# 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

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

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

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

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