# CAT Practice : Number System: Remainders

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The following topics are covered in the CAT quant section from Number system - Remainders. Detailed explanatory answers, solution videos and slide decks are also provided.
1. ### Remainders - Sum of digits

The sum of the digits of a number N is 23. The remainder when N is divided by 11 is 7. What is the remainder when N is divided by 33?

1. 7
2. 29
3. 16
4. 13
2. ### Number Theory - Binomial Theorem

What is the remainder when (13100 + 17100) is divided by 25?

1. 0
2. 2
3. 4
4. 11
3. ### Remainders

A number when divided by 18 leaves a remainder 7. The same number when divided by 12 leaves a remainder n. How many values can n take?

1. 2
2. 0
3. 1
4. 3
4. ### Remainders

N leaves a remainder of 4 when divided by 33, what are the possible remainders when N is divided by 55?

1. 3
2. 5
3. 4
4. 2
5. ### Remainders - factorization properties

What is the remainder when we divide 390 + 590 by 34?

1. 0
2. 17
3. 33
4. 1
6. ### Remainders - Squares

N2 leaves a remainder of 1 when divided by 24. What are the possible remainders we can get if we divide N by 12?

1. 1, 5, 7 and 11
2. 1 and 5
3. 5, 9, and 11
4. 1 and 11
1, 5, 7 and 11
• Possible remainders
• Hard
7. ### Remainders, coprime numbers

A prime number p greater than 100 leaves a remainder q on division by 28. How many values can q take?

1. 8
2. 12
3. 9
4. 15
8. ### Remainders and LCM

How many positive integers are there from 0 to 1000 that leave a remainder of 3 on division by 7 and a remainder of 2 on division by 4?

1. 32
2. 36
3. 24
4. 19
9. ### Remainders - basics

Three numbers leave remainders of 43, 47 and 49 on division by N. The sum of the three numbers leaves a remainder 9 on division by N. What are the values N can take?

1. 65
2. 96
3. 125
4. More than one value is possible
More than one value is possible
• Remainders - basics
• Medium
10. ### Remainders

A number leaves a remainder 3 on division by 14, and leaves a remainder k on division by 35. How many possible values can k take?

1. 3
2. 2
3. 5
4. 4
11. ### Remainders - Large number

Consider a large number N = 1234567891011121314………979899100. What is the remainder when first 100 digits of N is divided by 9?

1. 0
2. 8
3. 1
4. 5
12. ### Divisibility - Large Number

Given a number, N = 555 + 175 – 725, then which of the following is true?

1. N is divisible by both 7 and 13
2. N is divisible by both 3 and 17
3. N is divisible by 17 but not 3
4. N is divisible by 11 but not 17
N is divisible by both 3 and 17
• Divisibility - Large Number
• Medium
13. ### Same remainder

The integers 573921 and 575713 when divided by a 3 digit number leave the same remainder. What is that 3 digit number?

1. 206
2. 256
3. 274
4. 189
14. ### Remainder - Large number

If N = (243 + 253 + 263 + 273), then N divided by 102 leaves a remainder of?

1. 18
2. 12
3. 1
4. 0
0
• Remainder - Large number
• Medium

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