# Number System Aptitude Questions and Answers:

#### Overview:

 Questions and Answers Type: MCQ (Multiple Choice Questions). Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Number System Aptitude Questions and Answers. Number of Questions: 10 Questions with Solutions.

1. Which of the following number is completely divisible by $$15 \ ?$$

1. $$2625$$
2. $$4130$$
3. $$5000$$
4. $$2260$$

Answer: (a) $$2625$$

Solution: A number is divisible by $$15$$ will also divisible by $$3$$ and from the given options only $$2625$$ is divisible by $$15$$ and $$3$$.

1. Which of the following number is completely divisible by $$13 \ ?$$

1. $$4339$$
2. $$4329$$
3. $$3325$$
4. $$3335$$

Answer: (b) $$4329$$

Solution: The number $$13$$ is a prime number and from the options only $$4329$$ is divisible by $$13$$.

1. Which of the following condition satisfied for a number to be divisible by $$51 \ ?$$

1. The number also divisible by $$17$$ and $$3$$
2. The number also divisible by $$5$$ and $$3$$
3. The number also divisible by $$7$$ and $$3$$
4. both a and c

Answer: (a) The number also divisible by $$17$$ and $$3$$.

Solution: A number to be divisible by $$51$$, also divisible by $$17$$ and $$3$$, because $$3$$ and $$17$$ are the co-prime numbers. $$51$$ is the product of the $$3$$ and $$17$$.

1. Which of the following condition satisfied for a number to be divisible by $$39 \ ?$$

1. The number also divisible by $$14$$ and $$3$$
2. The number also divisible by $$13$$ and $$3$$
3. The number also divisible by $$9$$ and $$3$$
4. both b and c

Answer: (b) The number also divisible by $$13$$ and $$3$$

Solution: A number to be divisible by $$39$$, also divisible by $$13$$ and $$3$$, because $$3$$ and $$13$$ are the co-prime numbers. $$39$$ is the product of the $$3$$ and $$13$$.

1. Which of the following number is not a perfect square?

1. $$25868$$
2. $$26562$$
3. $$26163$$
4. All of the above

Answer: (d) All of the above

Solution: A perfect square can not be end with $$2, 3, 7, \ and \ 8$$

1. Which of the following is the greatest four digits number, when divided by $$2, 4, \ and \ 5$$ leaves a remainder of $$10 \ ?$$

1. $$1320$$
2. $$2110$$
3. $$1540$$
4. $$6660$$

Answer: (b) $$2110$$

Solution: The LCM of the numbers $$2, 4, \ and \ 5$$ is $$20$$, and from the given options only $$2110$$ is the greatest 4 digits number divisible by $$20$$ leaves the remainder $$10$$

1. Find the factors of the number $$110$$?

1. $$10$$
2. $$6$$
3. $$8$$
4. $$7$$

Answer: (c) $$8$$

Solution: $$110 = 2 \times 5 \times 11$$ $$= 2^1 \times 5^1 \times 11^1$$ then factors of composite number $$= (1 + 1)(1 + 1)(1 + 1)$$ $$= 2 \times 2 \times 2 = 8$$

1. Find the remainder of the expression $$\frac{8 \times 9 \times 11}{5}$$?

1. $$1$$
2. $$2$$
3. $$3$$
4. $$4$$

Answer: (b) $$2$$

Solution: According to basic remainder theorem,$$\frac{8 \times 9 \times 11}{5}$$ $$= \frac{3 \times 4 \times 1}{5} = \frac{12}{5} = 2 \ (Remainder)$$

1. Find the remainder of the expression $$\frac{2^{33}}{5}$$?

1. $$2$$
2. $$4$$
3. $$6$$
4. $$8$$

Answer: (a) $$2$$

Solution: According to polynomial remainder theorem, $$\frac{2^{33}}{5} = \frac{(2^3)^{11}}{5}$$ $$= \frac{(5 + 3)^{11}}{5} = \frac{3^{11}}{5}$$ $$= \frac{(3^2)^5 \times 3}{5} = \frac{(5 + 4)^5 \times 3}{5}$$ $$= \frac{4^5 \times 3}{5} = \frac{2^{10} \times 3}{5}$$ $$= \frac{(2^3)^3 \times 2 \times 3}{5} = \frac{(5 + 3)^3 \times 6}{5}$$ $$= \frac{3^3 \times (5 + 1)}{5} = \frac{3^3 \times 1}{5}$$ $$= \frac{27}{5} = 2 \ (Remainder)$$

1. Find the remainder of the expression $$\frac{3 \times 7 \times 9}{2}$$?

1. $$2$$
2. $$1$$
3. $$3$$
4. $$4$$

Answer: (b) $$1$$

Solution: According to basic remainder theorem,$$\frac{3 \times 7 \times 9}{2}$$ $$= \frac{1 \times 1 \times 1}{2} = \frac{1}{2} = 1 \ (Remainder)$$