### 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?

- 7
- 29
- 16
- 13

**Correct Answer**Choice (B).

29 Correct answer- Explanatory Answer
- Sum of the digits
- Hard

### Number Theory - Binomial Theorem

What is the remainder when (13

^{100}+ 17^{100}) is divided by 25?- 0
- 2
- 4
- 11

**Correct Answer**Choice (B).

2 Correct answer- Explanatory Answer
- Binomial Theorem Ahoy!
- Hard

### 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?

- 2
- 0
- 1
- 3

**Correct Answer**Choice (A).

2 Correct answer- Explanatory Answer
- Possible remainders
- Medium

### Remainders

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

- 3
- 5
- 4
- 2

**Correct Answer**Choice (B).

5 Correct answer- Explanatory Answer
- Possible remainders
- Medium

### Remainders - factorization properties

What is the remainder when we divide 3

^{90}+ 5^{90}by 34?- 0
- 17
- 33
- 1

**Correct Answer**Choice (A).

0 Correct answer- Explanatory Answer
- a
^{n}+ b^{n} - Medium

### Remainders - Squares

N

^{2}leaves a remainder of 1 when divided by 24. What are the possible remainders we can get if we divide N by 12?- 1, 5, 7 and 11
- 1 and 5
- 5, 9, and 11
- 1 and 11

**Correct Answer**Choice (A).

1, 5, 7 and 11 Correct answer- Explanatory Answer
- Possible remainders
- Hard

### Remainders, coprime numbers

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

- 8
- 12
- 9
- 15

**Correct Answer**Choice (B).

12 Correct answer- Explanatory Answer
- Euler's phi function
- Medium

### 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?

- 32
- 36
- 24
- 19

**Correct Answer**Choice (B).

36 Correct answer- Explanatory Answer
- Remainders and LCM
- Medium

### 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?

- 65
- 96
- 125
- More than one value is possible

**Correct Answer**Choice (D).

More than one value is possible Correct answer- Explanatory Answer
- Remainders - basics
- Medium

### 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?

- 3
- 2
- 5
- 4

**Correct Answer**Choice (C).

5 Correct answer- Explanatory Answer
- Possible remainders
- Medium

### Remainders - Large number

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

- 0
- 8
- 1
- 5

**Correct Answer**Choice (D).

5 Correct answer- Explanatory Answer
- Remainders - Large number
- Hard

### Divisibility - Large Number

Given a number, N = 55

^{5}+ 17^{5}– 72^{5}, then which of the following is true?- N is divisible by both 7 and 13
- N is divisible by both 3 and 17
- N is divisible by 17 but not 3
- N is divisible by 11 but not 17

**Correct Answer**Choice (B).

N is divisible by both 3 and 17 Correct answer- Explanatory Answer
- Divisibility - Large Number
- Medium

### Same remainder

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

- 206
- 256
- 274
- 189

**Correct Answer**Choice (B).

256 Correct answer- Explanatory Answer
- Same remainder
- Medium

### Remainder - Large number

If N = (24

^{3}+ 25^{3}+ 26^{3}+ 27^{3}), then N divided by 102 leaves a remainder of?- 18
- 12
- 1
- 0

**Correct Answer**Choice (D).

0 Correct answer- Explanatory Answer
- Remainder - Large number
- Medium

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- Percents Profits & Interests
- DI - Bar Graphs
- Geometry
- VA - Sentence Rearrangement
- Speed Time Races
- DI - Pie Charts
- Coordinate Geometry
- VA - Sentence Elimination
- Ratio Mixtures, Averages
- DI - Multiple Graphs
- Trigonometry
- VA - Sentence Correction
- Logarithms and Exponents
- DI - Word Problems
- Mensuration
- VA - Para Completion
- Pipes Cisterns
- DI - Line Graphs
- Permutation; Probability
- VA - Text Completion