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 one of the following is the HCF of 20 and 25?
- 2
- 3
- 5
- 10

Answer: (c) 5

Solution:

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.

- Find the HCF of the numbers 30, 45, 60?
- 5
- 10
- 15
- 3

Answer: (c) 15

Solution:

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.

- Which one of the following is the HCF of \(\frac{9}{8}\) and \(\frac{7}{6}\)?
- \(\frac{1}{24}\)
- \(\frac{2}{27}\)
- \(\frac{1}{20}\)
- \(\frac{2}{15}\)

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

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

$$ HCF = \frac{HCF \ of \ (9,7)}{LCM \ of \ (8,6)} $$ $$ = \frac{1}{24} $$

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

$$ HCF = \frac{HCF \ of \ (9,7)}{LCM \ of \ (8,6)} $$ $$ = \frac{1}{24} $$

- Which one of the following is the HCF of \(\frac{12}{9}\), \(\frac{12}{7}\), and \(\frac{15}{7}\)?
- \(\frac{1}{21}\)
- \(\frac{1}{18}\)
- \(\frac{1}{25}\)
- \(\frac{1}{24}\)

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

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

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

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

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

- Find the HCF of 25, \(\frac{15}{9}\), and \(\frac{30}{12}\)?
- \(\frac{3}{25}\)
- \(\frac{5}{32}\)
- \(\frac{4}{27}\)
- \(\frac{5}{36}\)

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

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

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

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

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

- Find the HCF of 56, 60, 80?
- 2
- 3
- 4
- 6

Answer: (c) 4

Solution:

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.

- Which one of the following is the HCF of 150, 180, and 220?
- 5
- 10
- 15
- 20

Answer: (b) 10

Solution:

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.

- Find the HCF of 50, \(\frac{55}{9}\), and 65?
- \(\frac{5}{9}\)
- \(\frac{7}{9}\)
- \(\frac{9}{7}\)
- \(\frac{5}{11}\)

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

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

$$ HCF = \frac{HCF \ of \ (50, 55, 65)}{LCM \ of \ (1, 9, 1)} $$ $$ = \frac{5}{9} $$

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

$$ HCF = \frac{HCF \ of \ (50, 55, 65)}{LCM \ of \ (1, 9, 1)} $$ $$ = \frac{5}{9} $$

- Find the HCF of 150, 125, and \(\frac{200}{9}\)?
- \(\frac{25}{9}\)
- \(\frac{20}{9}\)
- \(\frac{24}{9}\)
- \(\frac{28}{9}\)

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

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

$$ HCF = \frac{HCF \ of \ (150, 125, 200)}{LCM \ of \ (1, 1, 9)} $$ $$ = \frac{25}{9} $$

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

$$ HCF = \frac{HCF \ of \ (150, 125, 200)}{LCM \ of \ (1, 1, 9)} $$ $$ = \frac{25}{9} $$

- Which one of the following is the HCF of \(\frac{180}{77}\), \(\frac{155}{88}\), and 99?
- \(\frac{11}{715}\),
- \(\frac{1}{616}\),
- \(\frac{2}{525}\),
- \(\frac{1}{414}\),

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

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

$$ HCF = \frac{HCF \ of \ (180, 155, 99)}{LCM \ of \ (77, 88, 1)} $$ $$ = \frac{1}{616} $$

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

$$ HCF = \frac{HCF \ of \ (180, 155, 99)}{LCM \ of \ (77, 88, 1)} $$ $$ = \frac{1}{616} $$

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
Questions and Answers-16
Questions and Answers-17
Questions and Answers-18
Questions and Answers-19
Questions and Answers-20