# 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. The HCF and LCM of two numbers are 22 and 2400 respectively. If one number is 264 then find another number?

1. 100
2. 150
3. 200
4. 250

Solution: Given, HCF = 22

LCM = 2400

First number = 264

Let the second number is $$x$$ then $$Product \ of \ two \ numbers = HCF \times LCM$$ $$264 \times x = 22 \times 2400$$ $$x = \frac{22 \times 2400}{264}$$ $$x = \frac{52800}{264}$$ $$x = 200$$ Hence the second number is 200.

1. Find the smallest sum of rupees which contains Rs 1.25, Rs 15, Rs 2.50, and Rs 10?

1. 30
2. 35
3. 40
4. 45

Solution: Given, Rs 1.25, Rs 15, Rs 2.50, and Rs 10 then

LCM of 1.25, 15, 2.50, and 10

It can be also written

$$(LCM \ of \ 125, 1500, 250, 1000) \times 0.01$$ $$= 3000 \times 0.01$$ $$= 30$$ Hence Rs 30 is the smallest sum of rupees.

1. Three women start walking together to the same way around a circular track of 15 km. If their speeds are 3, 4, and 5 km per hour respectively then find how much time they will take to meet together again?

1. 10 hours
2. 12 hours
3. 15 hours
4. 18 hours

Answer: (c) 15 hours

Solution: Time taken by the women to complete one revolution of the circular way $$= \frac{15}{3}, \frac{15}{4}, \ and \ \frac{15}{5} \ hours$$ $$= \frac{5}{1}, \frac{15}{4}, \ and \ \frac{3}{1} \ hours$$ Taking LCM of $$\frac{5}{1}, \frac{15}{4}, \ and \ \frac{3}{1}$$ $$= \frac{LCM \ of \ 5, 15, 3}{HCF \ of \ 1, 4, 1}$$ $$= \frac{15}{1}$$ $$15 \ hours$$ Hence the women will meet together again after 15 hours.

1. The LCM and HCF of two numbers are 1350 and 25 respectively. If one number is 125 then find another number?

1. 200
2. 270
3. 290
4. 300

Solution: Given, LCM = 1350

HCF = 25

First number = 125

Let the second number is $$x$$ then $$Product \ of \ two \ numbers = HCF \times LCM$$ $$125 \times x = 25 \times 1350$$ $$x = \frac{25 \times 1350}{125}$$ $$x = \frac{33750}{125}$$ $$x = 270$$ Hence the second number is 270.

1. If HCF of 575 and 325 is 65 then find the LCM of the same numbers?

1. 2525
2. 2775
3. 2825
4. 2875

HCF = 65 then $$Product \ of \ two \ numbers = HCF \times LCM$$ $$LCM = \frac{Product \ of \ two \ numbers}{HCF}$$ $$LCM = \frac{575 \times 325}{65}$$ $$LCM = \frac{186,875}{65}$$ $$LCM = 2875$$