided by 13, the remainder is
- 5
- 8
- 9
- 4
Q3.CAT 2018
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
Answer: 5
Q4.CAT 2005
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
- 10
- 0
- 7
- 1
Q5.CAT 2003
How many even integers n, where $100 \leq n \leq 200$ , are divisible neither by seven nor by nine?
- 40
- 37
- 39
- 38
Q6.CAT 2002
When $2^{256}$ is divided by 17, the remainder would be
- 1
- 16
- 14
- None of these
Q7.CAT 2001
Let $b$ be a positive integer and $a = b^2 - b$ . If $b \geq 4$ , then $a^2 - 2a$ is divisible by
- 15
- 20
- 24
- All of these
Q8.CAT 2000
Let N = 1421 * 1423 * 1425. What is the remainder when N is divided by 12?
- 0
- 9
- 3
- 6
Q9.CAT 2000
Let N = $55^3 + 17^3 - 72^3$ . N is divisible by:
- both 7 and 13
- both 3 and 13
- both 17 and 7
- both 3 and 17
Q10.CAT 1998
A certain number, when divided by 899, leaves a remainder 63. Find the remainder when the same number is divided by 29.
- 5
- 4
- 1
- Cannot be determined
Q11.CAT 1997
If m and n are integers divisible by 5, which of the following is not necessarily true?
- m - n is divisible by 5
- $m^2$ - $n^2$ is divisible by 25
- m + n is divisible by 10
- None of these
Q12.CAT 1991
Let k be a positive integer such that k+4 is divisible by 7. Then the smallest positive integer n, greater than 2, such that k+2n is divisible by 7 equals
- 9
- 7
- 5
- 3

14+ more Remainders questions inside

Get the full CAT Remainders set with timed practice, bookmarks and analysis — free to start.

Start practising free

CAT Remainders previous year questions with solutions — AthenaPrep

CAT Remainders Questions & Solutions

Q1.CAT 2024

When $3^{333}$ is divided by 11, the remainder is

Q2.CAT 2024

If $10^{68}$ is divided by 13, the remainder is

Q3.CAT 2018

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

Answer: 5

Q4.CAT 2005

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

Q5.CAT 2003

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

Q6.CAT 2002

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

1
16
14
None of these

Q7.CAT 2001

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

15
20
24
All of these

Q8.CAT 2000

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

Q9.CAT 2000

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

both 7 and 13
both 3 and 13
both 17 and 7
both 3 and 17

Q10.CAT 1998

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

5
4
1
Cannot be determined

Q11.CAT 1997

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

m - n is divisible by 5
$m^2$ - $n^2$ is divisible by 25
m + n is divisible by 10
None of these

Q12.CAT 1991

Let k be a positive integer such that k+4 is divisible by 7. Then the smallest positive integer n, greater than 2, such that k+2n is divisible by 7 equals

14+ more Remainders questions inside

Get the full CAT Remainders set with timed practice, bookmarks and analysis — free to start.

Start practising free

CAT Remainders previous year questions with solutions — AthenaPrep