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. |

- Which of the following number is completely divisible by \(15 \ ?\)
- \(2625\)
- \(4130\)
- \(5000\)
- \(2260\)

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 \(3\).

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

- Which of the following number is completely divisible by \(13 \ ?\)
- \(4339\)
- \(4329\)
- \(3325\)
- \(3335\)

Answer: (b) \(4329\)

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

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

- Which of the following condition satisfied for a number to be divisible by \(51 \ ?\)
- The number also divisible by \(17\) and \(3\)
- The number also divisible by \(5\) and \(3\)
- The number also divisible by \(7\) and \(3\)
- 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 \(17\).

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 \(17\).

- Which of the following condition satisfied for a number to be divisible by \(39 \ ?\)
- The number also divisible by \(14\) and \(3\)
- The number also divisible by \(13\) and \(3\)
- The number also divisible by \(9\) and \(3\)
- 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 \(13\).

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 \(13\).

- Which of the following number is not a perfect square?
- \(25868\)
- \(26562\)
- \(26163\)
- All of the above

Answer: (d) All of the above

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

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

- Which of the following is the greatest four digits number, when divided by \(2, 4, \ and \ 5\) leaves a remainder of \(10 \ ?\)
- \(1320\)
- \(2110\)
- \(1540\)
- \(6660\)

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 \(10\)

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 \(10\)

- Find the factors of the number \(110\)?
- \(10\)
- \(6\)
- \(8\)
- \(7\)

Answer: (c) \(8\)

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

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

- Find the remainder of the expression \(\frac{8 \times 9 \times 11}{5}\)?
- \(1\)
- \(2\)
- \(3\)
- \(4\)

Answer: (b) \(2\)

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

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

- Find the remainder of the expression \(\frac{2^{33}}{5}\)?
- \(2\)
- \(4\)
- \(6\)
- \(8\)

Answer: (a) \(2\)

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

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

- Find the remainder of the expression \(\frac{3 \times 7 \times 9}{2}\)?
- \(2\)
- \(1\)
- \(3\)
- \(4\)

Answer: (b) \(1\)

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

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

Lec 1: Introduction to Number System
Lec 2: Factors of Composite Number
Questions and Answers-1
Lec 3: Basic Remainder Theorem
Questions and Answers-2
Lec 4: Polynomial Remainder Theorem
Questions and Answers-3
Questions and Answers-4
Questions and Answers-5
Lec 5: LCM of Numbers
Questions and Answers-6
Lec 6: HCF of Numbers
Questions and Answers-7
Questions and Answers-8
Lec 7: Divisibility Rules of Numbers
Questions and Answers-9
Questions and Answers-10
Questions and Answers-11
Questions and Answers-12
Questions and Answers-13
Questions and Answers-14
Questions and Answers-15
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