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,$$\frac{3 \times 7 \times 9}{2}$$ $$= \frac{1 \times 1 \times 1}{2} = \frac{1}{2} = 1 \ (Remainder)$$