Number System 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 one of the following is the HCF of 20 and 25?

    1. 2
    2. 3
    3. 5
    4. 10


Answer: (c) 5

Solution:

Step(1): Factorize the numbers into their prime factors.$$ 20 = 2 \times 2 \times 5 = 2^{2} \times 5^{1} $$ $$ 25 = 5 \times 5 = 5^{2} $$ Step(2): Collect all the common factors with their minimum available power.$$ = 5^{1} $$ Step(3): Multiply the collected factors.$$ = 5 $$ Here, 5 is the highest positive number that can divide 20, and 25 exactly.


  1. Find the HCF of the numbers 30, 45, 60?

    1. 5
    2. 10
    3. 15
    4. 3


Answer: (c) 15

Solution:

Step(1): Factorize the numbers into their prime factors.$$ 30 = 2 \times 3 \times 5 = 2^{1} \times 3^{1} \times 5^{1} $$ $$ 45 = 3 \times 3 \times 5 = 3^{2} \times 5^{1} $$ $$ 60 = 2 \times 2 \times 3 \times 5 = 2^{2} \times 3^{1} \times 5^{1} $$ Step(2): Collect all the common factors with their minimum available power.$$ = 3^{1}, and \ 5^{1} $$ Step(3): Multiply the collected factors.$$ = 3 \times 5 = 15 $$ Here, 15 is the highest positive number that can divide 30, 45, and 60 exactly.


  1. Which one of the following is the HCF of \(\frac{9}{8}\) and \(\frac{7}{6}\)?

    1. \(\frac{1}{24}\)
    2. \(\frac{2}{27}\)
    3. \(\frac{1}{20}\)
    4. \(\frac{2}{15}\)


Answer: (a) \(\frac{1}{24}\)

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)
$$ HCF = \frac{HCF \ of \ (9,7)}{LCM \ of \ (8,6)} $$ $$ = \frac{1}{24} $$

  1. Which one of the following is the HCF of \(\frac{12}{9}\), \(\frac{12}{7}\), and \(\frac{15}{7}\)?

    1. \(\frac{1}{21}\)
    2. \(\frac{1}{18}\)
    3. \(\frac{1}{25}\)
    4. \(\frac{1}{24}\)


Answer: (a) \(\frac{1}{21}\)

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)
$$ HCF = \frac{HCF \ of \ (12, 12, 15)}{LCM \ of \ (9, 7, 7)} $$ $$ = \frac{3}{63} = \frac{1}{21} $$

  1. Find the HCF of 25, \(\frac{15}{9}\), and \(\frac{30}{12}\)?

    1. \(\frac{3}{25}\)
    2. \(\frac{5}{32}\)
    3. \(\frac{4}{27}\)
    4. \(\frac{5}{36}\)


Answer: (d) \(\frac{5}{36}\)

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)
$$ HCF = \frac{HCF \ of \ (25, 15, 30)}{LCM \ of \ (1, 9, 12)} $$ $$ = \frac{5}{36} $$

  1. Find the HCF of 56, 60, 80?

    1. 2
    2. 3
    3. 4
    4. 6


Answer: (c) 4

Solution:

Step(1): Factorize the numbers into their prime factors.$$ 56 = 2 \times 2 \times 2 \times 7 = 2^{3} \times 7^{1} $$ $$ 60 = 2 \times 2 \times 3 \times 5 = 2^{2} \times 3^{1} \times 5^{1} $$ $$ 80 = 2 \times 2 \times 2 \times 2 \times 5 = 2^{4} \times 5^{1} $$ Step(2): Collect all the common factors with their minimum available power.$$ = 2^{2} $$ Step(3): Multiply the collected factors.$$ = 2^{2} = 4 $$ Here, 4 is the highest positive number that can divide 56, 60, and 80 exactly.


  1. Which one of the following is the HCF of 150, 180, and 220?

    1. 5
    2. 10
    3. 15
    4. 20


Answer: (b) 10

Solution:

Step(1): Factorize the numbers into their prime factors.$$ 150 = 2 \times 3 \times 5 \times 5 = 2^{1} \times 3^{1} \times 5^{2} $$ $$ 180 = 2 \times 2 \times 3 \times 3 \times 5 = 2^{2} \times 3^{2} \times 5^{1} $$ $$ 220 = 2 \times 2 \times 5 \times 11 = 2^{2} \times 5^{1} \times 11^{1} $$ Step(2): Collect all the common factors with their minimum available power.$$ = 2^{1} and \ 5^{1} $$ Step(3): Multiply the collected factors.$$ = 2 \times 5 = 10 $$ Here, 10 is the highest positive number that can divide 150, 180, and 220 exactly.


  1. Find the HCF of 50, \(\frac{55}{9}\), and 65?

    1. \(\frac{5}{9}\)
    2. \(\frac{7}{9}\)
    3. \(\frac{9}{7}\)
    4. \(\frac{5}{11}\)


Answer: (a) \(\frac{5}{9}\)

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)
$$ HCF = \frac{HCF \ of \ (50, 55, 65)}{LCM \ of \ (1, 9, 1)} $$ $$ = \frac{5}{9} $$

  1. Find the HCF of 150, 125, and \(\frac{200}{9}\)?

    1. \(\frac{25}{9}\)
    2. \(\frac{20}{9}\)
    3. \(\frac{24}{9}\)
    4. \(\frac{28}{9}\)


Answer: (a) \(\frac{25}{9}\)

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)
$$ HCF = \frac{HCF \ of \ (150, 125, 200)}{LCM \ of \ (1, 1, 9)} $$ $$ = \frac{25}{9} $$

  1. Which one of the following is the HCF of \(\frac{180}{77}\), \(\frac{155}{88}\), and 99?

    1. \(\frac{11}{715}\),
    2. \(\frac{1}{616}\),
    3. \(\frac{2}{525}\),
    4. \(\frac{1}{414}\),


Answer: (b) \(\frac{1}{616}\),

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)
$$ HCF = \frac{HCF \ of \ (180, 155, 99)}{LCM \ of \ (77, 88, 1)} $$ $$ = \frac{1}{616} $$